review article a review of active yaw control system for...

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Review Article A Review of Active Yaw Control System for Vehicle Handling and Stability Enhancement M. K. Aripin, 1 Yahaya Md Sam, 2 Kumeresan A. Danapalasingam, 2 Kemao Peng, 3 N. Hamzah, 4 and M. F. Ismail 5 1 Control, Instrumentation & Automation Department, Faculty of Electrical Engineering, Universiti Teknikal Malaysia Melaka, 76100 Durian Tunggal, Melaka, Malaysia 2 Department of Control & Mechatronics, Faculty of Electrical Engineering, Universiti Teknologi Malaysia, 81310 UTM Johor Bahru, Johor, Malaysia 3 Temasek Laboratories, National University of Singapore 5A Engineering Drive 1, Singapore 117411 4 Faculty of Electrical Engineering, UiTM Pulau Pinang, 13500 Permatang Pauh, Pulau Pinang, Malaysia 5 Industrial Automation Section, Universiti Kuala Lumpur Malaysia France Institute, Section 14, Jalan Teras Jernang, 43650 Bandar Baru Bangi, Selangor, Malaysia Correspondence should be addressed to M. K. Aripin; [email protected] Received 23 January 2014; Revised 8 May 2014; Accepted 15 May 2014; Published 12 June 2014 Academic Editor: Aboelmagd Noureldin Copyright © 2014 M. K. Aripin et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Yaw stability control system plays a significant role in vehicle lateral dynamics in order to improve the vehicle handling and stability performances. However, not many researches have been focused on the transient performances improvement of vehicle yaw rate and sideslip tracking control. is paper reviews the vital elements for control system design of an active yaw stability control system; the vehicle dynamic models, control objectives, active chassis control, and control strategies with the focus on identifying suitable criteria for improved transient performances. Each element is discussed and compared in terms of their underlying theory, strengths, weaknesses, and applicability. Based on this, we conclude that the sliding mode control with nonlinear sliding surface based on composite nonlinear feedback is a potential control strategy for improving the transient performances of yaw rate and sideslip tracking control. 1. Introduction In vehicle dynamic control of road-vehicle, controlling the lateral dynamic motion is very important where it will determine the stability of the vehicle. One of the prominent approaches that are reported in the literature for lateral dynamics control is a yaw stability control system. In order to design an effective control system, it is essential to determine an appropriate element of yaw stability control system. In this paper, the elements of yaw stability control system, that is, vehicle dynamic models, control objectives, active chassis control, and its control strategies as depicted in Figure 1, are extensively reviewed. e linear and nonlinear vehicle models that described the behaviour of lateral dynamic are explained for controller design and evaluation purpose. To achieve the control objec- tives, it is essential to control the variables of yaw rate and sideslip angle in order to ensure the vehicle stable. It is required that the actual yaw rate and sideslip angle have fast responses and good tracking capability in following the desired responses. During critical driving condition or manoeuvre, inappropriate commands by the driver to control the steering and braking can cause the vehicle to become unstable and lead to an accident. erefore, an active control for yaw stability control system is essential to assist the driver to keep the vehicle stable on the desired path. By implementing an active chassis control of steering or braking or integration of both systems, the active yaw control system can be realized. Hindawi Publishing Corporation International Journal of Vehicular Technology Volume 2014, Article ID 437515, 15 pages http://dx.doi.org/10.1155/2014/437515

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Page 1: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

Review ArticleA Review of Active Yaw Control System for Vehicle Handlingand Stability Enhancement

M K Aripin1 Yahaya Md Sam2 Kumeresan A Danapalasingam2 Kemao Peng3

N Hamzah4 and M F Ismail5

1 Control Instrumentation amp Automation Department Faculty of Electrical Engineering Universiti Teknikal Malaysia Melaka76100 Durian Tunggal Melaka Malaysia

2 Department of Control amp Mechatronics Faculty of Electrical Engineering Universiti Teknologi Malaysia81310 UTM Johor Bahru Johor Malaysia

3 Temasek Laboratories National University of Singapore 5A Engineering Drive 1 Singapore 1174114 Faculty of Electrical Engineering UiTM Pulau Pinang 13500 Permatang Pauh Pulau Pinang Malaysia5 Industrial Automation Section Universiti Kuala Lumpur Malaysia France Institute Section 14 Jalan Teras Jernang43650 Bandar Baru Bangi Selangor Malaysia

Correspondence should be addressed to M K Aripin khairiaripinutemedumy

Received 23 January 2014 Revised 8 May 2014 Accepted 15 May 2014 Published 12 June 2014

Academic Editor Aboelmagd Noureldin

Copyright copy 2014 M K Aripin et al This is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

Yaw stability control system plays a significant role in vehicle lateral dynamics in order to improve the vehicle handling and stabilityperformances However not many researches have been focused on the transient performances improvement of vehicle yaw rateand sideslip tracking control This paper reviews the vital elements for control system design of an active yaw stability controlsystem the vehicle dynamic models control objectives active chassis control and control strategies with the focus on identifyingsuitable criteria for improved transient performances Each element is discussed and compared in terms of their underlying theorystrengths weaknesses and applicability Based on this we conclude that the sliding mode control with nonlinear sliding surfacebased on composite nonlinear feedback is a potential control strategy for improving the transient performances of yaw rate andsideslip tracking control

1 Introduction

In vehicle dynamic control of road-vehicle controlling thelateral dynamic motion is very important where it willdetermine the stability of the vehicle One of the prominentapproaches that are reported in the literature for lateraldynamics control is a yaw stability control system In order todesign an effective control system it is essential to determinean appropriate element of yaw stability control system Inthis paper the elements of yaw stability control system thatis vehicle dynamic models control objectives active chassiscontrol and its control strategies as depicted in Figure 1 areextensively reviewed

The linear and nonlinear vehicle models that describedthe behaviour of lateral dynamic are explained for controller

design and evaluation purpose To achieve the control objec-tives it is essential to control the variables of yaw rate andsideslip angle in order to ensure the vehicle stable It isrequired that the actual yaw rate and sideslip angle havefast responses and good tracking capability in followingthe desired responses During critical driving condition ormanoeuvre inappropriate commands by the driver to controlthe steering and braking can cause the vehicle to becomeunstable and lead to an accident Therefore an active controlfor yaw stability control system is essential to assist thedriver to keep the vehicle stable on the desired path Byimplementing an active chassis control of steering or brakingor integration of both systems the active yaw control systemcan be realized

Hindawi Publishing CorporationInternational Journal of Vehicular TechnologyVolume 2014 Article ID 437515 15 pageshttpdxdoiorg1011552014437515

2 International Journal of Vehicular Technology

Vehicle dynamics control

Vertical dynamics control Longitudinal dynamics control Lateral dynamics control

Lane warning detection system Lane keeping systemYaw stability control system

Vehicle dynamics models Active chassis controlControl objectives Control strategies

Figure 1 Yaw stability control system for vehicle lateral dynamic

Vehicle dynamic models

Linearized modelNonlinear model

8 DOF7 DOF 14 DOF 2 DOF

Figure 2 Vehicle dynamic models

In real driving condition the lateral dynamics of vehicleare incorporated with uncertainties such as different roadsurface condition varying vehicle parameters and crosswinddisturbance In yaw stability control system these pertur-bations could influence the yaw rate and sideslip trackingcontrol performances From the control system point ofview the transient performances of tracking control areessential However from the reviewed control strategies inthe literature the controllers are not designed to cater thismatter Therefore an appropriate robust control strategyshould be proposed to improve the transient performances ofthe yaw rate and sideslip tracking control in the presence ofuncertainties and disturbances As a finding from the reviewsthis paper briefly discussed a possible high performancerobust tracking control strategy that can be implemented foryaw stability control system

The review begins with vehicle dynamics models inSection 2 The yaw stability control objectives are discussedin Section 3 and followed by active chassis control for inSection 4 Yaw stability control strategies and problems arereviewed in Sections 5 and 6 respectively In Section 7 a highperformance robust tracking controller using sliding modecontrol and composite nonlinear feedback is discussed Thecontroller evaluation is discussed in Section 8 and endedwithconclusion in Section 9

2 Vehicle Dynamics Models

In order to examine analyse and design the controllerfor yaw stability control system vehicle dynamics modelsare essential where the mathematical modelling of vehicledynamic motion is obtained based on Newtonrsquos 2nd lawthat describes the forces and moments acting on the vehiclebody and tires In general there are two categories of vehicledynamic model that is nonlinear vehicle model and lin-earized vehicle model as depicted in Figure 2 The followingsubsections will discuss the nonlinear vehicle model forsimulation and linearized vehicle model for controller designpurpose

21 Vehicle Model for Simulation The nonlinear vehiclemodel is regularly used to represent and simulate the actualvehicle for controller evaluation and validation In recentyears researches in [1ndash5] have utilized nonlinear vehiclemodel for vehicle handling and stability improvement stud-ies Figure 3 shows the typical nonlinear vehicle model incornering manoeuvre

The input of this model is front wheel steer angle 120575119891while the output variables to be controlled are vehicle sideslip120573 and yaw rate 119903 The vehicle parameters are vehicle widthtrack 119889 distance from front and rear axle to centre of

International Journal of Vehicular Technology 3

Fx1 120575f120575f

Fy1

d

Fx2

Fy2

x

120573

y rMz

lf

lr

Fx3

Fy3

Fy4

Fx4

d

Figure 3 Nonlinear vehicle model [6]

gravity (CG) 119897119891 and 119897119903 respectively The vehicle forwardvelocity of centre of gravity (CG) is V lateral velocity isV119910 and longitudinal velocity is V119909 Other important vehicleparameters are vehicle mass 119898 moment of inertia 119868119911 andfrontrear tire cornering stiffness 119862119891119862119903 The wheels arenumbered as subscript number with (1) for front-left (2) forfront-right (3) for rear-left and (4) for rear-right

Longitudinal tire force 119865119909119894 depends directly on tire slipratio 120582119894 while lateral tire force 119865119910119894 depends directly ontire sideslip angle 120572119894 For smaller slip angle and slip ratiolateral tire force is described as a linear function of the tirecornering stiffness and tire sideslip angle while longitudinaltire force is described as a linear function of the brakingstiffness and the tire slip ratio For larger slip angle and slipratio longitudinal and lateral tire forces exhibit a nonlinearcharacteristics Vehicle dynamic motion with nonlinear tireforces represents a nonlinear system The nonlinear lateraland longitudinal tire forces can be described using prominentPacejka tire model as implemented in [1 4 7] or Dugoff tiremodel as utilized in [8ndash10] while studies in [11] used both tiremodels

The nonlinear vehicle model could have different numberof degree-of-freedom (DOF) where it represents the dynam-ics motions and complexity of vehicle models As utilized in[2 12ndash14] the 7 DOF vehicle model represents the dynamicmotions of vehicle body that is longitudinal lateral yawand four wheels The dynamic equations for the longitudinallateral and yaw motions of the vehicle body are described asfollowsLongitudinal Motion One has the following

119898119886119909 = 119898(V119909 minus 119903V119910)

= (1198651199091 + 1198651199092) cos 120575119891 + 1198651199093 + 1198651199094 minus (1198651199101 + 1198651199102) sin 120575119891(1)

Lateral Motion One has the following

119898119886119910 = 119898(V119910 + 119903V119909)

= (1198651199091 + 1198651199092) sin 120575119891 + (1198651199101 + 1198651199102) cos 120575119891 + 1198651199103 + 1198651199104

(2)

Yaw Motion One has the following

119868119911 119903 = 119897119891 (1198651199101 cos 120575119891 + 1198651199102 cos 120575119891 + 1198651199091 sin 120575119891 + 1198651199092 sin 120575119891)

minus 119897119903 (1198651199103 + 1198651199104) +119872119911

(3)

where 119872119911 is yaw moment that must be taken into accountthat is 119872119911 gt 0 if the tires tends to turn at 119911-axis In (2) thelateral acceleration 119886119910 can be expressed in terms of vehicleforward speed V yaw rate 119903 and sideslip 120573 as follows

119886119910 = V119910 + 119903V119909 = V (119903 + 120573) (4)

Therefore the output variable of sideslip120573of two-trackmodelcan be obtained as follows

120573 =1

119898V[cos120573 (cos 120575119891 (1198651199091 + 1198651199092) minus sin 120575119891 (1198651199101 + 1198651199102))

minus sin120573 (sin 120575119891 (1198651199091 + 1198651199092) minus sin 120575119891 (1198651199101 + 1198651199102))]

minus 119903

(5)

while the output variable of yaw rate 119903 can be determinedfrom (3) and obtained as follows

119903 =1

119868119911

[119897119891 (1198651199101 cos 120575119891 + 1198651199102 cos 120575119891 + 1198651199091 sin 120575119891 + 1198651199092 sin 120575119891)

minus119897119903 (1198651199103 + 1198651199104) +119872119911]

(6)

In vehicle dynamic studies each wheel represents 1 DOFThus there are 4 DOF for road-vehicle with 4 wheels Thedynamic motion for each wheel is described as follows

119868119908119894119894 = minus119877119908119894119865119909119894 + 119879119890119894 minus 119879119887119894 (7)

where is wheel angular acceleration 119899 119877119908 is wheel radius119868119908 is wheel inertia 119879119887119894 is braking torque and 119879119890119894 is drivingtorque

Another nonlinear vehicle model used in the previousresearch is 8 DOF vehicle model that is extensively usedin [4 5 9ndash11 15ndash18] For more accurate simulation andvalidation the 14 DOF vehicle model is used in [1 19 20]Thecomparison between the number ofDOFof nonlinear vehiclemodels that have been discussed above can be summarizedand compared in Table 1

Another nonlinear vehicle model used for simulationuses a multi-degree-of-freedom vehicle model based oncommercial vehicle dynamics software that is CarSim as

4 International Journal of Vehicular Technology

Table 1 Number DOF of nonlinear vehicle models

Number ofDOF Dynamic motions Output variable

7 DOF

(i) Longitudinal

Yaw rate amp Sideslip(ii) Lateral(iii) Vertical(iv) Rotational of 4 wheels

8 DOF

(i) Longitudinal

Yaw rate roll rate andsideslip

(ii) Lateral(iii) Vertical(iv) Roll(v) Rotational of 4 wheels

14 DOF

(i) Longitudinal

Yaw rate roll rate pitchrate and sideslip

(ii) Lateral(iii) Vertical(iv) Roll(v) Pitch(vi) Bounce(vii) Rotational of 4 wheels(viii) Vertical oscillations of4 wheels

implemented in [21ndash26] By using this software based vehiclemodel the dynamic behaviour of vehicle is more precisesimilar to a real vehicle However for yaw rate and sidesliptracking control in yaw stability control system the 7 DOFnonlinear vehicle model as discussed in the above equationsand shown in Table 1 is adequate for simulation and evalua-tion of the design controller

22 Vehicle Model for Controller Design In vehicle dynamicstudies the classical bicycle model as shown in Figure 4is prominently used for yaw stability control analysis andcontroller design as utilized in [1 3 8 26ndash30] This modelis linearized from the nonlinear vehicle model based on thefollowing assumptions

(i) Tires forces operate in the linear region(ii) The vehicle moves on plane surfaceflat road (planar

motion)(iii) Left and right wheels at the front and rear axle are

lumped in singlewheel at the centre line of the vehicle(iv) Constant vehicle speed ie the longitudinal accelera-

tion equal to zero (119886119909=0)(v) Steering angle and sideslip angle are assumed small

(asymp 0)(vi) No braking is applied at all wheels(vii) Centre of gravity (CG) is not shifted as vehicle mass

is changing(viii) 2 front wheels have the same steering angle(ix) Desired vehicle sideslip is assumed to be zero in

steady state

Fyr

lr

y

120573 x

r

lf

Fyf

120572f 120575f

120572r

Figure 4 Bicycle model [31]

In the simplest formof planarmotion thismodel consists of 2DOF for lateral and yaw motions as describe in the followingequationsLateral Motion One has the following

119898V ( 120573 + 119903) = (119865119910119891 + 119865119910119903) minus 119903 (8)

Yaw Motion One has the following

119868119911 119903 = 119897119891 sdot 119865119910119891 minus 119897119903 sdot 119865119910119903 (9)

In thismodel the front and rear lateral tire forces119865119910119891 and119865119910119903respectively exhibit linear characteristics and described as alinear function of the front and rear cornering stiffness 119862119891and 119862119903 as follows

119865119910119891 = 119862119891120572119891

119865119910119903 = 119862119903120572119903

(10)

where the front and rear tire sideslip angle 120572119891 and 120572119903 forlinear tire forces are given in the following equations

120572119891 = 120575119891 minus 120573 minus119897119891119903

V

120572119903 = minus 120573 +119897119903119903

V

(11)

By rearranging and simplifying (8)ndash(11) the differentialequations of sideslip and yaw rate variables can be simplifiedas a linear state space model as follows

= 119860119909 + 119861119906

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 119906

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891

(12)

where120573 and 119903 are state or output variables119862119891 and119862119903 are frontand rear tire cornering stiffness respectively 119898 is vehicle

International Journal of Vehicular Technology 5

Control objectives

Yaw rate Side slip Yaw rate and side slip

Figure 5 Yaw stability control objectives

mass 119868119911 is moment of inertia 119897119891 and 119897119903 are distance fromfront and rear axle to centre of gravity respectively V isvehicle speed and front tire steer angle 120575119891 is the input 119906to the model Notice that vehicle speed V is assumed alwaysconstant which means the vehicle is not involved with accel-erating and braking Hence only lateral and yaw motions areanalysed

Besides that the bicycle model is also regularly used asdesired or referencemodel to generate the desired response ofthe yaw rate and sideslip angle based on steady state conditionor approximated first order response In designing the controlstrategy based on vehicle active chassis control the linearstate space model in (13) is essential

3 Yaw Stability Control Objectives

A vehicle yaw rate 119903 and sideslip angle 120573 are significantvariables in vehicle yaw stability control system As stated in[32] control objectives of yaw stability control system maybe classified into three categories that is yaw rate controlsideslip control and combination of yaw rate and sideslipcontrol as illustrated in Figure 5

One of the control objectives of yaw stability controlsystem is yaw rate r An ability to control the actual yawrate close to desired response will improve the handling ormanoeuvrability of the vehicle The desired yaw rate whichis generated by reference model should be tracked by thecontroller in order to improve the handling performance asmentioned in [2 4 13 15 18 27 33 34] In the steady statecondition the desired yaw rate response 119903119889 can be obtainedby using the following equation

119903119889 =V

(119897119891 + 119897119903) + 119896119906119904V2sdot 120575119891 (13)

where stability factor 119896119906119904 is depending on the vehicle param-eters and defined as follows

119896119906119904 =119898(119897119903119862119903 minus 119897119891119862119891)

(119897119891 + 119897119903) 119862119891119862119903

(14)

Another control objective is the vehicle sideslip angle 120573that is the deviation angle between the vehicle longitudinalaxis and longitudinal axis and its motion direction Thecontrol of sideslip angle close to steady state conditionmeanscontrolling the lateral stability of the vehicle For the steadystate condition the desired sideslip is always zero that is120573119889 = 0 as mentioned in [1 6 9 11 17 26 35] Therefore toimprove the vehicle handling and stability performances it

is essential to control both yaw rate and sideslip responsesIn order to achieve these control objectives the proposedcontroller must be able to perform the control task of the yawrate and sideslip tracking control

4 Active Chassis Control

Steering and braking subsystems or actuator are part of thevehicle chassis The active control of yaw stability controlsystem can be realized through active chassis control thatis direct yaw moment control or active steering control orintegrated actives steering and direct yaw moment controlas shown in Figure 6 In direct yaw moment control whichcan be implemented by active braking or active differentialtorque distribution the required yawmoment is generated bythe designed controller that controls the desired yaw rate andsideslip In active steering control the wheel steer angle thatcommanded by the driver is modified by adding correctivesteer angle from the designed controllerThis control strategycan be implemented either using active front steering (AFS)or active rear steering (ARS) or four-wheel active steering(4WAS) control In order to control two variables of the yawrate and sideslip effectively two different controlmechanismsare required Thus related research works on the integrationof two vehicle chassis control that is integrated active steer-ing and direct yaw moment control have been extensivelyconducted recentlyThe review of direct yawmoment controlactive steering control and integrated active steering anddirect yaw moment control are discussed in the followingsubsections

41 Direct YawMoment Control Direct yawmoment controlis one of the prominent methods for yaw stability controlwhere extensive research works using this method have beenconducted with different control strategies and algorithms asreported in [1 3 5 8 9 15ndash18 25 26 30 36] It is recognizedas an effective method to enhance the vehicle lateral stabilityduring critical drivingmanoeuvre by controlling the slip ratioof individual wheel As illustrated in Figure 7 the requiredcorrective yaw moment Δ119872119911 which is generated by thetransverse distribution of braking forces between the vehiclewheels is calculated by the designed controller based on theerror between actual and desired vehicle model that havebeen discussed in Section 2 Another approach of direct yawmoment control is active distribution torque By using anactive differential device as established in [19 20 37 38]the left-right driving torque is distributed by this device togenerate the required corrective yaw moment Δ119872119911

As mentioned in Section 2 direct yaw moment controldesign is based on the linear state space model As describedin (15)119872119911 is considered as control input and front steer angle120575119891119889 is assumed as disturbance

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 120575119891119889 + [

11988731198874]119872119911

6 International Journal of Vehicular Technology

Direct yaw moment control Active steering control Integrated active steering and direct yaw moment control

Active chassis control

Active braking

Active differential AFS ARS 4WAS

Figure 6 Active chassis control

120575fd

120573d

rd ΔMz

120573 r

Desired vehicle model

Actual vehicle model

Controller

Figure 7 Direct yaw moment control [15]

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889 +[

[

0

1

119868119911

]

]

119872119911

(15)

Although direct yaw moment control could enhance thevehicle stability for critical driving conditions it may be lesseffective for emergency braking on split road surface Athigh vehicle speed steady state cornering direct yawmomentcontrol could decrease the yaw rate and increase a burdento the driver To overcome this disadvantage active steeringcontrol is proposed

42 Active Steering Control Active steering control is anotherapproach to improving the vehicle yaw stability especiallyfor steady state driving condition where the lateral tireforce is operated in the linear region Research works ofactive steering control have been continuously conducted inorder to improve the handling and stability performances asreported in [7 13 39ndash42] In general active steering controlcan be divided into three categories that is active frontsteering (AFS) control active rear steering (ARS) controland four-wheel active steering (4WAS) control as shown inFigure 6 As road-vehicle normally has front-wheel steeringAFS control becomes favourite approach among researchersas it can be combined with active braking andor suspensioncontrol In the AFS control diagram as shown in Figure 8 the

front wheel steers angle is a sumof steer angle commanded bythe driver 120575119891119889 and a corrective steer angle 120575119888 generated by thecontroller This corrective steer angle is computed based onyaw rate and sideslip tracking errors 1198901 and 1198902 as implementedin [6 43ndash47]

For control design and analysis of AFS control the linearstate state spacemodel as described in (16) is used Noted thatthis equation is similar to equation (12) but the front wheelsteer angle 120575119891 = 120575119891119889 + 120575119888

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

(120575119891119889 + 120575119888)

(16)

On the other hand ARS control is used to improve thevehicle response for low speed cornering manoeuvres withthe input to the control system being the rear steering angle120575119903 In order to enhance the manoeuvrability at low speedand the handling stability at high speed combination of AFScontrol and ARS called 4WAS control has been proposed asimplemented in [24 48 49] By implementing 4WAS controlthe lateral and yaw motion can be controlled simultaneouslyusing two independent control inputs Noting that frontwheel steer angle 120575119891 and rear wheel steer angle 120575119903 with therear axles of rear tire cornering stiffness119862119903 and distance fromrear axle to centre of gravity 119897119903 are taken into account in theinput matric

International Journal of Vehicular Technology 7

ControllerDesired vehicle model

Actual vehicle model 120575fd

120573d

rd 120575c 120575fd + 120575c 120573 re1 120573 minus 120573

d

=e2 r minus rd

Figure 8 Active front steering control [45]

ControllerDesired vehicle model

Actual vehicle model

120575fd

120573d

rd120575c

120575fd + 120575c

120573 r

ΔMz

e1 120573 minus 120573d

=e2 r minus rd

Figure 9 Integrated active front steering-direct yaw moment control [53]

43 Integrated Active Chassis Control The integrated activechassis control has become a popular research topic in vehicledynamics control as discussed in [50] Vehicle dynamicscontrol can be greatly achieved by integrating the activechassis control of active steering active braking and activesuspension or active stabiliser as implemented in [12 23 5152] Since road-vehicle is usually equipped with front-wheelsteering and braking system an integration and coordinationof active front steering and direct yaw moment control arethe favourite approaches to achieving the objectives of yawrate and sideslip control as reported in [2 10 11 27 28 53ndash59] In this approach the corrective front wheel steers angle120575119888 and corrective yaw moment Δ119872119911 are considered as twoindependent control inputs to the vehicle as illustrated inFigure 9

For controller analysis and design of integrated activefront steering-direct yaw moment control the linear statespace model used is describe as follows

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V0

119862119891119897119891

119868119911

1

119868119911

]]]]

]

[120575119888

Δ119872119911] +

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889

(17)

The principle of active chassis control of steering and brakingfor yaw stability control has been discussed From theabove discussion the differences advantages and disad-vantages of each active chassis control can be digested astabulated in Table 2 From this table it can be observed

that by implementing integrated active front steering-directyaw moment control the lateral and yaw motions can becontrolled simultaneously using two independent controlinputs from two different actuators that is steering andbraking Thus this approach could enhance the vehicle yawstability where the yaw rate and sideslip can be controlledeffectively in emergency manoeuvres and the steady statedriving condition

As a conclusion active chassis control is essential foractive yaw stability control system Therefore to achieve theyaw stability control objectives the control strategies for yawrate and sideslip tracking control are developed based on thisactive chassis control The following section will review anddiscuss the control strategies and algorithms that have beendeveloped in the past

5 Yaw Stability Control Strategies

From the literature various control strategies have beenexplored and utilized based on particular algorithm for activeyaw stability control such as classical PID controller in [1]LMI based and static state feedback control in [2 8 33]119867infincontrol theory in [4 13 25] sliding mode control (SMC) in[1 7 23 24 35 38 53] optimal guaranteed cost coordinationcontroller (OGCC) in [10] adaptive based control in [11]mixed-sensitivity minimization control techniques in [16]classical controllers PI in [49 60] internal model control(IMC) in [37] quantitative feedback theory (QFT) in [45]and 120583-synthesis control in [48] Besides that a combinationor integration of different two control schemes to ensurethe robustness of yaw stability control has been exploredsuch as SMC and backstepping method in [3] SMC andFuzzy Logic Control in [12] and LQR with SMC in [17] Asdiscussed in [20] the IMC and SMC algorithms are designed

8 International Journal of Vehicular Technology

Table2Ty

peso

factivec

hassiscontrol

Vehicle

actuator

Activ

echassiscontrol

Advantages

Disa

dvantages

Brakes

Dire

ctyawmom

entcon

trol

(DYC

)Ac

tiveb

raking

activ

edifferentia

l(i)

Effectiv

efor

criticald

rivingcond

ition

(ii)G

oodforsideslip

wheelslipcontrol

(i)Lesseffectiv

efor

brakingon

split

road

surfa

ce(ii)D

ecreasey

awratedu

ringste

adysta

tedrivingcond

ition

(iii)Ac

tived

ifferentia

lneedextrad

evices

Steerin

gAc

tives

teeringcontrol

(ASC

)

Activ

efront

steering(A

FS)

control

(i)Eff

ectiv

efor

steadysta

tedrivingcond

ition

(ii)E

asetointegratew

ithbrakingcontrol

(iii)Goo

dfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Activ

erearsteering(A

RS)

control

(i)Re

arwheelste

eranglec

anbe

controlled

(ii)G

oodfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

4wheelsa

ctives

teering

(4WAS)

control

(i)Tw

odifferent

steer

inpu

ts(ii)G

ooffor

yawratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Steerin

gandbrake

Integrated

AFS

-DYC

control

(i)Tw

odifferent

inpu

tsfro

mtwodifferent

actuator

(steeringandbraking)

(ii)G

oodfory

awrateandsid

eslip

control

Effectiv

efor

criticaland

steadysta

tedrivingcond

ition

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 2: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

2 International Journal of Vehicular Technology

Vehicle dynamics control

Vertical dynamics control Longitudinal dynamics control Lateral dynamics control

Lane warning detection system Lane keeping systemYaw stability control system

Vehicle dynamics models Active chassis controlControl objectives Control strategies

Figure 1 Yaw stability control system for vehicle lateral dynamic

Vehicle dynamic models

Linearized modelNonlinear model

8 DOF7 DOF 14 DOF 2 DOF

Figure 2 Vehicle dynamic models

In real driving condition the lateral dynamics of vehicleare incorporated with uncertainties such as different roadsurface condition varying vehicle parameters and crosswinddisturbance In yaw stability control system these pertur-bations could influence the yaw rate and sideslip trackingcontrol performances From the control system point ofview the transient performances of tracking control areessential However from the reviewed control strategies inthe literature the controllers are not designed to cater thismatter Therefore an appropriate robust control strategyshould be proposed to improve the transient performances ofthe yaw rate and sideslip tracking control in the presence ofuncertainties and disturbances As a finding from the reviewsthis paper briefly discussed a possible high performancerobust tracking control strategy that can be implemented foryaw stability control system

The review begins with vehicle dynamics models inSection 2 The yaw stability control objectives are discussedin Section 3 and followed by active chassis control for inSection 4 Yaw stability control strategies and problems arereviewed in Sections 5 and 6 respectively In Section 7 a highperformance robust tracking controller using sliding modecontrol and composite nonlinear feedback is discussed Thecontroller evaluation is discussed in Section 8 and endedwithconclusion in Section 9

2 Vehicle Dynamics Models

In order to examine analyse and design the controllerfor yaw stability control system vehicle dynamics modelsare essential where the mathematical modelling of vehicledynamic motion is obtained based on Newtonrsquos 2nd lawthat describes the forces and moments acting on the vehiclebody and tires In general there are two categories of vehicledynamic model that is nonlinear vehicle model and lin-earized vehicle model as depicted in Figure 2 The followingsubsections will discuss the nonlinear vehicle model forsimulation and linearized vehicle model for controller designpurpose

21 Vehicle Model for Simulation The nonlinear vehiclemodel is regularly used to represent and simulate the actualvehicle for controller evaluation and validation In recentyears researches in [1ndash5] have utilized nonlinear vehiclemodel for vehicle handling and stability improvement stud-ies Figure 3 shows the typical nonlinear vehicle model incornering manoeuvre

The input of this model is front wheel steer angle 120575119891while the output variables to be controlled are vehicle sideslip120573 and yaw rate 119903 The vehicle parameters are vehicle widthtrack 119889 distance from front and rear axle to centre of

International Journal of Vehicular Technology 3

Fx1 120575f120575f

Fy1

d

Fx2

Fy2

x

120573

y rMz

lf

lr

Fx3

Fy3

Fy4

Fx4

d

Figure 3 Nonlinear vehicle model [6]

gravity (CG) 119897119891 and 119897119903 respectively The vehicle forwardvelocity of centre of gravity (CG) is V lateral velocity isV119910 and longitudinal velocity is V119909 Other important vehicleparameters are vehicle mass 119898 moment of inertia 119868119911 andfrontrear tire cornering stiffness 119862119891119862119903 The wheels arenumbered as subscript number with (1) for front-left (2) forfront-right (3) for rear-left and (4) for rear-right

Longitudinal tire force 119865119909119894 depends directly on tire slipratio 120582119894 while lateral tire force 119865119910119894 depends directly ontire sideslip angle 120572119894 For smaller slip angle and slip ratiolateral tire force is described as a linear function of the tirecornering stiffness and tire sideslip angle while longitudinaltire force is described as a linear function of the brakingstiffness and the tire slip ratio For larger slip angle and slipratio longitudinal and lateral tire forces exhibit a nonlinearcharacteristics Vehicle dynamic motion with nonlinear tireforces represents a nonlinear system The nonlinear lateraland longitudinal tire forces can be described using prominentPacejka tire model as implemented in [1 4 7] or Dugoff tiremodel as utilized in [8ndash10] while studies in [11] used both tiremodels

The nonlinear vehicle model could have different numberof degree-of-freedom (DOF) where it represents the dynam-ics motions and complexity of vehicle models As utilized in[2 12ndash14] the 7 DOF vehicle model represents the dynamicmotions of vehicle body that is longitudinal lateral yawand four wheels The dynamic equations for the longitudinallateral and yaw motions of the vehicle body are described asfollowsLongitudinal Motion One has the following

119898119886119909 = 119898(V119909 minus 119903V119910)

= (1198651199091 + 1198651199092) cos 120575119891 + 1198651199093 + 1198651199094 minus (1198651199101 + 1198651199102) sin 120575119891(1)

Lateral Motion One has the following

119898119886119910 = 119898(V119910 + 119903V119909)

= (1198651199091 + 1198651199092) sin 120575119891 + (1198651199101 + 1198651199102) cos 120575119891 + 1198651199103 + 1198651199104

(2)

Yaw Motion One has the following

119868119911 119903 = 119897119891 (1198651199101 cos 120575119891 + 1198651199102 cos 120575119891 + 1198651199091 sin 120575119891 + 1198651199092 sin 120575119891)

minus 119897119903 (1198651199103 + 1198651199104) +119872119911

(3)

where 119872119911 is yaw moment that must be taken into accountthat is 119872119911 gt 0 if the tires tends to turn at 119911-axis In (2) thelateral acceleration 119886119910 can be expressed in terms of vehicleforward speed V yaw rate 119903 and sideslip 120573 as follows

119886119910 = V119910 + 119903V119909 = V (119903 + 120573) (4)

Therefore the output variable of sideslip120573of two-trackmodelcan be obtained as follows

120573 =1

119898V[cos120573 (cos 120575119891 (1198651199091 + 1198651199092) minus sin 120575119891 (1198651199101 + 1198651199102))

minus sin120573 (sin 120575119891 (1198651199091 + 1198651199092) minus sin 120575119891 (1198651199101 + 1198651199102))]

minus 119903

(5)

while the output variable of yaw rate 119903 can be determinedfrom (3) and obtained as follows

119903 =1

119868119911

[119897119891 (1198651199101 cos 120575119891 + 1198651199102 cos 120575119891 + 1198651199091 sin 120575119891 + 1198651199092 sin 120575119891)

minus119897119903 (1198651199103 + 1198651199104) +119872119911]

(6)

In vehicle dynamic studies each wheel represents 1 DOFThus there are 4 DOF for road-vehicle with 4 wheels Thedynamic motion for each wheel is described as follows

119868119908119894119894 = minus119877119908119894119865119909119894 + 119879119890119894 minus 119879119887119894 (7)

where is wheel angular acceleration 119899 119877119908 is wheel radius119868119908 is wheel inertia 119879119887119894 is braking torque and 119879119890119894 is drivingtorque

Another nonlinear vehicle model used in the previousresearch is 8 DOF vehicle model that is extensively usedin [4 5 9ndash11 15ndash18] For more accurate simulation andvalidation the 14 DOF vehicle model is used in [1 19 20]Thecomparison between the number ofDOFof nonlinear vehiclemodels that have been discussed above can be summarizedand compared in Table 1

Another nonlinear vehicle model used for simulationuses a multi-degree-of-freedom vehicle model based oncommercial vehicle dynamics software that is CarSim as

4 International Journal of Vehicular Technology

Table 1 Number DOF of nonlinear vehicle models

Number ofDOF Dynamic motions Output variable

7 DOF

(i) Longitudinal

Yaw rate amp Sideslip(ii) Lateral(iii) Vertical(iv) Rotational of 4 wheels

8 DOF

(i) Longitudinal

Yaw rate roll rate andsideslip

(ii) Lateral(iii) Vertical(iv) Roll(v) Rotational of 4 wheels

14 DOF

(i) Longitudinal

Yaw rate roll rate pitchrate and sideslip

(ii) Lateral(iii) Vertical(iv) Roll(v) Pitch(vi) Bounce(vii) Rotational of 4 wheels(viii) Vertical oscillations of4 wheels

implemented in [21ndash26] By using this software based vehiclemodel the dynamic behaviour of vehicle is more precisesimilar to a real vehicle However for yaw rate and sidesliptracking control in yaw stability control system the 7 DOFnonlinear vehicle model as discussed in the above equationsand shown in Table 1 is adequate for simulation and evalua-tion of the design controller

22 Vehicle Model for Controller Design In vehicle dynamicstudies the classical bicycle model as shown in Figure 4is prominently used for yaw stability control analysis andcontroller design as utilized in [1 3 8 26ndash30] This modelis linearized from the nonlinear vehicle model based on thefollowing assumptions

(i) Tires forces operate in the linear region(ii) The vehicle moves on plane surfaceflat road (planar

motion)(iii) Left and right wheels at the front and rear axle are

lumped in singlewheel at the centre line of the vehicle(iv) Constant vehicle speed ie the longitudinal accelera-

tion equal to zero (119886119909=0)(v) Steering angle and sideslip angle are assumed small

(asymp 0)(vi) No braking is applied at all wheels(vii) Centre of gravity (CG) is not shifted as vehicle mass

is changing(viii) 2 front wheels have the same steering angle(ix) Desired vehicle sideslip is assumed to be zero in

steady state

Fyr

lr

y

120573 x

r

lf

Fyf

120572f 120575f

120572r

Figure 4 Bicycle model [31]

In the simplest formof planarmotion thismodel consists of 2DOF for lateral and yaw motions as describe in the followingequationsLateral Motion One has the following

119898V ( 120573 + 119903) = (119865119910119891 + 119865119910119903) minus 119903 (8)

Yaw Motion One has the following

119868119911 119903 = 119897119891 sdot 119865119910119891 minus 119897119903 sdot 119865119910119903 (9)

In thismodel the front and rear lateral tire forces119865119910119891 and119865119910119903respectively exhibit linear characteristics and described as alinear function of the front and rear cornering stiffness 119862119891and 119862119903 as follows

119865119910119891 = 119862119891120572119891

119865119910119903 = 119862119903120572119903

(10)

where the front and rear tire sideslip angle 120572119891 and 120572119903 forlinear tire forces are given in the following equations

120572119891 = 120575119891 minus 120573 minus119897119891119903

V

120572119903 = minus 120573 +119897119903119903

V

(11)

By rearranging and simplifying (8)ndash(11) the differentialequations of sideslip and yaw rate variables can be simplifiedas a linear state space model as follows

= 119860119909 + 119861119906

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 119906

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891

(12)

where120573 and 119903 are state or output variables119862119891 and119862119903 are frontand rear tire cornering stiffness respectively 119898 is vehicle

International Journal of Vehicular Technology 5

Control objectives

Yaw rate Side slip Yaw rate and side slip

Figure 5 Yaw stability control objectives

mass 119868119911 is moment of inertia 119897119891 and 119897119903 are distance fromfront and rear axle to centre of gravity respectively V isvehicle speed and front tire steer angle 120575119891 is the input 119906to the model Notice that vehicle speed V is assumed alwaysconstant which means the vehicle is not involved with accel-erating and braking Hence only lateral and yaw motions areanalysed

Besides that the bicycle model is also regularly used asdesired or referencemodel to generate the desired response ofthe yaw rate and sideslip angle based on steady state conditionor approximated first order response In designing the controlstrategy based on vehicle active chassis control the linearstate space model in (13) is essential

3 Yaw Stability Control Objectives

A vehicle yaw rate 119903 and sideslip angle 120573 are significantvariables in vehicle yaw stability control system As stated in[32] control objectives of yaw stability control system maybe classified into three categories that is yaw rate controlsideslip control and combination of yaw rate and sideslipcontrol as illustrated in Figure 5

One of the control objectives of yaw stability controlsystem is yaw rate r An ability to control the actual yawrate close to desired response will improve the handling ormanoeuvrability of the vehicle The desired yaw rate whichis generated by reference model should be tracked by thecontroller in order to improve the handling performance asmentioned in [2 4 13 15 18 27 33 34] In the steady statecondition the desired yaw rate response 119903119889 can be obtainedby using the following equation

119903119889 =V

(119897119891 + 119897119903) + 119896119906119904V2sdot 120575119891 (13)

where stability factor 119896119906119904 is depending on the vehicle param-eters and defined as follows

119896119906119904 =119898(119897119903119862119903 minus 119897119891119862119891)

(119897119891 + 119897119903) 119862119891119862119903

(14)

Another control objective is the vehicle sideslip angle 120573that is the deviation angle between the vehicle longitudinalaxis and longitudinal axis and its motion direction Thecontrol of sideslip angle close to steady state conditionmeanscontrolling the lateral stability of the vehicle For the steadystate condition the desired sideslip is always zero that is120573119889 = 0 as mentioned in [1 6 9 11 17 26 35] Therefore toimprove the vehicle handling and stability performances it

is essential to control both yaw rate and sideslip responsesIn order to achieve these control objectives the proposedcontroller must be able to perform the control task of the yawrate and sideslip tracking control

4 Active Chassis Control

Steering and braking subsystems or actuator are part of thevehicle chassis The active control of yaw stability controlsystem can be realized through active chassis control thatis direct yaw moment control or active steering control orintegrated actives steering and direct yaw moment controlas shown in Figure 6 In direct yaw moment control whichcan be implemented by active braking or active differentialtorque distribution the required yawmoment is generated bythe designed controller that controls the desired yaw rate andsideslip In active steering control the wheel steer angle thatcommanded by the driver is modified by adding correctivesteer angle from the designed controllerThis control strategycan be implemented either using active front steering (AFS)or active rear steering (ARS) or four-wheel active steering(4WAS) control In order to control two variables of the yawrate and sideslip effectively two different controlmechanismsare required Thus related research works on the integrationof two vehicle chassis control that is integrated active steer-ing and direct yaw moment control have been extensivelyconducted recentlyThe review of direct yawmoment controlactive steering control and integrated active steering anddirect yaw moment control are discussed in the followingsubsections

41 Direct YawMoment Control Direct yawmoment controlis one of the prominent methods for yaw stability controlwhere extensive research works using this method have beenconducted with different control strategies and algorithms asreported in [1 3 5 8 9 15ndash18 25 26 30 36] It is recognizedas an effective method to enhance the vehicle lateral stabilityduring critical drivingmanoeuvre by controlling the slip ratioof individual wheel As illustrated in Figure 7 the requiredcorrective yaw moment Δ119872119911 which is generated by thetransverse distribution of braking forces between the vehiclewheels is calculated by the designed controller based on theerror between actual and desired vehicle model that havebeen discussed in Section 2 Another approach of direct yawmoment control is active distribution torque By using anactive differential device as established in [19 20 37 38]the left-right driving torque is distributed by this device togenerate the required corrective yaw moment Δ119872119911

As mentioned in Section 2 direct yaw moment controldesign is based on the linear state space model As describedin (15)119872119911 is considered as control input and front steer angle120575119891119889 is assumed as disturbance

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 120575119891119889 + [

11988731198874]119872119911

6 International Journal of Vehicular Technology

Direct yaw moment control Active steering control Integrated active steering and direct yaw moment control

Active chassis control

Active braking

Active differential AFS ARS 4WAS

Figure 6 Active chassis control

120575fd

120573d

rd ΔMz

120573 r

Desired vehicle model

Actual vehicle model

Controller

Figure 7 Direct yaw moment control [15]

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889 +[

[

0

1

119868119911

]

]

119872119911

(15)

Although direct yaw moment control could enhance thevehicle stability for critical driving conditions it may be lesseffective for emergency braking on split road surface Athigh vehicle speed steady state cornering direct yawmomentcontrol could decrease the yaw rate and increase a burdento the driver To overcome this disadvantage active steeringcontrol is proposed

42 Active Steering Control Active steering control is anotherapproach to improving the vehicle yaw stability especiallyfor steady state driving condition where the lateral tireforce is operated in the linear region Research works ofactive steering control have been continuously conducted inorder to improve the handling and stability performances asreported in [7 13 39ndash42] In general active steering controlcan be divided into three categories that is active frontsteering (AFS) control active rear steering (ARS) controland four-wheel active steering (4WAS) control as shown inFigure 6 As road-vehicle normally has front-wheel steeringAFS control becomes favourite approach among researchersas it can be combined with active braking andor suspensioncontrol In the AFS control diagram as shown in Figure 8 the

front wheel steers angle is a sumof steer angle commanded bythe driver 120575119891119889 and a corrective steer angle 120575119888 generated by thecontroller This corrective steer angle is computed based onyaw rate and sideslip tracking errors 1198901 and 1198902 as implementedin [6 43ndash47]

For control design and analysis of AFS control the linearstate state spacemodel as described in (16) is used Noted thatthis equation is similar to equation (12) but the front wheelsteer angle 120575119891 = 120575119891119889 + 120575119888

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

(120575119891119889 + 120575119888)

(16)

On the other hand ARS control is used to improve thevehicle response for low speed cornering manoeuvres withthe input to the control system being the rear steering angle120575119903 In order to enhance the manoeuvrability at low speedand the handling stability at high speed combination of AFScontrol and ARS called 4WAS control has been proposed asimplemented in [24 48 49] By implementing 4WAS controlthe lateral and yaw motion can be controlled simultaneouslyusing two independent control inputs Noting that frontwheel steer angle 120575119891 and rear wheel steer angle 120575119903 with therear axles of rear tire cornering stiffness119862119903 and distance fromrear axle to centre of gravity 119897119903 are taken into account in theinput matric

International Journal of Vehicular Technology 7

ControllerDesired vehicle model

Actual vehicle model 120575fd

120573d

rd 120575c 120575fd + 120575c 120573 re1 120573 minus 120573

d

=e2 r minus rd

Figure 8 Active front steering control [45]

ControllerDesired vehicle model

Actual vehicle model

120575fd

120573d

rd120575c

120575fd + 120575c

120573 r

ΔMz

e1 120573 minus 120573d

=e2 r minus rd

Figure 9 Integrated active front steering-direct yaw moment control [53]

43 Integrated Active Chassis Control The integrated activechassis control has become a popular research topic in vehicledynamics control as discussed in [50] Vehicle dynamicscontrol can be greatly achieved by integrating the activechassis control of active steering active braking and activesuspension or active stabiliser as implemented in [12 23 5152] Since road-vehicle is usually equipped with front-wheelsteering and braking system an integration and coordinationof active front steering and direct yaw moment control arethe favourite approaches to achieving the objectives of yawrate and sideslip control as reported in [2 10 11 27 28 53ndash59] In this approach the corrective front wheel steers angle120575119888 and corrective yaw moment Δ119872119911 are considered as twoindependent control inputs to the vehicle as illustrated inFigure 9

For controller analysis and design of integrated activefront steering-direct yaw moment control the linear statespace model used is describe as follows

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V0

119862119891119897119891

119868119911

1

119868119911

]]]]

]

[120575119888

Δ119872119911] +

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889

(17)

The principle of active chassis control of steering and brakingfor yaw stability control has been discussed From theabove discussion the differences advantages and disad-vantages of each active chassis control can be digested astabulated in Table 2 From this table it can be observed

that by implementing integrated active front steering-directyaw moment control the lateral and yaw motions can becontrolled simultaneously using two independent controlinputs from two different actuators that is steering andbraking Thus this approach could enhance the vehicle yawstability where the yaw rate and sideslip can be controlledeffectively in emergency manoeuvres and the steady statedriving condition

As a conclusion active chassis control is essential foractive yaw stability control system Therefore to achieve theyaw stability control objectives the control strategies for yawrate and sideslip tracking control are developed based on thisactive chassis control The following section will review anddiscuss the control strategies and algorithms that have beendeveloped in the past

5 Yaw Stability Control Strategies

From the literature various control strategies have beenexplored and utilized based on particular algorithm for activeyaw stability control such as classical PID controller in [1]LMI based and static state feedback control in [2 8 33]119867infincontrol theory in [4 13 25] sliding mode control (SMC) in[1 7 23 24 35 38 53] optimal guaranteed cost coordinationcontroller (OGCC) in [10] adaptive based control in [11]mixed-sensitivity minimization control techniques in [16]classical controllers PI in [49 60] internal model control(IMC) in [37] quantitative feedback theory (QFT) in [45]and 120583-synthesis control in [48] Besides that a combinationor integration of different two control schemes to ensurethe robustness of yaw stability control has been exploredsuch as SMC and backstepping method in [3] SMC andFuzzy Logic Control in [12] and LQR with SMC in [17] Asdiscussed in [20] the IMC and SMC algorithms are designed

8 International Journal of Vehicular Technology

Table2Ty

peso

factivec

hassiscontrol

Vehicle

actuator

Activ

echassiscontrol

Advantages

Disa

dvantages

Brakes

Dire

ctyawmom

entcon

trol

(DYC

)Ac

tiveb

raking

activ

edifferentia

l(i)

Effectiv

efor

criticald

rivingcond

ition

(ii)G

oodforsideslip

wheelslipcontrol

(i)Lesseffectiv

efor

brakingon

split

road

surfa

ce(ii)D

ecreasey

awratedu

ringste

adysta

tedrivingcond

ition

(iii)Ac

tived

ifferentia

lneedextrad

evices

Steerin

gAc

tives

teeringcontrol

(ASC

)

Activ

efront

steering(A

FS)

control

(i)Eff

ectiv

efor

steadysta

tedrivingcond

ition

(ii)E

asetointegratew

ithbrakingcontrol

(iii)Goo

dfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Activ

erearsteering(A

RS)

control

(i)Re

arwheelste

eranglec

anbe

controlled

(ii)G

oodfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

4wheelsa

ctives

teering

(4WAS)

control

(i)Tw

odifferent

steer

inpu

ts(ii)G

ooffor

yawratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Steerin

gandbrake

Integrated

AFS

-DYC

control

(i)Tw

odifferent

inpu

tsfro

mtwodifferent

actuator

(steeringandbraking)

(ii)G

oodfory

awrateandsid

eslip

control

Effectiv

efor

criticaland

steadysta

tedrivingcond

ition

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 3: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

International Journal of Vehicular Technology 3

Fx1 120575f120575f

Fy1

d

Fx2

Fy2

x

120573

y rMz

lf

lr

Fx3

Fy3

Fy4

Fx4

d

Figure 3 Nonlinear vehicle model [6]

gravity (CG) 119897119891 and 119897119903 respectively The vehicle forwardvelocity of centre of gravity (CG) is V lateral velocity isV119910 and longitudinal velocity is V119909 Other important vehicleparameters are vehicle mass 119898 moment of inertia 119868119911 andfrontrear tire cornering stiffness 119862119891119862119903 The wheels arenumbered as subscript number with (1) for front-left (2) forfront-right (3) for rear-left and (4) for rear-right

Longitudinal tire force 119865119909119894 depends directly on tire slipratio 120582119894 while lateral tire force 119865119910119894 depends directly ontire sideslip angle 120572119894 For smaller slip angle and slip ratiolateral tire force is described as a linear function of the tirecornering stiffness and tire sideslip angle while longitudinaltire force is described as a linear function of the brakingstiffness and the tire slip ratio For larger slip angle and slipratio longitudinal and lateral tire forces exhibit a nonlinearcharacteristics Vehicle dynamic motion with nonlinear tireforces represents a nonlinear system The nonlinear lateraland longitudinal tire forces can be described using prominentPacejka tire model as implemented in [1 4 7] or Dugoff tiremodel as utilized in [8ndash10] while studies in [11] used both tiremodels

The nonlinear vehicle model could have different numberof degree-of-freedom (DOF) where it represents the dynam-ics motions and complexity of vehicle models As utilized in[2 12ndash14] the 7 DOF vehicle model represents the dynamicmotions of vehicle body that is longitudinal lateral yawand four wheels The dynamic equations for the longitudinallateral and yaw motions of the vehicle body are described asfollowsLongitudinal Motion One has the following

119898119886119909 = 119898(V119909 minus 119903V119910)

= (1198651199091 + 1198651199092) cos 120575119891 + 1198651199093 + 1198651199094 minus (1198651199101 + 1198651199102) sin 120575119891(1)

Lateral Motion One has the following

119898119886119910 = 119898(V119910 + 119903V119909)

= (1198651199091 + 1198651199092) sin 120575119891 + (1198651199101 + 1198651199102) cos 120575119891 + 1198651199103 + 1198651199104

(2)

Yaw Motion One has the following

119868119911 119903 = 119897119891 (1198651199101 cos 120575119891 + 1198651199102 cos 120575119891 + 1198651199091 sin 120575119891 + 1198651199092 sin 120575119891)

minus 119897119903 (1198651199103 + 1198651199104) +119872119911

(3)

where 119872119911 is yaw moment that must be taken into accountthat is 119872119911 gt 0 if the tires tends to turn at 119911-axis In (2) thelateral acceleration 119886119910 can be expressed in terms of vehicleforward speed V yaw rate 119903 and sideslip 120573 as follows

119886119910 = V119910 + 119903V119909 = V (119903 + 120573) (4)

Therefore the output variable of sideslip120573of two-trackmodelcan be obtained as follows

120573 =1

119898V[cos120573 (cos 120575119891 (1198651199091 + 1198651199092) minus sin 120575119891 (1198651199101 + 1198651199102))

minus sin120573 (sin 120575119891 (1198651199091 + 1198651199092) minus sin 120575119891 (1198651199101 + 1198651199102))]

minus 119903

(5)

while the output variable of yaw rate 119903 can be determinedfrom (3) and obtained as follows

119903 =1

119868119911

[119897119891 (1198651199101 cos 120575119891 + 1198651199102 cos 120575119891 + 1198651199091 sin 120575119891 + 1198651199092 sin 120575119891)

minus119897119903 (1198651199103 + 1198651199104) +119872119911]

(6)

In vehicle dynamic studies each wheel represents 1 DOFThus there are 4 DOF for road-vehicle with 4 wheels Thedynamic motion for each wheel is described as follows

119868119908119894119894 = minus119877119908119894119865119909119894 + 119879119890119894 minus 119879119887119894 (7)

where is wheel angular acceleration 119899 119877119908 is wheel radius119868119908 is wheel inertia 119879119887119894 is braking torque and 119879119890119894 is drivingtorque

Another nonlinear vehicle model used in the previousresearch is 8 DOF vehicle model that is extensively usedin [4 5 9ndash11 15ndash18] For more accurate simulation andvalidation the 14 DOF vehicle model is used in [1 19 20]Thecomparison between the number ofDOFof nonlinear vehiclemodels that have been discussed above can be summarizedand compared in Table 1

Another nonlinear vehicle model used for simulationuses a multi-degree-of-freedom vehicle model based oncommercial vehicle dynamics software that is CarSim as

4 International Journal of Vehicular Technology

Table 1 Number DOF of nonlinear vehicle models

Number ofDOF Dynamic motions Output variable

7 DOF

(i) Longitudinal

Yaw rate amp Sideslip(ii) Lateral(iii) Vertical(iv) Rotational of 4 wheels

8 DOF

(i) Longitudinal

Yaw rate roll rate andsideslip

(ii) Lateral(iii) Vertical(iv) Roll(v) Rotational of 4 wheels

14 DOF

(i) Longitudinal

Yaw rate roll rate pitchrate and sideslip

(ii) Lateral(iii) Vertical(iv) Roll(v) Pitch(vi) Bounce(vii) Rotational of 4 wheels(viii) Vertical oscillations of4 wheels

implemented in [21ndash26] By using this software based vehiclemodel the dynamic behaviour of vehicle is more precisesimilar to a real vehicle However for yaw rate and sidesliptracking control in yaw stability control system the 7 DOFnonlinear vehicle model as discussed in the above equationsand shown in Table 1 is adequate for simulation and evalua-tion of the design controller

22 Vehicle Model for Controller Design In vehicle dynamicstudies the classical bicycle model as shown in Figure 4is prominently used for yaw stability control analysis andcontroller design as utilized in [1 3 8 26ndash30] This modelis linearized from the nonlinear vehicle model based on thefollowing assumptions

(i) Tires forces operate in the linear region(ii) The vehicle moves on plane surfaceflat road (planar

motion)(iii) Left and right wheels at the front and rear axle are

lumped in singlewheel at the centre line of the vehicle(iv) Constant vehicle speed ie the longitudinal accelera-

tion equal to zero (119886119909=0)(v) Steering angle and sideslip angle are assumed small

(asymp 0)(vi) No braking is applied at all wheels(vii) Centre of gravity (CG) is not shifted as vehicle mass

is changing(viii) 2 front wheels have the same steering angle(ix) Desired vehicle sideslip is assumed to be zero in

steady state

Fyr

lr

y

120573 x

r

lf

Fyf

120572f 120575f

120572r

Figure 4 Bicycle model [31]

In the simplest formof planarmotion thismodel consists of 2DOF for lateral and yaw motions as describe in the followingequationsLateral Motion One has the following

119898V ( 120573 + 119903) = (119865119910119891 + 119865119910119903) minus 119903 (8)

Yaw Motion One has the following

119868119911 119903 = 119897119891 sdot 119865119910119891 minus 119897119903 sdot 119865119910119903 (9)

In thismodel the front and rear lateral tire forces119865119910119891 and119865119910119903respectively exhibit linear characteristics and described as alinear function of the front and rear cornering stiffness 119862119891and 119862119903 as follows

119865119910119891 = 119862119891120572119891

119865119910119903 = 119862119903120572119903

(10)

where the front and rear tire sideslip angle 120572119891 and 120572119903 forlinear tire forces are given in the following equations

120572119891 = 120575119891 minus 120573 minus119897119891119903

V

120572119903 = minus 120573 +119897119903119903

V

(11)

By rearranging and simplifying (8)ndash(11) the differentialequations of sideslip and yaw rate variables can be simplifiedas a linear state space model as follows

= 119860119909 + 119861119906

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 119906

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891

(12)

where120573 and 119903 are state or output variables119862119891 and119862119903 are frontand rear tire cornering stiffness respectively 119898 is vehicle

International Journal of Vehicular Technology 5

Control objectives

Yaw rate Side slip Yaw rate and side slip

Figure 5 Yaw stability control objectives

mass 119868119911 is moment of inertia 119897119891 and 119897119903 are distance fromfront and rear axle to centre of gravity respectively V isvehicle speed and front tire steer angle 120575119891 is the input 119906to the model Notice that vehicle speed V is assumed alwaysconstant which means the vehicle is not involved with accel-erating and braking Hence only lateral and yaw motions areanalysed

Besides that the bicycle model is also regularly used asdesired or referencemodel to generate the desired response ofthe yaw rate and sideslip angle based on steady state conditionor approximated first order response In designing the controlstrategy based on vehicle active chassis control the linearstate space model in (13) is essential

3 Yaw Stability Control Objectives

A vehicle yaw rate 119903 and sideslip angle 120573 are significantvariables in vehicle yaw stability control system As stated in[32] control objectives of yaw stability control system maybe classified into three categories that is yaw rate controlsideslip control and combination of yaw rate and sideslipcontrol as illustrated in Figure 5

One of the control objectives of yaw stability controlsystem is yaw rate r An ability to control the actual yawrate close to desired response will improve the handling ormanoeuvrability of the vehicle The desired yaw rate whichis generated by reference model should be tracked by thecontroller in order to improve the handling performance asmentioned in [2 4 13 15 18 27 33 34] In the steady statecondition the desired yaw rate response 119903119889 can be obtainedby using the following equation

119903119889 =V

(119897119891 + 119897119903) + 119896119906119904V2sdot 120575119891 (13)

where stability factor 119896119906119904 is depending on the vehicle param-eters and defined as follows

119896119906119904 =119898(119897119903119862119903 minus 119897119891119862119891)

(119897119891 + 119897119903) 119862119891119862119903

(14)

Another control objective is the vehicle sideslip angle 120573that is the deviation angle between the vehicle longitudinalaxis and longitudinal axis and its motion direction Thecontrol of sideslip angle close to steady state conditionmeanscontrolling the lateral stability of the vehicle For the steadystate condition the desired sideslip is always zero that is120573119889 = 0 as mentioned in [1 6 9 11 17 26 35] Therefore toimprove the vehicle handling and stability performances it

is essential to control both yaw rate and sideslip responsesIn order to achieve these control objectives the proposedcontroller must be able to perform the control task of the yawrate and sideslip tracking control

4 Active Chassis Control

Steering and braking subsystems or actuator are part of thevehicle chassis The active control of yaw stability controlsystem can be realized through active chassis control thatis direct yaw moment control or active steering control orintegrated actives steering and direct yaw moment controlas shown in Figure 6 In direct yaw moment control whichcan be implemented by active braking or active differentialtorque distribution the required yawmoment is generated bythe designed controller that controls the desired yaw rate andsideslip In active steering control the wheel steer angle thatcommanded by the driver is modified by adding correctivesteer angle from the designed controllerThis control strategycan be implemented either using active front steering (AFS)or active rear steering (ARS) or four-wheel active steering(4WAS) control In order to control two variables of the yawrate and sideslip effectively two different controlmechanismsare required Thus related research works on the integrationof two vehicle chassis control that is integrated active steer-ing and direct yaw moment control have been extensivelyconducted recentlyThe review of direct yawmoment controlactive steering control and integrated active steering anddirect yaw moment control are discussed in the followingsubsections

41 Direct YawMoment Control Direct yawmoment controlis one of the prominent methods for yaw stability controlwhere extensive research works using this method have beenconducted with different control strategies and algorithms asreported in [1 3 5 8 9 15ndash18 25 26 30 36] It is recognizedas an effective method to enhance the vehicle lateral stabilityduring critical drivingmanoeuvre by controlling the slip ratioof individual wheel As illustrated in Figure 7 the requiredcorrective yaw moment Δ119872119911 which is generated by thetransverse distribution of braking forces between the vehiclewheels is calculated by the designed controller based on theerror between actual and desired vehicle model that havebeen discussed in Section 2 Another approach of direct yawmoment control is active distribution torque By using anactive differential device as established in [19 20 37 38]the left-right driving torque is distributed by this device togenerate the required corrective yaw moment Δ119872119911

As mentioned in Section 2 direct yaw moment controldesign is based on the linear state space model As describedin (15)119872119911 is considered as control input and front steer angle120575119891119889 is assumed as disturbance

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 120575119891119889 + [

11988731198874]119872119911

6 International Journal of Vehicular Technology

Direct yaw moment control Active steering control Integrated active steering and direct yaw moment control

Active chassis control

Active braking

Active differential AFS ARS 4WAS

Figure 6 Active chassis control

120575fd

120573d

rd ΔMz

120573 r

Desired vehicle model

Actual vehicle model

Controller

Figure 7 Direct yaw moment control [15]

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889 +[

[

0

1

119868119911

]

]

119872119911

(15)

Although direct yaw moment control could enhance thevehicle stability for critical driving conditions it may be lesseffective for emergency braking on split road surface Athigh vehicle speed steady state cornering direct yawmomentcontrol could decrease the yaw rate and increase a burdento the driver To overcome this disadvantage active steeringcontrol is proposed

42 Active Steering Control Active steering control is anotherapproach to improving the vehicle yaw stability especiallyfor steady state driving condition where the lateral tireforce is operated in the linear region Research works ofactive steering control have been continuously conducted inorder to improve the handling and stability performances asreported in [7 13 39ndash42] In general active steering controlcan be divided into three categories that is active frontsteering (AFS) control active rear steering (ARS) controland four-wheel active steering (4WAS) control as shown inFigure 6 As road-vehicle normally has front-wheel steeringAFS control becomes favourite approach among researchersas it can be combined with active braking andor suspensioncontrol In the AFS control diagram as shown in Figure 8 the

front wheel steers angle is a sumof steer angle commanded bythe driver 120575119891119889 and a corrective steer angle 120575119888 generated by thecontroller This corrective steer angle is computed based onyaw rate and sideslip tracking errors 1198901 and 1198902 as implementedin [6 43ndash47]

For control design and analysis of AFS control the linearstate state spacemodel as described in (16) is used Noted thatthis equation is similar to equation (12) but the front wheelsteer angle 120575119891 = 120575119891119889 + 120575119888

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

(120575119891119889 + 120575119888)

(16)

On the other hand ARS control is used to improve thevehicle response for low speed cornering manoeuvres withthe input to the control system being the rear steering angle120575119903 In order to enhance the manoeuvrability at low speedand the handling stability at high speed combination of AFScontrol and ARS called 4WAS control has been proposed asimplemented in [24 48 49] By implementing 4WAS controlthe lateral and yaw motion can be controlled simultaneouslyusing two independent control inputs Noting that frontwheel steer angle 120575119891 and rear wheel steer angle 120575119903 with therear axles of rear tire cornering stiffness119862119903 and distance fromrear axle to centre of gravity 119897119903 are taken into account in theinput matric

International Journal of Vehicular Technology 7

ControllerDesired vehicle model

Actual vehicle model 120575fd

120573d

rd 120575c 120575fd + 120575c 120573 re1 120573 minus 120573

d

=e2 r minus rd

Figure 8 Active front steering control [45]

ControllerDesired vehicle model

Actual vehicle model

120575fd

120573d

rd120575c

120575fd + 120575c

120573 r

ΔMz

e1 120573 minus 120573d

=e2 r minus rd

Figure 9 Integrated active front steering-direct yaw moment control [53]

43 Integrated Active Chassis Control The integrated activechassis control has become a popular research topic in vehicledynamics control as discussed in [50] Vehicle dynamicscontrol can be greatly achieved by integrating the activechassis control of active steering active braking and activesuspension or active stabiliser as implemented in [12 23 5152] Since road-vehicle is usually equipped with front-wheelsteering and braking system an integration and coordinationof active front steering and direct yaw moment control arethe favourite approaches to achieving the objectives of yawrate and sideslip control as reported in [2 10 11 27 28 53ndash59] In this approach the corrective front wheel steers angle120575119888 and corrective yaw moment Δ119872119911 are considered as twoindependent control inputs to the vehicle as illustrated inFigure 9

For controller analysis and design of integrated activefront steering-direct yaw moment control the linear statespace model used is describe as follows

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V0

119862119891119897119891

119868119911

1

119868119911

]]]]

]

[120575119888

Δ119872119911] +

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889

(17)

The principle of active chassis control of steering and brakingfor yaw stability control has been discussed From theabove discussion the differences advantages and disad-vantages of each active chassis control can be digested astabulated in Table 2 From this table it can be observed

that by implementing integrated active front steering-directyaw moment control the lateral and yaw motions can becontrolled simultaneously using two independent controlinputs from two different actuators that is steering andbraking Thus this approach could enhance the vehicle yawstability where the yaw rate and sideslip can be controlledeffectively in emergency manoeuvres and the steady statedriving condition

As a conclusion active chassis control is essential foractive yaw stability control system Therefore to achieve theyaw stability control objectives the control strategies for yawrate and sideslip tracking control are developed based on thisactive chassis control The following section will review anddiscuss the control strategies and algorithms that have beendeveloped in the past

5 Yaw Stability Control Strategies

From the literature various control strategies have beenexplored and utilized based on particular algorithm for activeyaw stability control such as classical PID controller in [1]LMI based and static state feedback control in [2 8 33]119867infincontrol theory in [4 13 25] sliding mode control (SMC) in[1 7 23 24 35 38 53] optimal guaranteed cost coordinationcontroller (OGCC) in [10] adaptive based control in [11]mixed-sensitivity minimization control techniques in [16]classical controllers PI in [49 60] internal model control(IMC) in [37] quantitative feedback theory (QFT) in [45]and 120583-synthesis control in [48] Besides that a combinationor integration of different two control schemes to ensurethe robustness of yaw stability control has been exploredsuch as SMC and backstepping method in [3] SMC andFuzzy Logic Control in [12] and LQR with SMC in [17] Asdiscussed in [20] the IMC and SMC algorithms are designed

8 International Journal of Vehicular Technology

Table2Ty

peso

factivec

hassiscontrol

Vehicle

actuator

Activ

echassiscontrol

Advantages

Disa

dvantages

Brakes

Dire

ctyawmom

entcon

trol

(DYC

)Ac

tiveb

raking

activ

edifferentia

l(i)

Effectiv

efor

criticald

rivingcond

ition

(ii)G

oodforsideslip

wheelslipcontrol

(i)Lesseffectiv

efor

brakingon

split

road

surfa

ce(ii)D

ecreasey

awratedu

ringste

adysta

tedrivingcond

ition

(iii)Ac

tived

ifferentia

lneedextrad

evices

Steerin

gAc

tives

teeringcontrol

(ASC

)

Activ

efront

steering(A

FS)

control

(i)Eff

ectiv

efor

steadysta

tedrivingcond

ition

(ii)E

asetointegratew

ithbrakingcontrol

(iii)Goo

dfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Activ

erearsteering(A

RS)

control

(i)Re

arwheelste

eranglec

anbe

controlled

(ii)G

oodfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

4wheelsa

ctives

teering

(4WAS)

control

(i)Tw

odifferent

steer

inpu

ts(ii)G

ooffor

yawratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Steerin

gandbrake

Integrated

AFS

-DYC

control

(i)Tw

odifferent

inpu

tsfro

mtwodifferent

actuator

(steeringandbraking)

(ii)G

oodfory

awrateandsid

eslip

control

Effectiv

efor

criticaland

steadysta

tedrivingcond

ition

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 4: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

4 International Journal of Vehicular Technology

Table 1 Number DOF of nonlinear vehicle models

Number ofDOF Dynamic motions Output variable

7 DOF

(i) Longitudinal

Yaw rate amp Sideslip(ii) Lateral(iii) Vertical(iv) Rotational of 4 wheels

8 DOF

(i) Longitudinal

Yaw rate roll rate andsideslip

(ii) Lateral(iii) Vertical(iv) Roll(v) Rotational of 4 wheels

14 DOF

(i) Longitudinal

Yaw rate roll rate pitchrate and sideslip

(ii) Lateral(iii) Vertical(iv) Roll(v) Pitch(vi) Bounce(vii) Rotational of 4 wheels(viii) Vertical oscillations of4 wheels

implemented in [21ndash26] By using this software based vehiclemodel the dynamic behaviour of vehicle is more precisesimilar to a real vehicle However for yaw rate and sidesliptracking control in yaw stability control system the 7 DOFnonlinear vehicle model as discussed in the above equationsand shown in Table 1 is adequate for simulation and evalua-tion of the design controller

22 Vehicle Model for Controller Design In vehicle dynamicstudies the classical bicycle model as shown in Figure 4is prominently used for yaw stability control analysis andcontroller design as utilized in [1 3 8 26ndash30] This modelis linearized from the nonlinear vehicle model based on thefollowing assumptions

(i) Tires forces operate in the linear region(ii) The vehicle moves on plane surfaceflat road (planar

motion)(iii) Left and right wheels at the front and rear axle are

lumped in singlewheel at the centre line of the vehicle(iv) Constant vehicle speed ie the longitudinal accelera-

tion equal to zero (119886119909=0)(v) Steering angle and sideslip angle are assumed small

(asymp 0)(vi) No braking is applied at all wheels(vii) Centre of gravity (CG) is not shifted as vehicle mass

is changing(viii) 2 front wheels have the same steering angle(ix) Desired vehicle sideslip is assumed to be zero in

steady state

Fyr

lr

y

120573 x

r

lf

Fyf

120572f 120575f

120572r

Figure 4 Bicycle model [31]

In the simplest formof planarmotion thismodel consists of 2DOF for lateral and yaw motions as describe in the followingequationsLateral Motion One has the following

119898V ( 120573 + 119903) = (119865119910119891 + 119865119910119903) minus 119903 (8)

Yaw Motion One has the following

119868119911 119903 = 119897119891 sdot 119865119910119891 minus 119897119903 sdot 119865119910119903 (9)

In thismodel the front and rear lateral tire forces119865119910119891 and119865119910119903respectively exhibit linear characteristics and described as alinear function of the front and rear cornering stiffness 119862119891and 119862119903 as follows

119865119910119891 = 119862119891120572119891

119865119910119903 = 119862119903120572119903

(10)

where the front and rear tire sideslip angle 120572119891 and 120572119903 forlinear tire forces are given in the following equations

120572119891 = 120575119891 minus 120573 minus119897119891119903

V

120572119903 = minus 120573 +119897119903119903

V

(11)

By rearranging and simplifying (8)ndash(11) the differentialequations of sideslip and yaw rate variables can be simplifiedas a linear state space model as follows

= 119860119909 + 119861119906

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 119906

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891

(12)

where120573 and 119903 are state or output variables119862119891 and119862119903 are frontand rear tire cornering stiffness respectively 119898 is vehicle

International Journal of Vehicular Technology 5

Control objectives

Yaw rate Side slip Yaw rate and side slip

Figure 5 Yaw stability control objectives

mass 119868119911 is moment of inertia 119897119891 and 119897119903 are distance fromfront and rear axle to centre of gravity respectively V isvehicle speed and front tire steer angle 120575119891 is the input 119906to the model Notice that vehicle speed V is assumed alwaysconstant which means the vehicle is not involved with accel-erating and braking Hence only lateral and yaw motions areanalysed

Besides that the bicycle model is also regularly used asdesired or referencemodel to generate the desired response ofthe yaw rate and sideslip angle based on steady state conditionor approximated first order response In designing the controlstrategy based on vehicle active chassis control the linearstate space model in (13) is essential

3 Yaw Stability Control Objectives

A vehicle yaw rate 119903 and sideslip angle 120573 are significantvariables in vehicle yaw stability control system As stated in[32] control objectives of yaw stability control system maybe classified into three categories that is yaw rate controlsideslip control and combination of yaw rate and sideslipcontrol as illustrated in Figure 5

One of the control objectives of yaw stability controlsystem is yaw rate r An ability to control the actual yawrate close to desired response will improve the handling ormanoeuvrability of the vehicle The desired yaw rate whichis generated by reference model should be tracked by thecontroller in order to improve the handling performance asmentioned in [2 4 13 15 18 27 33 34] In the steady statecondition the desired yaw rate response 119903119889 can be obtainedby using the following equation

119903119889 =V

(119897119891 + 119897119903) + 119896119906119904V2sdot 120575119891 (13)

where stability factor 119896119906119904 is depending on the vehicle param-eters and defined as follows

119896119906119904 =119898(119897119903119862119903 minus 119897119891119862119891)

(119897119891 + 119897119903) 119862119891119862119903

(14)

Another control objective is the vehicle sideslip angle 120573that is the deviation angle between the vehicle longitudinalaxis and longitudinal axis and its motion direction Thecontrol of sideslip angle close to steady state conditionmeanscontrolling the lateral stability of the vehicle For the steadystate condition the desired sideslip is always zero that is120573119889 = 0 as mentioned in [1 6 9 11 17 26 35] Therefore toimprove the vehicle handling and stability performances it

is essential to control both yaw rate and sideslip responsesIn order to achieve these control objectives the proposedcontroller must be able to perform the control task of the yawrate and sideslip tracking control

4 Active Chassis Control

Steering and braking subsystems or actuator are part of thevehicle chassis The active control of yaw stability controlsystem can be realized through active chassis control thatis direct yaw moment control or active steering control orintegrated actives steering and direct yaw moment controlas shown in Figure 6 In direct yaw moment control whichcan be implemented by active braking or active differentialtorque distribution the required yawmoment is generated bythe designed controller that controls the desired yaw rate andsideslip In active steering control the wheel steer angle thatcommanded by the driver is modified by adding correctivesteer angle from the designed controllerThis control strategycan be implemented either using active front steering (AFS)or active rear steering (ARS) or four-wheel active steering(4WAS) control In order to control two variables of the yawrate and sideslip effectively two different controlmechanismsare required Thus related research works on the integrationof two vehicle chassis control that is integrated active steer-ing and direct yaw moment control have been extensivelyconducted recentlyThe review of direct yawmoment controlactive steering control and integrated active steering anddirect yaw moment control are discussed in the followingsubsections

41 Direct YawMoment Control Direct yawmoment controlis one of the prominent methods for yaw stability controlwhere extensive research works using this method have beenconducted with different control strategies and algorithms asreported in [1 3 5 8 9 15ndash18 25 26 30 36] It is recognizedas an effective method to enhance the vehicle lateral stabilityduring critical drivingmanoeuvre by controlling the slip ratioof individual wheel As illustrated in Figure 7 the requiredcorrective yaw moment Δ119872119911 which is generated by thetransverse distribution of braking forces between the vehiclewheels is calculated by the designed controller based on theerror between actual and desired vehicle model that havebeen discussed in Section 2 Another approach of direct yawmoment control is active distribution torque By using anactive differential device as established in [19 20 37 38]the left-right driving torque is distributed by this device togenerate the required corrective yaw moment Δ119872119911

As mentioned in Section 2 direct yaw moment controldesign is based on the linear state space model As describedin (15)119872119911 is considered as control input and front steer angle120575119891119889 is assumed as disturbance

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 120575119891119889 + [

11988731198874]119872119911

6 International Journal of Vehicular Technology

Direct yaw moment control Active steering control Integrated active steering and direct yaw moment control

Active chassis control

Active braking

Active differential AFS ARS 4WAS

Figure 6 Active chassis control

120575fd

120573d

rd ΔMz

120573 r

Desired vehicle model

Actual vehicle model

Controller

Figure 7 Direct yaw moment control [15]

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889 +[

[

0

1

119868119911

]

]

119872119911

(15)

Although direct yaw moment control could enhance thevehicle stability for critical driving conditions it may be lesseffective for emergency braking on split road surface Athigh vehicle speed steady state cornering direct yawmomentcontrol could decrease the yaw rate and increase a burdento the driver To overcome this disadvantage active steeringcontrol is proposed

42 Active Steering Control Active steering control is anotherapproach to improving the vehicle yaw stability especiallyfor steady state driving condition where the lateral tireforce is operated in the linear region Research works ofactive steering control have been continuously conducted inorder to improve the handling and stability performances asreported in [7 13 39ndash42] In general active steering controlcan be divided into three categories that is active frontsteering (AFS) control active rear steering (ARS) controland four-wheel active steering (4WAS) control as shown inFigure 6 As road-vehicle normally has front-wheel steeringAFS control becomes favourite approach among researchersas it can be combined with active braking andor suspensioncontrol In the AFS control diagram as shown in Figure 8 the

front wheel steers angle is a sumof steer angle commanded bythe driver 120575119891119889 and a corrective steer angle 120575119888 generated by thecontroller This corrective steer angle is computed based onyaw rate and sideslip tracking errors 1198901 and 1198902 as implementedin [6 43ndash47]

For control design and analysis of AFS control the linearstate state spacemodel as described in (16) is used Noted thatthis equation is similar to equation (12) but the front wheelsteer angle 120575119891 = 120575119891119889 + 120575119888

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

(120575119891119889 + 120575119888)

(16)

On the other hand ARS control is used to improve thevehicle response for low speed cornering manoeuvres withthe input to the control system being the rear steering angle120575119903 In order to enhance the manoeuvrability at low speedand the handling stability at high speed combination of AFScontrol and ARS called 4WAS control has been proposed asimplemented in [24 48 49] By implementing 4WAS controlthe lateral and yaw motion can be controlled simultaneouslyusing two independent control inputs Noting that frontwheel steer angle 120575119891 and rear wheel steer angle 120575119903 with therear axles of rear tire cornering stiffness119862119903 and distance fromrear axle to centre of gravity 119897119903 are taken into account in theinput matric

International Journal of Vehicular Technology 7

ControllerDesired vehicle model

Actual vehicle model 120575fd

120573d

rd 120575c 120575fd + 120575c 120573 re1 120573 minus 120573

d

=e2 r minus rd

Figure 8 Active front steering control [45]

ControllerDesired vehicle model

Actual vehicle model

120575fd

120573d

rd120575c

120575fd + 120575c

120573 r

ΔMz

e1 120573 minus 120573d

=e2 r minus rd

Figure 9 Integrated active front steering-direct yaw moment control [53]

43 Integrated Active Chassis Control The integrated activechassis control has become a popular research topic in vehicledynamics control as discussed in [50] Vehicle dynamicscontrol can be greatly achieved by integrating the activechassis control of active steering active braking and activesuspension or active stabiliser as implemented in [12 23 5152] Since road-vehicle is usually equipped with front-wheelsteering and braking system an integration and coordinationof active front steering and direct yaw moment control arethe favourite approaches to achieving the objectives of yawrate and sideslip control as reported in [2 10 11 27 28 53ndash59] In this approach the corrective front wheel steers angle120575119888 and corrective yaw moment Δ119872119911 are considered as twoindependent control inputs to the vehicle as illustrated inFigure 9

For controller analysis and design of integrated activefront steering-direct yaw moment control the linear statespace model used is describe as follows

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V0

119862119891119897119891

119868119911

1

119868119911

]]]]

]

[120575119888

Δ119872119911] +

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889

(17)

The principle of active chassis control of steering and brakingfor yaw stability control has been discussed From theabove discussion the differences advantages and disad-vantages of each active chassis control can be digested astabulated in Table 2 From this table it can be observed

that by implementing integrated active front steering-directyaw moment control the lateral and yaw motions can becontrolled simultaneously using two independent controlinputs from two different actuators that is steering andbraking Thus this approach could enhance the vehicle yawstability where the yaw rate and sideslip can be controlledeffectively in emergency manoeuvres and the steady statedriving condition

As a conclusion active chassis control is essential foractive yaw stability control system Therefore to achieve theyaw stability control objectives the control strategies for yawrate and sideslip tracking control are developed based on thisactive chassis control The following section will review anddiscuss the control strategies and algorithms that have beendeveloped in the past

5 Yaw Stability Control Strategies

From the literature various control strategies have beenexplored and utilized based on particular algorithm for activeyaw stability control such as classical PID controller in [1]LMI based and static state feedback control in [2 8 33]119867infincontrol theory in [4 13 25] sliding mode control (SMC) in[1 7 23 24 35 38 53] optimal guaranteed cost coordinationcontroller (OGCC) in [10] adaptive based control in [11]mixed-sensitivity minimization control techniques in [16]classical controllers PI in [49 60] internal model control(IMC) in [37] quantitative feedback theory (QFT) in [45]and 120583-synthesis control in [48] Besides that a combinationor integration of different two control schemes to ensurethe robustness of yaw stability control has been exploredsuch as SMC and backstepping method in [3] SMC andFuzzy Logic Control in [12] and LQR with SMC in [17] Asdiscussed in [20] the IMC and SMC algorithms are designed

8 International Journal of Vehicular Technology

Table2Ty

peso

factivec

hassiscontrol

Vehicle

actuator

Activ

echassiscontrol

Advantages

Disa

dvantages

Brakes

Dire

ctyawmom

entcon

trol

(DYC

)Ac

tiveb

raking

activ

edifferentia

l(i)

Effectiv

efor

criticald

rivingcond

ition

(ii)G

oodforsideslip

wheelslipcontrol

(i)Lesseffectiv

efor

brakingon

split

road

surfa

ce(ii)D

ecreasey

awratedu

ringste

adysta

tedrivingcond

ition

(iii)Ac

tived

ifferentia

lneedextrad

evices

Steerin

gAc

tives

teeringcontrol

(ASC

)

Activ

efront

steering(A

FS)

control

(i)Eff

ectiv

efor

steadysta

tedrivingcond

ition

(ii)E

asetointegratew

ithbrakingcontrol

(iii)Goo

dfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Activ

erearsteering(A

RS)

control

(i)Re

arwheelste

eranglec

anbe

controlled

(ii)G

oodfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

4wheelsa

ctives

teering

(4WAS)

control

(i)Tw

odifferent

steer

inpu

ts(ii)G

ooffor

yawratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Steerin

gandbrake

Integrated

AFS

-DYC

control

(i)Tw

odifferent

inpu

tsfro

mtwodifferent

actuator

(steeringandbraking)

(ii)G

oodfory

awrateandsid

eslip

control

Effectiv

efor

criticaland

steadysta

tedrivingcond

ition

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 5: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

International Journal of Vehicular Technology 5

Control objectives

Yaw rate Side slip Yaw rate and side slip

Figure 5 Yaw stability control objectives

mass 119868119911 is moment of inertia 119897119891 and 119897119903 are distance fromfront and rear axle to centre of gravity respectively V isvehicle speed and front tire steer angle 120575119891 is the input 119906to the model Notice that vehicle speed V is assumed alwaysconstant which means the vehicle is not involved with accel-erating and braking Hence only lateral and yaw motions areanalysed

Besides that the bicycle model is also regularly used asdesired or referencemodel to generate the desired response ofthe yaw rate and sideslip angle based on steady state conditionor approximated first order response In designing the controlstrategy based on vehicle active chassis control the linearstate space model in (13) is essential

3 Yaw Stability Control Objectives

A vehicle yaw rate 119903 and sideslip angle 120573 are significantvariables in vehicle yaw stability control system As stated in[32] control objectives of yaw stability control system maybe classified into three categories that is yaw rate controlsideslip control and combination of yaw rate and sideslipcontrol as illustrated in Figure 5

One of the control objectives of yaw stability controlsystem is yaw rate r An ability to control the actual yawrate close to desired response will improve the handling ormanoeuvrability of the vehicle The desired yaw rate whichis generated by reference model should be tracked by thecontroller in order to improve the handling performance asmentioned in [2 4 13 15 18 27 33 34] In the steady statecondition the desired yaw rate response 119903119889 can be obtainedby using the following equation

119903119889 =V

(119897119891 + 119897119903) + 119896119906119904V2sdot 120575119891 (13)

where stability factor 119896119906119904 is depending on the vehicle param-eters and defined as follows

119896119906119904 =119898(119897119903119862119903 minus 119897119891119862119891)

(119897119891 + 119897119903) 119862119891119862119903

(14)

Another control objective is the vehicle sideslip angle 120573that is the deviation angle between the vehicle longitudinalaxis and longitudinal axis and its motion direction Thecontrol of sideslip angle close to steady state conditionmeanscontrolling the lateral stability of the vehicle For the steadystate condition the desired sideslip is always zero that is120573119889 = 0 as mentioned in [1 6 9 11 17 26 35] Therefore toimprove the vehicle handling and stability performances it

is essential to control both yaw rate and sideslip responsesIn order to achieve these control objectives the proposedcontroller must be able to perform the control task of the yawrate and sideslip tracking control

4 Active Chassis Control

Steering and braking subsystems or actuator are part of thevehicle chassis The active control of yaw stability controlsystem can be realized through active chassis control thatis direct yaw moment control or active steering control orintegrated actives steering and direct yaw moment controlas shown in Figure 6 In direct yaw moment control whichcan be implemented by active braking or active differentialtorque distribution the required yawmoment is generated bythe designed controller that controls the desired yaw rate andsideslip In active steering control the wheel steer angle thatcommanded by the driver is modified by adding correctivesteer angle from the designed controllerThis control strategycan be implemented either using active front steering (AFS)or active rear steering (ARS) or four-wheel active steering(4WAS) control In order to control two variables of the yawrate and sideslip effectively two different controlmechanismsare required Thus related research works on the integrationof two vehicle chassis control that is integrated active steer-ing and direct yaw moment control have been extensivelyconducted recentlyThe review of direct yawmoment controlactive steering control and integrated active steering anddirect yaw moment control are discussed in the followingsubsections

41 Direct YawMoment Control Direct yawmoment controlis one of the prominent methods for yaw stability controlwhere extensive research works using this method have beenconducted with different control strategies and algorithms asreported in [1 3 5 8 9 15ndash18 25 26 30 36] It is recognizedas an effective method to enhance the vehicle lateral stabilityduring critical drivingmanoeuvre by controlling the slip ratioof individual wheel As illustrated in Figure 7 the requiredcorrective yaw moment Δ119872119911 which is generated by thetransverse distribution of braking forces between the vehiclewheels is calculated by the designed controller based on theerror between actual and desired vehicle model that havebeen discussed in Section 2 Another approach of direct yawmoment control is active distribution torque By using anactive differential device as established in [19 20 37 38]the left-right driving torque is distributed by this device togenerate the required corrective yaw moment Δ119872119911

As mentioned in Section 2 direct yaw moment controldesign is based on the linear state space model As describedin (15)119872119911 is considered as control input and front steer angle120575119891119889 is assumed as disturbance

[120573

119903] = [

11988611 1198861211988621 11988622

] [120573

119903] + [

11988711198872] 120575119891119889 + [

11988731198874]119872119911

6 International Journal of Vehicular Technology

Direct yaw moment control Active steering control Integrated active steering and direct yaw moment control

Active chassis control

Active braking

Active differential AFS ARS 4WAS

Figure 6 Active chassis control

120575fd

120573d

rd ΔMz

120573 r

Desired vehicle model

Actual vehicle model

Controller

Figure 7 Direct yaw moment control [15]

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889 +[

[

0

1

119868119911

]

]

119872119911

(15)

Although direct yaw moment control could enhance thevehicle stability for critical driving conditions it may be lesseffective for emergency braking on split road surface Athigh vehicle speed steady state cornering direct yawmomentcontrol could decrease the yaw rate and increase a burdento the driver To overcome this disadvantage active steeringcontrol is proposed

42 Active Steering Control Active steering control is anotherapproach to improving the vehicle yaw stability especiallyfor steady state driving condition where the lateral tireforce is operated in the linear region Research works ofactive steering control have been continuously conducted inorder to improve the handling and stability performances asreported in [7 13 39ndash42] In general active steering controlcan be divided into three categories that is active frontsteering (AFS) control active rear steering (ARS) controland four-wheel active steering (4WAS) control as shown inFigure 6 As road-vehicle normally has front-wheel steeringAFS control becomes favourite approach among researchersas it can be combined with active braking andor suspensioncontrol In the AFS control diagram as shown in Figure 8 the

front wheel steers angle is a sumof steer angle commanded bythe driver 120575119891119889 and a corrective steer angle 120575119888 generated by thecontroller This corrective steer angle is computed based onyaw rate and sideslip tracking errors 1198901 and 1198902 as implementedin [6 43ndash47]

For control design and analysis of AFS control the linearstate state spacemodel as described in (16) is used Noted thatthis equation is similar to equation (12) but the front wheelsteer angle 120575119891 = 120575119891119889 + 120575119888

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

(120575119891119889 + 120575119888)

(16)

On the other hand ARS control is used to improve thevehicle response for low speed cornering manoeuvres withthe input to the control system being the rear steering angle120575119903 In order to enhance the manoeuvrability at low speedand the handling stability at high speed combination of AFScontrol and ARS called 4WAS control has been proposed asimplemented in [24 48 49] By implementing 4WAS controlthe lateral and yaw motion can be controlled simultaneouslyusing two independent control inputs Noting that frontwheel steer angle 120575119891 and rear wheel steer angle 120575119903 with therear axles of rear tire cornering stiffness119862119903 and distance fromrear axle to centre of gravity 119897119903 are taken into account in theinput matric

International Journal of Vehicular Technology 7

ControllerDesired vehicle model

Actual vehicle model 120575fd

120573d

rd 120575c 120575fd + 120575c 120573 re1 120573 minus 120573

d

=e2 r minus rd

Figure 8 Active front steering control [45]

ControllerDesired vehicle model

Actual vehicle model

120575fd

120573d

rd120575c

120575fd + 120575c

120573 r

ΔMz

e1 120573 minus 120573d

=e2 r minus rd

Figure 9 Integrated active front steering-direct yaw moment control [53]

43 Integrated Active Chassis Control The integrated activechassis control has become a popular research topic in vehicledynamics control as discussed in [50] Vehicle dynamicscontrol can be greatly achieved by integrating the activechassis control of active steering active braking and activesuspension or active stabiliser as implemented in [12 23 5152] Since road-vehicle is usually equipped with front-wheelsteering and braking system an integration and coordinationof active front steering and direct yaw moment control arethe favourite approaches to achieving the objectives of yawrate and sideslip control as reported in [2 10 11 27 28 53ndash59] In this approach the corrective front wheel steers angle120575119888 and corrective yaw moment Δ119872119911 are considered as twoindependent control inputs to the vehicle as illustrated inFigure 9

For controller analysis and design of integrated activefront steering-direct yaw moment control the linear statespace model used is describe as follows

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V0

119862119891119897119891

119868119911

1

119868119911

]]]]

]

[120575119888

Δ119872119911] +

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889

(17)

The principle of active chassis control of steering and brakingfor yaw stability control has been discussed From theabove discussion the differences advantages and disad-vantages of each active chassis control can be digested astabulated in Table 2 From this table it can be observed

that by implementing integrated active front steering-directyaw moment control the lateral and yaw motions can becontrolled simultaneously using two independent controlinputs from two different actuators that is steering andbraking Thus this approach could enhance the vehicle yawstability where the yaw rate and sideslip can be controlledeffectively in emergency manoeuvres and the steady statedriving condition

As a conclusion active chassis control is essential foractive yaw stability control system Therefore to achieve theyaw stability control objectives the control strategies for yawrate and sideslip tracking control are developed based on thisactive chassis control The following section will review anddiscuss the control strategies and algorithms that have beendeveloped in the past

5 Yaw Stability Control Strategies

From the literature various control strategies have beenexplored and utilized based on particular algorithm for activeyaw stability control such as classical PID controller in [1]LMI based and static state feedback control in [2 8 33]119867infincontrol theory in [4 13 25] sliding mode control (SMC) in[1 7 23 24 35 38 53] optimal guaranteed cost coordinationcontroller (OGCC) in [10] adaptive based control in [11]mixed-sensitivity minimization control techniques in [16]classical controllers PI in [49 60] internal model control(IMC) in [37] quantitative feedback theory (QFT) in [45]and 120583-synthesis control in [48] Besides that a combinationor integration of different two control schemes to ensurethe robustness of yaw stability control has been exploredsuch as SMC and backstepping method in [3] SMC andFuzzy Logic Control in [12] and LQR with SMC in [17] Asdiscussed in [20] the IMC and SMC algorithms are designed

8 International Journal of Vehicular Technology

Table2Ty

peso

factivec

hassiscontrol

Vehicle

actuator

Activ

echassiscontrol

Advantages

Disa

dvantages

Brakes

Dire

ctyawmom

entcon

trol

(DYC

)Ac

tiveb

raking

activ

edifferentia

l(i)

Effectiv

efor

criticald

rivingcond

ition

(ii)G

oodforsideslip

wheelslipcontrol

(i)Lesseffectiv

efor

brakingon

split

road

surfa

ce(ii)D

ecreasey

awratedu

ringste

adysta

tedrivingcond

ition

(iii)Ac

tived

ifferentia

lneedextrad

evices

Steerin

gAc

tives

teeringcontrol

(ASC

)

Activ

efront

steering(A

FS)

control

(i)Eff

ectiv

efor

steadysta

tedrivingcond

ition

(ii)E

asetointegratew

ithbrakingcontrol

(iii)Goo

dfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Activ

erearsteering(A

RS)

control

(i)Re

arwheelste

eranglec

anbe

controlled

(ii)G

oodfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

4wheelsa

ctives

teering

(4WAS)

control

(i)Tw

odifferent

steer

inpu

ts(ii)G

ooffor

yawratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Steerin

gandbrake

Integrated

AFS

-DYC

control

(i)Tw

odifferent

inpu

tsfro

mtwodifferent

actuator

(steeringandbraking)

(ii)G

oodfory

awrateandsid

eslip

control

Effectiv

efor

criticaland

steadysta

tedrivingcond

ition

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 6: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

6 International Journal of Vehicular Technology

Direct yaw moment control Active steering control Integrated active steering and direct yaw moment control

Active chassis control

Active braking

Active differential AFS ARS 4WAS

Figure 6 Active chassis control

120575fd

120573d

rd ΔMz

120573 r

Desired vehicle model

Actual vehicle model

Controller

Figure 7 Direct yaw moment control [15]

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889 +[

[

0

1

119868119911

]

]

119872119911

(15)

Although direct yaw moment control could enhance thevehicle stability for critical driving conditions it may be lesseffective for emergency braking on split road surface Athigh vehicle speed steady state cornering direct yawmomentcontrol could decrease the yaw rate and increase a burdento the driver To overcome this disadvantage active steeringcontrol is proposed

42 Active Steering Control Active steering control is anotherapproach to improving the vehicle yaw stability especiallyfor steady state driving condition where the lateral tireforce is operated in the linear region Research works ofactive steering control have been continuously conducted inorder to improve the handling and stability performances asreported in [7 13 39ndash42] In general active steering controlcan be divided into three categories that is active frontsteering (AFS) control active rear steering (ARS) controland four-wheel active steering (4WAS) control as shown inFigure 6 As road-vehicle normally has front-wheel steeringAFS control becomes favourite approach among researchersas it can be combined with active braking andor suspensioncontrol In the AFS control diagram as shown in Figure 8 the

front wheel steers angle is a sumof steer angle commanded bythe driver 120575119891119889 and a corrective steer angle 120575119888 generated by thecontroller This corrective steer angle is computed based onyaw rate and sideslip tracking errors 1198901 and 1198902 as implementedin [6 43ndash47]

For control design and analysis of AFS control the linearstate state spacemodel as described in (16) is used Noted thatthis equation is similar to equation (12) but the front wheelsteer angle 120575119891 = 120575119891119889 + 120575119888

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

(120575119891119889 + 120575119888)

(16)

On the other hand ARS control is used to improve thevehicle response for low speed cornering manoeuvres withthe input to the control system being the rear steering angle120575119903 In order to enhance the manoeuvrability at low speedand the handling stability at high speed combination of AFScontrol and ARS called 4WAS control has been proposed asimplemented in [24 48 49] By implementing 4WAS controlthe lateral and yaw motion can be controlled simultaneouslyusing two independent control inputs Noting that frontwheel steer angle 120575119891 and rear wheel steer angle 120575119903 with therear axles of rear tire cornering stiffness119862119903 and distance fromrear axle to centre of gravity 119897119903 are taken into account in theinput matric

International Journal of Vehicular Technology 7

ControllerDesired vehicle model

Actual vehicle model 120575fd

120573d

rd 120575c 120575fd + 120575c 120573 re1 120573 minus 120573

d

=e2 r minus rd

Figure 8 Active front steering control [45]

ControllerDesired vehicle model

Actual vehicle model

120575fd

120573d

rd120575c

120575fd + 120575c

120573 r

ΔMz

e1 120573 minus 120573d

=e2 r minus rd

Figure 9 Integrated active front steering-direct yaw moment control [53]

43 Integrated Active Chassis Control The integrated activechassis control has become a popular research topic in vehicledynamics control as discussed in [50] Vehicle dynamicscontrol can be greatly achieved by integrating the activechassis control of active steering active braking and activesuspension or active stabiliser as implemented in [12 23 5152] Since road-vehicle is usually equipped with front-wheelsteering and braking system an integration and coordinationof active front steering and direct yaw moment control arethe favourite approaches to achieving the objectives of yawrate and sideslip control as reported in [2 10 11 27 28 53ndash59] In this approach the corrective front wheel steers angle120575119888 and corrective yaw moment Δ119872119911 are considered as twoindependent control inputs to the vehicle as illustrated inFigure 9

For controller analysis and design of integrated activefront steering-direct yaw moment control the linear statespace model used is describe as follows

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V0

119862119891119897119891

119868119911

1

119868119911

]]]]

]

[120575119888

Δ119872119911] +

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889

(17)

The principle of active chassis control of steering and brakingfor yaw stability control has been discussed From theabove discussion the differences advantages and disad-vantages of each active chassis control can be digested astabulated in Table 2 From this table it can be observed

that by implementing integrated active front steering-directyaw moment control the lateral and yaw motions can becontrolled simultaneously using two independent controlinputs from two different actuators that is steering andbraking Thus this approach could enhance the vehicle yawstability where the yaw rate and sideslip can be controlledeffectively in emergency manoeuvres and the steady statedriving condition

As a conclusion active chassis control is essential foractive yaw stability control system Therefore to achieve theyaw stability control objectives the control strategies for yawrate and sideslip tracking control are developed based on thisactive chassis control The following section will review anddiscuss the control strategies and algorithms that have beendeveloped in the past

5 Yaw Stability Control Strategies

From the literature various control strategies have beenexplored and utilized based on particular algorithm for activeyaw stability control such as classical PID controller in [1]LMI based and static state feedback control in [2 8 33]119867infincontrol theory in [4 13 25] sliding mode control (SMC) in[1 7 23 24 35 38 53] optimal guaranteed cost coordinationcontroller (OGCC) in [10] adaptive based control in [11]mixed-sensitivity minimization control techniques in [16]classical controllers PI in [49 60] internal model control(IMC) in [37] quantitative feedback theory (QFT) in [45]and 120583-synthesis control in [48] Besides that a combinationor integration of different two control schemes to ensurethe robustness of yaw stability control has been exploredsuch as SMC and backstepping method in [3] SMC andFuzzy Logic Control in [12] and LQR with SMC in [17] Asdiscussed in [20] the IMC and SMC algorithms are designed

8 International Journal of Vehicular Technology

Table2Ty

peso

factivec

hassiscontrol

Vehicle

actuator

Activ

echassiscontrol

Advantages

Disa

dvantages

Brakes

Dire

ctyawmom

entcon

trol

(DYC

)Ac

tiveb

raking

activ

edifferentia

l(i)

Effectiv

efor

criticald

rivingcond

ition

(ii)G

oodforsideslip

wheelslipcontrol

(i)Lesseffectiv

efor

brakingon

split

road

surfa

ce(ii)D

ecreasey

awratedu

ringste

adysta

tedrivingcond

ition

(iii)Ac

tived

ifferentia

lneedextrad

evices

Steerin

gAc

tives

teeringcontrol

(ASC

)

Activ

efront

steering(A

FS)

control

(i)Eff

ectiv

efor

steadysta

tedrivingcond

ition

(ii)E

asetointegratew

ithbrakingcontrol

(iii)Goo

dfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Activ

erearsteering(A

RS)

control

(i)Re

arwheelste

eranglec

anbe

controlled

(ii)G

oodfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

4wheelsa

ctives

teering

(4WAS)

control

(i)Tw

odifferent

steer

inpu

ts(ii)G

ooffor

yawratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Steerin

gandbrake

Integrated

AFS

-DYC

control

(i)Tw

odifferent

inpu

tsfro

mtwodifferent

actuator

(steeringandbraking)

(ii)G

oodfory

awrateandsid

eslip

control

Effectiv

efor

criticaland

steadysta

tedrivingcond

ition

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 7: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

International Journal of Vehicular Technology 7

ControllerDesired vehicle model

Actual vehicle model 120575fd

120573d

rd 120575c 120575fd + 120575c 120573 re1 120573 minus 120573

d

=e2 r minus rd

Figure 8 Active front steering control [45]

ControllerDesired vehicle model

Actual vehicle model

120575fd

120573d

rd120575c

120575fd + 120575c

120573 r

ΔMz

e1 120573 minus 120573d

=e2 r minus rd

Figure 9 Integrated active front steering-direct yaw moment control [53]

43 Integrated Active Chassis Control The integrated activechassis control has become a popular research topic in vehicledynamics control as discussed in [50] Vehicle dynamicscontrol can be greatly achieved by integrating the activechassis control of active steering active braking and activesuspension or active stabiliser as implemented in [12 23 5152] Since road-vehicle is usually equipped with front-wheelsteering and braking system an integration and coordinationof active front steering and direct yaw moment control arethe favourite approaches to achieving the objectives of yawrate and sideslip control as reported in [2 10 11 27 28 53ndash59] In this approach the corrective front wheel steers angle120575119888 and corrective yaw moment Δ119872119911 are considered as twoindependent control inputs to the vehicle as illustrated inFigure 9

For controller analysis and design of integrated activefront steering-direct yaw moment control the linear statespace model used is describe as follows

[120573

119903] =

[[[[

[

minus119862119891 minus 119862119903

119898Vminus1 +

119862119903119897119903 minus 119862119891119897119891

119898V2

119862119903119897119903 minus 119862119891119897119891

119868119911

minus1198621198911198972119891 minus 119862119903119897

2119903

119868119911V

]]]]

]

[120573

119903]

+

[[[[

[

119862119891

119898V0

119862119891119897119891

119868119911

1

119868119911

]]]]

]

[120575119888

Δ119872119911] +

[[[[

[

119862119891

119898V119862119891119897119891

119868119911

]]]]

]

120575119891119889

(17)

The principle of active chassis control of steering and brakingfor yaw stability control has been discussed From theabove discussion the differences advantages and disad-vantages of each active chassis control can be digested astabulated in Table 2 From this table it can be observed

that by implementing integrated active front steering-directyaw moment control the lateral and yaw motions can becontrolled simultaneously using two independent controlinputs from two different actuators that is steering andbraking Thus this approach could enhance the vehicle yawstability where the yaw rate and sideslip can be controlledeffectively in emergency manoeuvres and the steady statedriving condition

As a conclusion active chassis control is essential foractive yaw stability control system Therefore to achieve theyaw stability control objectives the control strategies for yawrate and sideslip tracking control are developed based on thisactive chassis control The following section will review anddiscuss the control strategies and algorithms that have beendeveloped in the past

5 Yaw Stability Control Strategies

From the literature various control strategies have beenexplored and utilized based on particular algorithm for activeyaw stability control such as classical PID controller in [1]LMI based and static state feedback control in [2 8 33]119867infincontrol theory in [4 13 25] sliding mode control (SMC) in[1 7 23 24 35 38 53] optimal guaranteed cost coordinationcontroller (OGCC) in [10] adaptive based control in [11]mixed-sensitivity minimization control techniques in [16]classical controllers PI in [49 60] internal model control(IMC) in [37] quantitative feedback theory (QFT) in [45]and 120583-synthesis control in [48] Besides that a combinationor integration of different two control schemes to ensurethe robustness of yaw stability control has been exploredsuch as SMC and backstepping method in [3] SMC andFuzzy Logic Control in [12] and LQR with SMC in [17] Asdiscussed in [20] the IMC and SMC algorithms are designed

8 International Journal of Vehicular Technology

Table2Ty

peso

factivec

hassiscontrol

Vehicle

actuator

Activ

echassiscontrol

Advantages

Disa

dvantages

Brakes

Dire

ctyawmom

entcon

trol

(DYC

)Ac

tiveb

raking

activ

edifferentia

l(i)

Effectiv

efor

criticald

rivingcond

ition

(ii)G

oodforsideslip

wheelslipcontrol

(i)Lesseffectiv

efor

brakingon

split

road

surfa

ce(ii)D

ecreasey

awratedu

ringste

adysta

tedrivingcond

ition

(iii)Ac

tived

ifferentia

lneedextrad

evices

Steerin

gAc

tives

teeringcontrol

(ASC

)

Activ

efront

steering(A

FS)

control

(i)Eff

ectiv

efor

steadysta

tedrivingcond

ition

(ii)E

asetointegratew

ithbrakingcontrol

(iii)Goo

dfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Activ

erearsteering(A

RS)

control

(i)Re

arwheelste

eranglec

anbe

controlled

(ii)G

oodfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

4wheelsa

ctives

teering

(4WAS)

control

(i)Tw

odifferent

steer

inpu

ts(ii)G

ooffor

yawratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Steerin

gandbrake

Integrated

AFS

-DYC

control

(i)Tw

odifferent

inpu

tsfro

mtwodifferent

actuator

(steeringandbraking)

(ii)G

oodfory

awrateandsid

eslip

control

Effectiv

efor

criticaland

steadysta

tedrivingcond

ition

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 8: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

8 International Journal of Vehicular Technology

Table2Ty

peso

factivec

hassiscontrol

Vehicle

actuator

Activ

echassiscontrol

Advantages

Disa

dvantages

Brakes

Dire

ctyawmom

entcon

trol

(DYC

)Ac

tiveb

raking

activ

edifferentia

l(i)

Effectiv

efor

criticald

rivingcond

ition

(ii)G

oodforsideslip

wheelslipcontrol

(i)Lesseffectiv

efor

brakingon

split

road

surfa

ce(ii)D

ecreasey

awratedu

ringste

adysta

tedrivingcond

ition

(iii)Ac

tived

ifferentia

lneedextrad

evices

Steerin

gAc

tives

teeringcontrol

(ASC

)

Activ

efront

steering(A

FS)

control

(i)Eff

ectiv

efor

steadysta

tedrivingcond

ition

(ii)E

asetointegratew

ithbrakingcontrol

(iii)Goo

dfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Activ

erearsteering(A

RS)

control

(i)Re

arwheelste

eranglec

anbe

controlled

(ii)G

oodfory

awratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

4wheelsa

ctives

teering

(4WAS)

control

(i)Tw

odifferent

steer

inpu

ts(ii)G

ooffor

yawratecontrol

Lesseffectiv

eduringcriticald

rivingcond

ition

Steerin

gandbrake

Integrated

AFS

-DYC

control

(i)Tw

odifferent

inpu

tsfro

mtwodifferent

actuator

(steeringandbraking)

(ii)G

oodfory

awrateandsid

eslip

control

Effectiv

efor

criticaland

steadysta

tedrivingcond

ition

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 9: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

International Journal of Vehicular Technology 9

for yaw stability control and the controllers performances arecompared and evaluated

The control strategies are designed based on active chassiscontrol as discussed in Section 4 In active braking or activedifferential which operates based on direct yaw momentcontrol (DYC) various robust control strategies have beendesigned As reported in [3] yaw stability control thatconsists of tire force observer and cascade controller that isbased on sliding mode and backstepping control method isdesigned To solve the external disturbance as discussed in[16] the robustness of mixed-sensitivity yaw stability con-troller is guaranteed for external crosswind and emergencymanoeuvres To cater the uncertainty from longitudinal tireforce the controller for wheel slip control is designed usingSMC algorithm for vehicle stability enhancement [17] Asdiscussed in [20] the second order sliding mode (SOSM)and enhanced internal mode control (IMC) are designedas feedback controller to ensure the robustness againstuncertainties and control saturation issues Both controllersrsquoperformances are compared and analysed for yaw controlimprovement based on rear active differential device Besidesthat the sliding mode control algorithm is also utilized todetermine the required yaw moment in order to minimizethe yaw rate error and side-slip angle for vehicle stabilityimprovement [22] To overcome the uncertainties parametersand guarantee robust yaw stability in [25] the control strategythat consists of disturbance observer to estimate feedforwardyaw moment and optimal gain-scheduled 119867infin is designedIn the study of [30] the robust yaw moment controller andvelocity-dependent state feedback controller are matrixed bysolving finite numbers linear matric inequality (LMI) Byusing this approach the designed controller is able to improvethe vehicle handling and lateral stability in the presence ofuncertainty parameters such as vehicle mass moment ofinertia cornering stiffness and variation of road surfaces andalso control saturation due to the physical limits of actuatorand tire forces

In active steering control robust control strategies aredesigned to overcome the uncertainties and external dis-turbance problems In [7] adaptive sliding mode controlis utilized to estimate the upper bounds of time-derivedhyperplane and uncertainties of lateral forces As discussedin [13] feedback 119867infin control is implemented for robuststabilization of yaw motion where speed and road adhesionvariations are considered as uncertainties and disturbanceinput As reported in [49] a proportional active front steeringcontrol and proportional-integral active rear steering controlare designed for four-wheel steering (4WS) vehicle withthe objective to overcome the uncertainties of vehicle massmoment of inertia and front and rear cornering stiffnesscoefficients To ensure a robust stability against system uncer-tainties the automatic path-tracking controller of 4WS vehi-cle based on sliding mode control algorithm is designed [24]In this study the cornering stiffness path radius fluctuationand crosswind disturbance are considered as uncertaintyparameters and external disturbance As reported in [42] themodel reference adaptive nonlinear controllers is proposedfor active steering systems to solve the uncertainties andnonlinearities of tirersquos lateral forces Quantitative feedback

theory (QFT) technique is implemented for robust activefront steering control in order to compensate for the yaw rateresponse in presence of uncertainties parameters and rejectthe disturbances [45] As discussed in [48] robust controllerfor 4WS vehicle is also designed based on 120583-synthesis controlalgorithm which considers the varying parameters inducedby the vehicle during driving conditions as uncertaintieswhile the study in [60] designed the steering control of visionbased autonomous vehicle based on the nested PID controlto ensure the robustness of the steering controller against thespeed variations and uncertainties of vehicle parameters

In integrated active chassis control an appropriate controlscheme is designed to meet the control objectives Studiesin [2 27 33] have designed the control scheme that consistsof reference model based on linear parameter-varying (LPV)formulation and static-state feedback controller with theobjective to ensure the robust performance for integratedactive front steering and active differential braking controlIn these studies tire slip angle longitudinal slips and vehicleforward speeds are represented as uncertainty parametersAs reported in [4] integrated robust model matching chassiscontroller that integrates active rear wheel steering controllongitudinal force compensation and active yaw momentcontrol is designed using 119867infin controller based on linearmatrix inequalities (LMIs) for vehicle handling and lanekeeping performance improvement In integrated active frontsteering-direct yaw moment control an optimal guaranteedcost control (OGCC) technique is utilized in [10] In thisstudy tire cornering stiffness is treated as uncertainty duringvariation of driving conditions As discussed in [11] anadaptive integrated control algorithm based on direct Lya-punovmethod is designed for integrated active front steeringand direct yaw moment control with cornering stiffness isconsidered as a variation parameter to ensure the robustnessof designed controller As reported in [23] sliding modecontroller is utilized for stabilising the forces and momentsin integrated control schemes that coordinated the steeringbraking and stabiliser In this study the integrated controlstructure is composed of a main loop controller and servoloop controller that computes and distributes the stabilizingforcesmoments respectively

From the above discussion these control strategies andalgorithms can be summarized and compared in terms oftheir active chassis control control objective advantagesand disadvantages as tabulated in Table 3 In conclusionan appropriate control strategy must be designed basedon particular algorithm Robust control algorithms such as119867infin SMC IMC OGCC QFT are essential to solve theuncertainties and disturbance problems that influenced theyaw stability control performances It is revealed that thedesigned controllers in the above discussion are able to trackthe desired yaw rate and vehicle sideslip response consideringexternal disturbances and system uncertainty

6 Yaw Stability Control Problems

In the real environments the dynamics of road-vehicle ishighly nonlinear and incorporated with uncertainties Vehi-cle motion with nonlinear tire forces represents a nonlinear

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 10: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

10 International Journal of Vehicular Technology

Table3Yawsta

bilitycontrolalgorith

ms

Con

trolalgorith

ms

Activ

echassiscontrol

Con

trolobjectiv

eAd

vantages

Disa

dvantages

PIDcontroller

DYC

sideslip

Anti-w

ind-up

strategy

toavoidhigh

overshoo

tand

larges

ettling

time

Uncertaintie

sare

notcon

sider

LMIstatic

statefeedback

Integrated

AFS

-actived

ifferentia

lYawrateandsid

eslip

robu

stforu

ncertaintie

sTransie

ntrespon

seim

provem

entisn

otconsider

Transie

ntrespon

seim

provem

entisn

otconsider

119867infin

Integrated

chassis

controlactiv

esteering

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

SMC

DYC

actives

teering

Yawrateandsid

eslip

robu

stforu

ncertaintie

sand

reject

distu

rbance

OGCC

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

s

Adaptiv

eintegratedcontrol

Integrated

AFS

-DYC

Yawrateandsid

eslip

Robu

stforu

ncertaintie

sMixed-sensitivity

minim

ization

control

DYC

Yawrate

Robu

stforu

ncertaintyrejectd

isturbance

PIcontroller

4WAS

Yawrate

Robu

stforu

ncertaintie

s

IMC

DYC

Yawrate

Robu

stforu

ncertainty

QFT

AFS

Yawrate

Robu

stforu

ncertaintie

srejectdistu

rbance

120583synthesis

control

4WAS

Yawrateandsid

eslip

Robu

stforu

ncertainties

SMC-

backste

pping

Yawrateandsid

eslip

Robu

stforn

onlin

earities

Uncertaintie

sare

not

considered

SMC-

FLC

Integrated

steeringbrakeand

suspensio

nYawratesideslip

and

roll

angle

Robu

stforu

ncertaintie

sand

nonlinearities

Transie

ntrespon

seim

provem

entisn

otconsider

SMC-

LQR

DYC

Yawrateandsid

eslip

Robu

stforu

ncertainty

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

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Page 11: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

International Journal of Vehicular Technology 11

system where the tire dynamic exhibit nonlinear character-istics especially during critical driving conditions such asa severe cornering manoeuvre The main problems of yawrate and sideslip tracking control are uncertainties causedfrom variations of dynamics parameters as discussed in theprevious section such as road surface adhesion coefficients[8 13 33 37 45] tire cornering stiffness [2 8 10ndash12 2024 30 48 49] vehicle mass [20 30 38 45 49] vehiclespeed [2 13 45] and moment of inertia [30 49] Besidesthat an external disturbance such as lateral crosswind mayinfluence the tracking control of desired yaw rate andsideslip response as reported in [4 6 13 24] Thereforeappropriate control strategies and algorithms are essentialto overcome these problems as discussed in the previoussection

From the view of control system engineering thetransient response performances of tracking control arevery important However the control strategies and algo-rithms discussed above are not accommodated for transientresponse improvement of the yaw rate and sideslip trackingcontrol in presence of uncertainties and disturbances Thedesigned controllers are only sufficient to track the desiredresponses in the presence of such problems Hence anappropriate control strategy that could improve the transientperformance of robust yaw rate and sideslip tracking controlshould be designed for an active yaw control system whichcan enhance the vehicle handling and stability performances

7 High Performance RobustTracking Controller

In this section a principle of possible robust tracking controlstrategy with high performance that can be implemented foryaw rate and sideslip tracking control is discussed Basedon the literature a sliding mode control with the nonlinearsliding surface can be proposed to improve the transientresponse of the yaw rate and sideslip tracking control inpresence of uncertainties and disturbances

71 SlidingModeControl (SMC) Slidingmode control (SMC)algorithm that had been developed in the two last decades isrecognized as an effective robust controller to cater for thematched and mismatched uncertainties and disturbances forlinear and nonlinear system It is also utilized as an observerfor estimation and identification purpose in engineeringsystem Various applications using SMC are successfullyimplemented as numerous research studies and reports havebeen published In vehicle and automotive studies SMC isone of the prominent control algorithms that is used as arobust control strategy as implemented in [3 17 38 53 61ndash63]

Sliding mode control design consists of two importantsteps that is designing a sliding surface and designing thecontrol law so that the system states are enforced to the slidingsurface The design of sliding surface is very important as itwill determine the dynamics of the system being control Inconventional SMC a linear sliding surface has a disadvantagein improving transient response performance of the system

14

12

1

08

06

04

02

00 2 4 6 8 10 12 14 16 18 20

Time (s)

Lightly damped system fast rise-time and large overshootHeavily damped system sluggish response and small overshootCNF control system varying damping ratio

Out

put r

espo

nse

fast and smooth response

Figure 10 CNF control technique for transient performancesimprovement [75]

due to constant closed loop damping ratio Therefore anonlinear sliding surface that changes a closed loop systemdamping ratio to achieve high performance of transientresponse and at the same time ensure the robustness hasbeen implemented in [64ndash69] In these studies the nonlinearsliding surface is designed based on the composite nonlinearfeedback (CNF) algorithm

72 Nonlinear Sliding Surface Based CNF The concept ofvarying closed loop damping ratio which could improvetransient response for uncertain system is based on com-posite nonlinear feedback (CNF) control technique Thistechnique that has been established in [70ndash74] is developedbased on state feedback law In practice it is desired thatthe control system to obtain fast response time with smallovershoot But in fact most of control schememakes a trade-off between these two transient performance parametersHence the CNF control technique keeps low damping ratioduring transient and varied to high damping ratio as theoutput response closed to the set point as illustrated inFigure 10

In general the design of the CNF control techniqueconsists of linear and nonlinear control law as describe asfollows

119906 = [119906Linear] + [119906Nonlinear]

119906 = [119865119909 + 119866119903] + [120588 (119903 119910) 1198611015840119875 (119909 minus 119909119890)]

(18)

where 119865 is feedback matrix 119866 is a scalar 119861 is input matrix119875 gt 0 is a solution of Lyapunov equation and 120588(119903 119910) is

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

International Journal of

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International Journal of

Page 12: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

12 International Journal of Vehicular Technology

nonlinear function which is not unique and can be chosenfrom the following equations

120588 (119903 119910) = minus 120573119890minus120572(119910minus119903)2

120588 (119903 119910) = minus 120573119890minus120572|119910minus119903|

120588 (119903 119910) = minus120573

1 minus 119890minus1(119890minus(1minus(119910minus119910

0)(119903minus119910

0))2minus 119890minus1)

(19)

Based on tracking error a nonlinear sliding surface adaptedfrom the CNF control law for an active yaw control systemcan be defined as follows

119904 = 119888119879119890 (119905) = [1198881 119868119898] [

1198901 (119905)

1198902 (119905)] (20)

where

1198881 = 119865 minus 120588 (119903 119910) 1198611015840119875 (21)

where 1198901(119905) and 1198902(119905) could represent the yaw rate and sidesliptracking error respectively119861 is an inputmatrix of the systemand 119868119898 is the identity matrix Then the nonlinear slidingsurface stability can be determined using Lyapunov stabilityanalysis and implement in the designed control law of SMC

Based on the above discussion the SMC with nonlinearsliding surface based on CNF technique could achieve highperformance for uncertain systems It could improve thetransient response performance in the presence of uncertain-ties and external disturbances In addition it is found that thiscontrol strategy has not yet been examined for vehicle yawstability control system and should be further investigatedTherefore this control technique has initiated a motivationto implement it for robust yaw rate and sideslip trackingcontrol in active yaw control systems It is expected that thisapproach could improve the vehicle handling and stabilityperformances

8 Controller Evaluations

In order to evaluate the performance of designing controllersimulations of emergency braking and driving manoeuvreswith the nonlinear vehicle model are usually carried outaccording to ISO or SAE standards The pure computersimulations cosimulation with other software or hardware inthe loop simulations (HILS) are the common approaches toconducting the yaw stability test with orwithout drivermodelfor open loop or closed loop analysis respectively

One of the typical emergency braking manoeuvres forvehicle yaw stability test is split-120583 braking as reported in[2 37 60] In this test the step input of brake torque isapplied to the vehicle in forward motion with constant speedon split road surface adhesion coefficient 120583 where one sideof the wheels is on low 120583 and the other sides of the wheelsare on high 120583 or vice versa This test is performed to testthe vehicle straight ahead driving stability Critical drivingmanoeuvres are also another efficient way to test the yawand lateral stability performances A step steer manoeuvrecan be implemented to evaluate the steady state and transient

behavioural response of the vehicle as conducted in [16 5355 63] Similarly the constant speed J-turnmanoeuvre is alsoconducted for such purpose as reported in [5 8 9 15 30 3345] Another type of critical drivingmanoeuvre is lane changemanoeuvre as implemented in [3 5 10 11 15 20 21 23 26 4546 53 55] This manoeuvre can be conducted for open loopsingle lane change or closed loop double lanes change withdriver model lane change on different road conditions lanechange on split-120583 road and lane change with braking effectWith steering angle input is in sinusoidal form the transienthandling behaviour can be evaluated and vehicle yaw andlateral stability can be analysed

Another test manoeuvres that can be implemented foryaw stability control are steer reversal test for transientperformance evaluation [16 19 20] constant speed steeringpad to evaluate the steady state vehicle performance [1920] steering wheel frequency sweep for the bandwidth andresonance peak analysis [20] and also fishhookmanoeuvre asmentioned in [2 25 27] In order to evaluate the yaw stabilitycontrol system performance in the presence of disturbancea crosswind disturbance as reported in [4 6 20 24] isconsidered as external disturbance that can influence thelateral dynamic stability

During critical driving manoeuvres the actual responseof vehiclersquos yaw rate and sideslip is obtained and analysedin presence of uncertainties and external disturbances Byperforming the test manoeuvres as discussed above it canbe concluded that the ability of the designed controller totrack the desired response should be validatedThe responsesare usually compared to uncontrolled vehiclersquos responses andother controllers for their steady state and transient responseperformances

9 Conclusion

This paper has extensively reviewed the elements of yawstability control system In designing yaw stability controllerall these elements that is vehicle models control objectivesactive chassis control and control strategies play an impor-tant role that contributes to the control system performancesFor controller design and evaluation a 2 DOF linear and7 DOF nonlinear vehicle models are essential In order toimprove the handling and stability performances the yaw rateand sideslip tracking control are themain objectives thatmustbe achieved by the design controller To realize an active yawstability control an active chassis control of steering brakingor integration of both chassis could be implemented with anappropriate control strategies and algorithms

In real driving condition the uncertainties and externaldisturbancemay influenced the yaw rate and sideslip trackingcontrol performances Hence the robust control algorithm isnecessary Based on this review it has been concluded thatsliding mode control (SMC) is the best robust controller toaddress these problems From the view of control systemtransient performances are very important for tracking con-trol However an existing SMC configuration does not havecapability to improve this transient performance To addressthis issue a nonlinear sliding surface of SMC is designed

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

Propagation

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Page 13: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

International Journal of Vehicular Technology 13

based on composite nonlinear feedback (CNF) algorithmThis is because the CNF algorithm has been proven inimproving transient performances as discussed above Forfuture works this control strategy will be implemented foryaw stability control system and the transient performancesof yaw rate and sideslip tracking control will be evaluated andcompared with classical SMC and other controllers

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper

Acknowledgments

The authors would like to thank to Ministry of Education ofMalaysia UTeM and UTM for the supports of the studies

References

[1] B Lacroix Z Liu and P Seers ldquoA comparison of two controlmethods for vehicle stability control by direct yaw momentrdquoApplied Mechanics and Materials vol 120 pp 203ndash217 2012

[2] S C Baslamisli I E Kose and G Anlas ldquoHandling stabilityimprovement through robust active front steering and activedifferential controlrdquo Vehicle System Dynamics vol 49 no 5 pp657ndash683 2011

[3] H Zhou andZ Liu ldquoVehicle yaw stability-control systemdesignbased on sliding mode and backstepping control approachrdquoIEEE Transactions on Vehicular Technology vol 59 no 7 pp3674ndash3678 2010

[4] J Wu Q Wang X Wei and H Tang ldquoStudies on improvingvehicle handling and lane keeping performance of closed-loop driver-vehicle system with integrated chassis controlrdquoMathematics and Computers in Simulation vol 80 no 12 pp2297ndash2308 2010

[5] G Tekin and Y S Unlusoy ldquoDesign and simulation of an inte-grated active yaw control system for road vehiclesrdquo InternationalJournal of Vehicle Design vol 52 no 1ndash4 pp 5ndash19 2010

[6] H Ohara and T Murakami ldquoA stability control by active anglecontrol of front-wheel in a vehicle systemrdquo IEEE Transactionson Industrial Electronics vol 55 no 3 pp 1277ndash1285 2008

[7] Y Ikeda ldquoActive steering control of vehicle by sliding modecontrolmdashswitching function design using SDRErdquo inProceedingsof the IEEE International Conference on Control Applications(CCA rsquo10) pp 1660ndash1665 Yokohama Japan September 2010

[8] H Du N Zhang and F Naghdy ldquoVelocity-dependent robustcontrol for improving vehicle lateral dynamicsrdquo TransportationResearch C Emerging Technologies vol 19 no 3 pp 454ndash4682011

[9] B L Boada M J L Boada and V Dıaz ldquoFuzzy-logic appliedto yaw moment control for vehicle stabilityrdquo Vehicle SystemDynamics vol 43 no 10 pp 753ndash770 2005

[10] X Yang Z Wang and W Peng ldquoCoordinated control of AFSand DYC for vehicle handling and stability based on optimalguaranteed cost theoryrdquo Vehicle System Dynamics vol 47 no 1pp 57ndash79 2009

[11] N Ding and S Taheri ldquoAn adaptive integrated algorithm foractive front steering and direct yaw moment control based ondirect Lyapunov methodrdquo Vehicle System Dynamics vol 48 no10 pp 1193ndash1213 2010

[12] S-B Lu Y-N Li S-B Choi L Zheng and M-S SeongldquoIntegrated control onMRvehicle suspension system associatedwith braking and steering controlrdquo Vehicle System Dynamicsvol 49 no 1-2 pp 361ndash380 2011

[13] S Mammar and D Koenig ldquoVehicle handling improvement byactive steeringrdquo Vehicle System Dynamics vol 38 no 3 pp 211ndash242 2002

[14] C Zhao W Xiang and P Richardson ldquoVehicle lateral controland yaw stability control through differential brakingrdquo in Pro-ceedings of the International Symposium on Industrial Electronics(ISIE rsquo06) pp 384ndash389 July 2006

[15] MMirzaei ldquoA new strategy forminimumusage of external yawmoment in vehicle dynamic control systemrdquo TransportationResearch C Emerging Technologies vol 18 no 2 pp 213ndash2242010

[16] V Cerone M Milanese and D Regruto ldquoYaw stability controldesign through a mixed-sensitivity approachrdquo IEEE Transac-tions on Control Systems Technology vol 17 no 5 pp 1096ndash11042009

[17] S Zheng H Tang Z Han and Y Zhang ldquoController designfor vehicle stability enhancementrdquoControl Engineering Practicevol 14 no 12 pp 1413ndash1421 2006

[18] E Esmailzadeh A Goodarzi and G R Vossoughi ldquoOptimalyaw moment control law for improved vehicle handlingrdquoMechatronics vol 13 no 7 pp 659ndash675 2003

[19] M Canale and L Fagiano ldquoComparing rear wheel steeringand rear active differential approaches to vehicle yaw controlrdquoVehicle System Dynamics vol 48 no 5 pp 529ndash546 2010

[20] M Canale L Fagiano A Ferrara and C Vecchio ldquoComparinginternalmodel control and sliding-mode approaches for vehicleyaw controlrdquo IEEE Transactions on Intelligent TransportationSystems vol 10 no 1 pp 31ndash41 2009

[21] S Moon W Cho and K Yi ldquoIntelligent vehicle safety controlstrategy in various driving situationsrdquoVehicle SystemDynamicsvol 48 no 1 pp 537ndash554 2010

[22] S Yim W Cho J Yoon and K Yi ldquoOptimum distribution ofyaw moment for unified chassis control with limitations on theactive front steering anglerdquo International Journal of AutomotiveTechnology vol 11 no 5 pp 665ndash672 2010

[23] D Li S Du and F Yu ldquoIntegrated vehicle chassis control basedon direct yaw moment active steering and active stabiliserrdquoVehicle System Dynamics vol 46 no 1 pp 341ndash351 2008

[24] T Hiraoka O Nishihara and H Kumamoto ldquoAutomatic path-tracking controller of a four-wheel steering vehiclerdquo VehicleSystem Dynamics vol 47 no 10 pp 1205ndash1227 2009

[25] S-H Yon O-S Jo S Yoo J-O Hahn and K I Lee ldquoVehiclelateral stability management using gain-scheduled robust con-trolrdquo Journal of Mechanical Science and Technology vol 20 no11 pp 1898ndash1913 2006

[26] S H Tamaddoni S Taheri and M Ahmadian ldquoOptimalpreview game theory approach to vehicle stability controllerdesignrdquo Vehicle System Dynamics vol 49 no 12 pp 1967ndash19792011

[27] S C Baslamisli I E Kose and G Anlas ldquoGain-scheduledintegrated active steering and differential control for vehiclehandling improvementrdquo Vehicle System Dynamics vol 47 no1 pp 99ndash119 2009

[28] P Falcone H Eric Tseng F Borrelli J Asgari and D HrovatldquoMPC-based yaw and lateral stabilisation via active frontsteering and brakingrdquo Vehicle System Dynamics vol 46 no 1pp 611ndash628 2008

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 14: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

14 International Journal of Vehicular Technology

[29] W Cho J Yoon J Kim J Hur and K Yi ldquoAn investigation intounified chassis control scheme for optimised vehicle stabilityand manoeuvrabilityrdquo Vehicle System Dynamics vol 46 no 1pp 87ndash105 2008

[30] H Du N Zhang and G Dong ldquoStabilizing vehicle lateraldynamics with considerations of parameter uncertainties andcontrol saturation through robust yaw controlrdquo IEEE Transac-tions onVehicular Technology vol 59 no 5 pp 2593ndash2597 2010

[31] Q Li G Shi J Wei and Y Lin ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[32] W J Manning and D A Crolla ldquoA review of yaw rate andsideslip controllers for passenger vehiclesrdquo Transactions of theInstitute of Measurement and Control vol 29 no 2 pp 117ndash1352007

[33] S C Baslamisli I E Kose andG Anlas ldquoDesign of active steer-ing and intelligent braking systems for road vehicle handlingimprovement a robust control approachrdquo in Proceedings of theIEEE International Conference on Control Applications (CCArsquo06) pp 909ndash914 Munich 2006

[34] P Yih and J C Gerdes ldquoModification of vehicle handlingcharacteristics via steer-by-wirerdquo IEEE Transactions on ControlSystems Technology vol 13 no 6 pp 965ndash976 2005

[35] B Kwak and Y Park ldquoRobust vehicle stability controller basedon multiple sliding mode controlrdquo in Proceedings of the SAEWorld Congress SAE 2001-01-10602001 2001

[36] P Raksincharoensak T Mizushima and M Nagai ldquoDirect yawmoment control systembased on driver behaviour recognitionrdquoVehicle System Dynamics vol 46 no 1 pp 911ndash921 2008

[37] M Canale L Fagiano M Milanese and P Borodani ldquoRobustvehicle yaw control using an active differential and IMCtechniquesrdquoControl Engineering Practice vol 15 no 8 pp 923ndash941 2007

[38] M Canale L Fagiano A Ferrara and C Vecchio ldquoVehicleyaw control via second-order sliding-mode techniquerdquo IEEETransactions on Industrial Electronics vol 55 no 11 pp 3908ndash3916 2008

[39] P Falcone F Borrelli J Asgari H E Tseng and D HrovatldquoPredictive active steering control for autonomous vehiclesystemsrdquo IEEE Transactions on Control Systems Technology vol15 no 3 pp 566ndash580 2007

[40] P Falcone F Borrelli H E Tseng J Asgari andDHrovat ldquoLin-ear time-varyingmodel predictive control and its application toactive steering systems stability analysis and experimental val-idationrdquo International Journal of Robust and Nonlinear Controlvol 18 no 8 pp 862ndash875 2008

[41] F Borrelli P Falcone T Keviczky J Asgari and D HrovatldquoMPC-based approach to active steering for autonomousvehicle systemsrdquo International Journal of Vehicle AutonomousSystems vol 3 no 2ndash4 pp 265ndash291 2005

[42] Y Kawaguchi H Eguchi T Fukao and K Osuka ldquoPassivity-based adaptive nonlinear control for active steeringrdquo in Pro-ceedings of the 16th IEEE International Conference on ControlApplications (CCA rsquo07) pp 214ndash219 October 2007

[43] S Singh ldquoDesign of front wheel active steering for improvedvehicle handling and stabilityrdquo in Proceedings of the SAEAutomotiveDynamicsamp Stability Conference SAE 2000-01-16192000

[44] W A H Oraby S M El-Demerdash A M Selim A Faizz andDA Crolla ldquoImprovement of vehicle lateral dynamics by activefront steering controlrdquo in Proceedings of the SAE Automotive

Dynamics Stability amp Controls Conference and Exhibition SAE2004-01-2081 2004

[45] J-Y Zhang J-W Kim K-B Lee and Y-B Kim ldquoDevelopmentof an active front steering (AFS) system with QFT controlrdquoInternational Journal of Automotive Technology vol 9 no 6 pp695ndash702 2008

[46] B Zheng and S Anwar ldquoYaw stability control of a steer-by-wireequipped vehicle via active front wheel steeringrdquoMechatronicsvol 19 no 6 pp 799ndash804 2009

[47] Q Li G Shi and J Wei ldquoYaw stability control using thefuzzy PID controller for active front steeringrdquo High TechnologyLetters vol 16 no 1 pp 94ndash98 2010

[48] G-D Yin N Chen J-X Wang and L-Y Wu ldquoA studyon 120583 -synthesis control for four-wheel steering system toenhance vehicle lateral stabilityrdquo Journal of Dynamic SystemsMeasurement and Control Transactions of the ASME vol 133no 1 Article ID 011002 2011

[49] R Marino S Scalzi and F Cinili ldquoNonlinear PI front and rearsteering control in four wheel steering vehiclesrdquo Vehicle SystemDynamics vol 45 no 12 pp 1149ndash1168 2007

[50] F Yu D-F Li and D A Crolla ldquoIntegrated vehicle dynamicscontrol-state-of-the art reviewrdquo in Proceedings of the IEEEVehicle Power and Propulsion Conference (VPPC rsquo08) pp 835ndash840 Harbin China September 2008

[51] L Fei and D Zhaoxiang ldquoIntegrated control of automotive fourwheel steering and active suspenion systems based on unifrommodelrdquo in Proceedings of the 9th International Conference onElectronic Measurement and Instruments (ICEMI rsquo09) pp 3551ndash3556 Beijing China August 2009

[52] S Zhou L Guo and S Zhang ldquoVehicle yaw stability controland its integration with roll stability controlrdquo in Proceedings ofthe Chinese Control and Decision Conference (CCDC rsquo08) pp3624ndash3629 July 2008

[53] A Hu and F He ldquoVariable structure control for active frontsteering and direct yaw momentrdquo in Proceedings of the 2ndInternational Conference on Artificial Intelligence ManagementScience and Electronic Commerce (AIMSEC rsquo11) pp 3587ndash3590Zhengzhou China August 2011

[54] A Hu and B Lv ldquoStudy on mixed robust control for integratedactive front steering and direct yaw momentrdquo in Proceedingsof the IEEE International Conference on Mechatronics andAutomation (ICMA rsquo10) pp 29ndash33 Xirsquoan China August 2010

[55] Z He and X Ji ldquoNonlinear robust control of integrated vehicledynamicsrdquoVehicle System Dynamics vol 50 no 2 pp 247ndash2802012

[56] C Ahn B Kim and M Lee ldquoModeling and control of an anti-lock brake and steering system for cooperative control on split-mu surfacesrdquo International Journal of Automotive Technologyvol 13 no 4 pp 571ndash581 2012

[57] C Poussot-Vassal O Sename L Dugard and S M SavaresildquoVehicle dynamic stability improvements through gain-scheduled steering and braking controlrdquo Vehicle SystemDynamics vol 49 no 10 pp 1597ndash1621 2011

[58] J Tjooslashnnas and T A Johansen ldquoStabilization of automotivevehicles using active steering and adaptive brake control allo-cationrdquo IEEE Transactions on Control Systems Technology vol18 no 3 pp 545ndash558 2010

[59] C Rengaraj and D Crolla ldquoIntegrated chassis control toimprove vehicle handling dynamics performancerdquo in Proceed-ings of the SAE World Congress and Exhibition SAE 2011-01-0958 April 2011

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 15: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

International Journal of Vehicular Technology 15

[60] RMarino S Scalzi andM Netto ldquoNested PID steering controlfor lane keeping in autonomous vehiclesrdquo Control EngineeringPractice vol 19 no 12 pp 1459ndash1467 2011

[61] T Shim S Chang and S Lee ldquoInvestigation of sliding-surface design on the performance of sliding mode controllerin antilock braking systemsrdquo IEEE Transactions on VehicularTechnology vol 57 no 2 pp 747ndash759 2008

[62] Y M Sam J H S Osman and M R A Ghani ldquoA class ofproportional-integral sliding mode control with application toactive suspension systemrdquo Systems and Control Letters vol 51no 3-4 pp 217ndash223 2004

[63] N Hamzah Y M Sam H Selamat and M K Aripin ldquoGA-based sliding mode controller for yaw stability improvementrdquoin Proceedings of the 9th Asian Control Conference (ASCC rsquo13)Istanbul Turkey 2013

[64] D Fulwani B Bandyopadhyay and L Fridman ldquoNon-linearsliding surface towards high performance robust controlrdquo IETControlTheory and Applications vol 6 no 2 pp 235ndash242 2012

[65] B Bandyopadhyay F Deepak I Postlethwaite and M CTurner ldquoA nonlinear sliding surface to improve performanceof a discrete-time input-delay systemrdquo International Journal ofControl vol 83 no 9 pp 1895ndash1906 2010

[66] B Bandyopadhyay and D Fulwani ldquoA robust tracking con-troller for uncertain MIMO plant using non-linear slidingsurfacerdquo in Proceedings of the IEEE International Conference onIndustrial Technology (ICIT rsquo09) Churchill Australia February2009

[67] B Bandyopadhyay and D Fulwani ldquoHigh-performance track-ing controller for discrete plant using nonlinear sliding surfacerdquoIEEE Transactions on Industrial Electronics vol 56 no 9 pp3628ndash3637 2009

[68] S Mondal and CMahanta ldquoA fast converging robust controllerusing adaptive second order sliding moderdquo ISA Transactionsvol 51 no 6 pp 713ndash721 2012

[69] S Mobayen V Johari Majd and M Sojoodi ldquoAn LMI-basedfinite-time tracker design using nonlinear sliding surfacesrdquoin Proceedings of the 20th Iranian Conference on ElectricalEngineering (ICEE rsquo12) pp 810ndash815 Tehran Iran May 2012

[70] Y He BM Chen andW Lan ldquoOn improving transient perfor-mance in tracking control for a class of nonlinear discrete-timesystems with input saturationrdquo IEEE Transactions on AutomaticControl vol 52 no 7 pp 1307ndash1313 2007

[71] G Cheng K Peng B M Chen and T H Lee ldquoImprovingtransient performance in tracking general references usingcomposite nonlinear feedback control and its application tohigh-speed XY-table positioning mechanismrdquo IEEE Transac-tions on Industrial Electronics vol 54 no 2 pp 1039ndash1051 2007

[72] Y He B M Chen and C Wu ldquoComposite nonlinear controlwith state and measurement feedback for general multivariablesystems with input saturationrdquo Systems and Control Letters vol54 no 5 pp 455ndash469 2005

[73] B M Chen T H Lee K Peng and V VenkataramananldquoComposite nonlinear feedback control for linear systems withinput saturation theory and an applicationrdquo IEEE Transactionson Automatic Control vol 48 no 3 pp 427ndash439 2003

[74] Z Lin M Pachter and S Ban ldquoToward improvement oftracking performancemdashnonlinear feedback for linear systemsrdquoInternational Journal of Control vol 70 no 1 pp 1ndash11 1998

[75] G Cheng B M Chen K Peng and T H Lee ldquoA MATLABtoolkit for composite nonlinear feedback controlmdashimprovingtransient response in tracking controlrdquo Journal of ControlTheory and Applications vol 8 no 3 pp 271ndash279 2010

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Page 16: Review Article A Review of Active Yaw Control System for ...downloads.hindawi.com/archive/2014/437515.pdf · Review Article A Review of Active Yaw Control System for Vehicle Handling

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of