Influence of Fuzzy-PID Controller on Semi-active Suspension System

Performance using Magnetorheological Damper fuzzy Model

Mohammadjavad Zeinalia, Saiful Amri Mazlanb

and Mohd Azizi Abdul Rahmanc

Malaysia-Japan International Institute of Technology, Universiti Teknologi Malaysia,

54100 Kuala Lumpur, Malaysia

ajavad_zeynaly@yahoo.com,

bamri@ic.utm.my,

cazizi.kl@utm.my

Keywords: Semi-active suspension, magnetorheological damper, fuzzy system, fuzzy PID.

Abstract. Semi-active suspension system is a promising device to improve performance of the

suspension system by using optimal controller for magnetorheological damper. The importance of

magnetorheological damper is the capability to control the semi-active suspension system by

adjusting the input current exerted to the coil of wire to produce magnetic field. In this paper, a

fuzzy-PID controller has been applied in a quarter car semi-active suspension system to examine the

performance of the system. The whole suspension system is modelled in Simulink

environment/MATLAB software in which a neuro-fuzzy model of magnetorheological damper is

utilized as a mathematical model of the damper. A disturbance profile is utilized to evaluate

performance of the system. Simulation results show that the proposed semi-active suspension

system has successfully absorbed disturbances much better than PID controller. In addition, the

accuracy of the magnetorheological damper model influences the performance of the semi-active

suspension system.

Introduction

Semi-active suspension system is a kind of suspension systems that outperforms passive

suspension system and consumes lower energy in comparison with active suspension system.

Magnetorheological (MR) damper is an ordinary appliance which is utilized in semi-active

suspension system. There are various designs of MR damper in order to achieve a specific

behaviour of MR damper [1–3]. Enormous studies have been done to investigate a mathematical

model of MR damper. As an example, Jin et al. [4] proposed a nonlinear Blackbox model, Choi et

al. [5] derived a polynomial model for MR damper and governed its inverse model and Schurter and

Roschke [6] presented a fuzzy model to predict and accurate model. In this paper an adaptive

network-based fuzzy inference system (ANFIS) approach [7] is developed to precisely describe the

behaviour of the MR damper and a mathematical model has been proposed to explain the inverse

model of the MR damper.

There are a number of controllers employed in the semi-active suspension system such as hybrid,

skyhook and groundhook controller [8], sliding mode [9] and fuzzy-PID controller with parallel

structure [10]. The aim of this paper is to improve the performance of proposed controller by

implementing an ANFIS model of MR damper. The specifications of both MR damper model and

inverse model are described in the next section. Then, the result of applying fuzzy-PID controller

and the MR damper prediction model is discussed in the results and discussion section.

System modelling

In this section, a two degree of freedom quarter car model is modelled and briefly discussed. In

addition, an ANFIS model of MR damper with three inputs of input current, displacement and

velocity is presented to obtain force as the output. The inverse model of MR damper is a

Applied Mechanics and Materials Vol. 663 (2014) pp 243-247Online available since 2014/Oct/08 at www.scientific.net© (2014) Trans Tech Publications, Switzerlanddoi:10.4028/www.scientific.net/AMM.663.243

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mathematical model which uses the experimental result to obtain the relationship between force and

velocity as the input and current as the output.

Semi-active suspension system

MR damper in semi-active suspension system

produces two different damping forces which are

passive and active. Passive damping force can be

described by multiplying passive damping coefficient

to the relative velocity of MR damper.

The active damping force of MR damper has a

complexity in calculating its value (see Fig. 1). Thus,

the model of the system can be explained as follows:

( ) ( )

( ) ( ) ( )t t ad

t t r t t t ad

Mz k z z c z z F

mz k z z k z z c z z F

= − + − −

= − − − − − +

(1)

where the M and m represent sprung and unsprung

mass, c is passive damping coefficient, Fad is active

damping force, K and Kt represent the stiffness

coefficients of the suspension system and tire, Z is

chassis displacement and Zr and Zt are road and tire

displacements, respectively.

Fig. 1: The physical model of semi-active

suspension system

Adaptive Network-based Fuzzy Inference System (ANFIS)

ANFIS is a prediction method in which both

fuzzy logic and neural networks are combined to

construct the structure [11]. The configuration of

this method is shown in Fig. 2.

Each input is divided into three membership

functions (MFs) which are Bell-shaped MFs.

Then, an if-then rule [12] is utilized to obtain 27

rules. In the last layer, all outputs of the if-then

rules are summed to estimate the value of the

MR damper’s force using experimental result.

Fig. 3 portrays the prediction result, damping

force in terms of peak velocity, of the proposed

ANFIS approach in comparison with

experimental result.

Fig. 2: Proposed ANFIS model’s structure

Inverse model of MR damper

The controller output is force while the MR damper input is current (I). In this section, a

simplified inverse model is presented to produce an appropriate input current for the ANFIS model

by using output of the control strategy. This model utilized damping force and velocity in order to

obtain the current. As can be seen in Fig. 3, the gradient of the graph damping force versus peak

velocity is constant in specific intervals. Therefore, the aim of this section is to realize the gradient

and intersection of the relationship between force divided by velocity ( Fv

) and current (I) and the

general equation can be described as follows: (It is assumed that if 0v = , then 0I = )

244 Automotive Engineering and Mobility Research

( )FI m bv

= + (2)

where m and b represent the gradient and intersection, respectively. These parameters are directly

related to the relative velocity of MR damper. Then, a linear relationship between m, b and relative

velocity is presented in the following equation.

4 67.296646 10 7.48467 10m v− −

= × − × and 3-0.918511401 +1.97494143 10b v

−= × (3)

The regression analysis of the proposed inverse model illustrates that this model has successfully

predicted the current (I). Thus, the above equation is simulated in Simulink environment as an

inverse model of MR damper.

Fig. 3: Damping force versus peak velocity

Fuzzy-PID controller design

An MR damper is used as a controllable shock absorber for controlling the semi-active

suspension system. A fuzzy-PID controller with parallel structure [13] is employed on the basis of a

proposed PID controller [10]. The values of PID gains KP, KI and KD are assumes as 0.13, 0.1 and

0.13, respectively [10]. The schematic of system using fuzzy-PID controller is shown in Fig. 4. This

figure portrays the location of controller, MR damper model and MR damper inverse model.

Xu et al [13] investigated the parameters of fuzzy-PID controller in terms of PID controller

parameters which are defined as follows:

( ),

4 2 max ,

euF F e

c i

ee e

K T te e

ω ω ω

ωω ω

∆∆ ∆

∆

= = ∆− ∆

and ( )4 2max ,

F

F d u e

c F

i e e

TK

T e e

ω ω

ω ω∆

=− ∆

(4)

where e and e∆ are the error and derivative of the error, respectively and u

ω , u

ω∆ , e

ω , and e

ω∆ are

the fuzzy-PID gains as defined in [10,13].

Fig. 4: Schematic of the semi-active suspension system

Applied Mechanics and Materials Vol. 663 245

Results and discussion

The performance of the proposed system has been studied and compared to the result of applied

PID controller and fuzzy-PID controller using a polynomial model. Fig. 5 shows the implemented

road profile as disturbance which consists of +0.02 m and -0.02 m step displacements.

Fig. 5: Schematic of disturbance applied to the system

Fig. 6 depicts the chassis displacement result of utilizing PID and fuzzy-PID controllers. The best

result belongs to fuzzy-PID controller using ANFIS model to estimate the damping force of MR

damper (see Table 1). This figure illustrates the capability of fuzzy-PID controller in improving the

performance of PID controller and the ability of ANFIS method to successfully learn the

relationship between MR damper effective inputs and output. The peak points created after positive

and negative step bumps are because of applying fuzzy systems in fuzzy-PID controller. As can be

seen in Fig. 6 and Table 1, an appropriate design of fuzzy sets can improve the overall performance

of the controller.

Fig. 6: Graph of chassis displacement using different controllers

Table 1: RMS values of chassis displacement using PID and fuzzy-PID controllers

Suspension Parameter Passive PID Fuzzy-PID (Using polynomial

model)

Fuzzy-PID (Using ANFIS

model)

Chassis Displacement

(Root Mean Square (m)) 0.0151 0.0125 0.0038 0.0024

246 Automotive Engineering and Mobility Research

Conclusion

A study on the application of fuzzy-PID controller with parallel structure has been carried out using

an adaptive network-based fuzzy inference system (ANFIS) model to describe the behaviour of

magnetorheological damper. An inverse model of MR damper is presented to prepare a proper input

for MR damper model in terms of controller’s output. The result of chassis displacement

demonstrates the capability of fuzzy-PID controllers with parallel structure to improve the

performance of control strategy in comparison with PID controller. In addition, the result of

utilizing ANFIS method as the model of the MR damper gives better performance in chassis

displacement than using MR damper polynomial model.

References

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Applied Mechanics and Materials Vol. 663 247

Automotive Engineering and Mobility Research 10.4028/www.scientific.net/AMM.663 Influence of Fuzzy-PID Controller on Semi-Active Suspension System Performance Using

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DOI References

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magnetorheological damper using a neuro-fuzzy system, Smart Mater. Struct. 22 (2013) 125013.

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http://dx.doi.org/10.1016/S0005-1098(99)00192-2