research article system identification and embedded controller design for pneumatic ... · 2019. 7....

Research ArticleSystem Identification and Embedded Controller Design forPneumatic Actuator with Stiffness Characteristic

Khairuddin Osman12 Ahmad rsquoAthif Mohd Faudzi23 M F Rahmat2 and Koichi Suzumori4

1 Department of Industrial Electronics Faculty of Electronic and Computer Engineering Universiti Teknikal Malaysia MelakaHang Tuah Jaya 76100 Durian Tunggal Melaka Malaysia

2 Department of Control and Mechatronics Engineering Faculty of Electrical Engineering Universiti Teknologi Malaysia81310 Skudai Johor Bahru Malaysia

3 Centre for Artificial Intelligence and Robotics Universiti Teknologi Malaysia 81310 Skudai Johor Bahru Malaysia4Graduate School of Natural Science and Technology Okayama University Okayama Japan

Correspondence should be addressed to Ahmad rsquoAthif Mohd Faudzi athiffkeutmmy

Received 19 December 2013 Revised 6 March 2014 Accepted 28 March 2014 Published 2 June 2014

Academic Editor ShengJun Wen

Copyright copy 2014 Khairuddin Osman et al This is an open access article distributed under the Creative Commons AttributionLicense which permits unrestricted use distribution and reproduction in any medium provided the original work is properlycited

This paper presents model and controller design applications to pneumatic actuator embedded system Two model strategies ofposition and force are proposed to realize compliance control for stiffness characteristic Model of the pneumatic actuator system(transfer function) is obtained from system identification (SI) method Next combination of predictive functional control withobserver (PFC-O) design is selected as a new control strategy for pneumatic system Performance assessment of the controller isperformed in MATLAB and validated through real-time experiments using national instrument (NI) devices and programmablesystem on chip (PSoC) microcontroller Result shows that the new controller is adapted to the system and able to successfullycontrol both simulation and real-time experiments

1 Introduction

Pneumatic control systems are widely explored in researchand development (RampD) activities by researchers and indus-try as they offer advantages such as easy and simple main-tenance relatively low cost self-cooling properties goodpower density (powerdimension rate) fast acting with highaccelerations and installation flexibility [1] The purpose of apneumatic control system is to solve problems of many non-linear characteristics such as valve dead zone problems massflow rate parameters and compliance variation Howeverpneumatic system is getting more complex intelligent anddifficult to model especially using mathematical calculationfor validation process System identification (SI) is usedto solve system modelling and unknown parameters andlinearizes the system from mathematical model drawbackSystem identification also can obtain the linear mathematicalmodel (transfer function) of the plant system from themeasured experimental data Zadeh presented that there are

a multitude of identification process techniques that canbe utilized [2] The application area of transfer functionhas become widespread to cover areas such as engineeringcomputer science financial sector industrial applicationsand many others [3]

Various researchers proposed modeling and controllerdesign in pneumatic system including system identificationmodel System identification not only can model the plantbut also can realize online identification and control ofpneumatic actuator in a real-time environment [4] Reference[5] presented a method of identification and controlling elec-tropneumatic servo drives via a mixed-reality environment(MRE) To precisely obtain the systemrsquos transfer function canbe difficult for nonlinear systemsThis causes a great difficultyin servopneumatic system modeling and control In order toavoid the complexity associated with nonlinear system mod-eling a MRE is employed to identify the transfer functionof the system using a recursive least squares (RLS) algorithmbased on the autoregressivemoving-average (ARMA)model

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2014 Article ID 271741 13 pageshttpdxdoiorg1011552014271741

2 Mathematical Problems in Engineering

Online system identification can be conducted effectively andefficiently using the proposed method Next the researchrealized online identification of the pneumatic positionalservomechanism necessary to determine the order of thenumerator and denominator of the system transfer [6] Thisresearch briefly describes two main parts that constitutean adaptive control The first part describes the design ofan optimal structure of mathematical model that allowsfor continuous identification The second part describes thedesign of an adaptive state-space controller whereby theadaptive control is implemented Another review on model-ing controller design and implement system identification topneumatic actuator has been proposed by various researchersas presented in [7 8] The implication of this research isto further improve the performance of existing pneumaticactuators

Controller design for pneumatic system to control theposition force compliance viscosity and so forth is a chal-lenging issue for improving its tracking performance Manycontroller designs were proposed to control pneumatic sys-tem such as proportional-integral-derivative (PID) artificialintelligence and robust controller Model predictive control(MPC) is one of the controllers that have been successfullyused in both industry and academia for the control of large-scale installations which are typically described by large-scale models with relatively slow dynamics The key elementin MPC is to repeatedly solve an optimization problembased on available measurements of the current state of theprocess The advantages of MPC over classic PID controlare its ability to steer the process in an optimal approachwhile taking proactively desired future behavior into accountto tackle multiple inputs and outputs simultaneously andto incorporate constraints Among the most popular MPCalgorithms are dynamic matrix control (DMC) model algo-rithm control (MAC) generalized predictive control (GPC)predictive functional control (PFC) and so forth [9] Eachcontroller has their own strategies advantages and theirspecific applications which assured good results UsuallyGPC is widely used in pneumatic systems However thesystem suffers from instability and it is difficult to beimplemented on this research real-time embedded systemIndustrial applications of PFC can be found in the defensesector automotive metallurgical industries miscellaneousprocess (chemical reactors and distillation excluded) andso forth [10] PFC is based on the same approach as allMPC strategies that is prediction of the future outputsand calculation of the manipulated variables for optimalcontrol using a simple algorithm Therefore PFC is alsobased on the same principle which uses an internal modelspecification of a reference trajectory and determination ofthe control law [11] The research is motivated by the PFCrsquoshigh-quality control performance with improved rise timeprecise tracking robust stabilization fast response and analgorithm that is easy to understand for implementation ona real-time embedded system

In recent years interest in exploiting several controllerdesigns on embedded systems has grown Examples ofimplementing the controller design for embedded system andtheir advantage were presented by [9 12 13] The embedded

Valves

Pressure sensor

Optical sensor

PSoC control board

Figure 1 Pneumatic system and its parts

system has been widely applied to manufacturing industryprocessing control communication instrumentation vehi-cle weapon system and so forth In addition the embeddedsystem is referred to as a dedicated computer applicationsystem which can be adapted into some specialized rigorousrequirements to function and power the application systemforward That is to say it can be centered on the engineeringapplication system based on computer technology and itshardware and software can be easily clippedThis allows real-time application by using a chip microprocessor dSPACEPC DSP and so forth In these cases the controller designsare not a supervisory controller anymore but directly steerthe actuators and as such also the process itself [14 15]

The related development of the pneumatic system usedin this research is presented in [16ndash19] Pneumatic systemcan be further divided into two types of actuator specificallywith position accuracy of 0169mm and position accuracyof 001mm The design of actuator with position accuracy of001mm was enhanced from position accuracy of 0169mmfor better performance during experimentation on the appli-cations but the system operation for both actuators is still thesame Design with position accuracy of 001mm will havea new position sensor with higher accuracy new tape typestripe code for better durability and new enhanced circuitdesign and will not have been implemented as yet in anyapplication Figure 1 shows all the parts of the pneumaticactuator at position accuracy of 001mmused in this researchThe actuator has 200mm stroke and can deliver maximumforce up to 120N KOGANEI-ZMAIR optical sensor isused where smaller pitch of 001mm can be detected Thepneumatic system presents the next generation of actuatordevelopment with new features that provide better controlhigher position and speed force accuracy communicationability and all-in-onemechanism for compact system designThe pneumatic actuator is equipped with programmablesystem on chip (PSoC) microcontroller which acts as thebrain for the system and performs the local control to suitthe requirements of any related applications Contractionand extension movements depend on the algorithm todrive the valve using pulse width modulation (PWM) dutycycle In addition the pneumatic actuator is able to analyzeposition force stiffness and viscosity However the existingsystem implements only a simple proportional-integral (PI)

Mathematical Problems in Engineering 3

controller design [16ndash19] Moreover there are other dis-advantages such as slow response time delay overshootissues and stretch-back may not function with lower stiffnessparameters The main contribution of this paper is to modela pneumatic system by using SI Of special importance is thatthe substitute PI controller used and improves the systemwith the new controller algorithm in embedded systemwherethe accuracy in position force and compliance for stiffnesscharacteristics is the main control objective

The rest of this paper is organized as follows In Section 2the model identification technique for this research isdescribed Section 3 describes the control strategy Section 4briefly explains stiffness characteristic Then Section 5describes the embedded controller development More-over Section 6 describes the experimental setup After thatSection 7 presents the analysis of data collection and dis-cussion about system performance Finally conclusions andfuture work are given in Section 8

2 Model Identification

System Identification (SI) technique is proposed to obtainreal-time model of the pneumatic system Two models areproposed position model and force model to realize thestiffness characteristic The plant mathematical models aredeveloped using MATLAB System Identification Toolboxfrom open-loop input-output experimental data Throughexperimental setup the hardware and Personal Computer(PC) communicate using Data Acquisition (DAQ) card overthe MATLAB software During experimental setup data willbe gathered and analyzed to support system identificationmodel and to observe the system dynamic The system iden-tification model will go through model estimation structureselection and validation for three models Good parametersidentification requires the usage of input signals that are richin frequencies There are several methods of generating thesignals such as Pseudo Random Binary Sequence (PRBS)sinusoidal stepmulti-sine and so forth Formodel estimationin position model square wave input signal is used whilepseudorandom binary sequence (PRBS) input signal is usedin force models In this research a lower sampling time of119905119904= 001 s is used It is identified that a smaller sampling time

could improve controller performance andmore samples canalso be taken for system identification process The PWMgenerator is designed to mimic the 8-bit PWMmodules andthe signal amplitude is set to 255 and minus255 on the PSoCmicrocontroller to ease implementation on this platform inthe future

There are few structures of parametric model that canbe used to represent certain system An example are Auto-Regressive with Exogenous Input (ARX) model Auto-RegressiveMovingAverage with Exogenous Input (ARMAX)model Output-Error (OE) model and Box-Jenkins (BJ)model [20] There are also other models that are not men-tioned in this paper The plant model is derived from themeasured input and output signals of a real plant that needs tobe identifiedThe ARX parametric model structure is chosenfor its good result which fulfills the criteria for SI model

after comparison with othermodel structures Assuming thatnoise is zero the following equation can be derived

119910 (119896) + 1198861119910 (119896 minus 1) + sdot sdot sdot + 119886

119899119886119910 (119896 minus 119899119886)

= 1198871119906 (119896 minus 119889) + 119887

2119906 (119896 minus 119889 minus 1)

+ sdot sdot sdot + 119887119899119887119906 (119896 minus 119889 minus 119899119887 + 1)

119884 (119911minus1

)

119880 (119911minus1)= 119911minus119889119861 (119911minus1

)

119860 (119911minus1)

(1)

where 119899119886 ge 119899119887 119889 is time delay 119899119886 is number of poles119899119887 is number of zeros 119906(119896) is input and 119910(119896) is outputA minimum phase model can be obtained using largesampling time whereas the nonminimum phase model canbe obtained using small value sampling time [20] Basicallythe models obtained are limited to second and third orderonly For example ARX model will have different structuresfrom lower degree of 2-2-1 structure to high degree of 3-3-1 Higher-order models may produce unstable output Inthis case the third-order model will represent the nearestmodel of the true plant After suitable model estimationand structure have been selected the next procedure isvalidation Model validation is to check the validity betweenthe measured data and the desired data under a validationrequirement The simplest validity check is by observingconvergence of training errors and assessing the predictionerrors for test data Using part of experimental data that wasnot used and reserved for model validation purposes theacceptance or rejection of certain obtainedmodel can be donebased on the following criteria using Akaikersquos final predictionerror (FPE) [20 21]

FPE = 119881 sdot(1 + 119899

119886119873)

(1 minus 119899119886119873)

(2)

where

119881 =1198902

(119896)

119873=119890119879

(119896) sdot 119890 (119896)

119873

119890 (119896) = [119890119896119890119896minus1

sdot sdot sdot 119890119896minus119873

]119879

(3)

where 119881 is loss function 119899119886is the number of approximated

parameters 119873 is the number of samples and 119890(119896) is errorvector According to Akaike the selection of model fromvarious orders can be done based on the smallest value of FPEor Akaikersquos information criteria (AIC)

AIC = log [119881 (1 +2119899119886

119873)] (4)

Other than FPE or AIC criterion best fitting criteria canalso be used These criterions show the preciseness of theapproximate model as compared to the true model This bestfit criterion is explained by [20 21] wheremodel selectionwillbe based on the highest percentage value

fit = 100 sdot [1 minusnorm (119910 minus 119910)

norm (119910 minus 119910)] (5)

where 119910 is true value 119910 is approximate value and 119910 is meanvalue


minus1 minus08 minus06 minus04 minus02 0 02 04 06 08 1minus1

minus05

0

05

1

Real part

Imag

inar

y pa

rt

Pole and zero

PositionPositionReference

ForceForce

Figure 2 Pole-zero plot for the models

All these processes are done through the System Iden-tification Toolbox in MATLAB The following discrete-timeopen-loop transfer functions for positionmodel shown in (6)and force model shown in (7) were identified for third-ordersystem as follows

119861Position (119911minus1

)

119860Position (119911minus1)

=0001269119911

minus1

+ 00004517119911minus2

minus 00003498119911minus3

1 minus 1932119911minus1+ 109119911

minus2minus 01577119911

minus3

(6)

119861Force (119911minus1

)

119860Force (119911minus1)

=004097119911

minus1

+ 004577119911minus2

+ 001379119911minus3

1 minus 06513119911minus1minus 02287119911


minus3

(7)

The criteria for both model validation processes are stablebecause all the poles of the open-loop discrete transferfunction lie within the unit circle of the z-plane as in Figure 2Based on the smallest values criteria of AIC and FPE bothmodels can be accepted In addition percentage of best fitting(fit) ismore than 90where the balances are losses because ofnonlinear factor such as dead zone friction and air leakage

3 Control Strategy

This research proposed the predictive functional control withobserver (PFC-O) design for pneumatic system The for-mulation of PFC can handle linear and nonlinear processes[10] Observer design is essential in order to estimate thestate of the pneumatic system model A state observer willprovide estimation of the internal state of a given systemfrom measurements of the input and output of the system

31 Predictive Functional Control (PFC) Many literatureapproaches of PFC and other MPC algorithms are designed

based on the state-space (matrix) form of the plantThe state-space form is preferable for several reasons easy generaliza-tion to multivariable systems and easy analysis of the closed-loop properties and allows online computation [10 22] Inthis section the pneumatic model as in (6) or (7) can beconverted into state-space form The PFC algorithm belowwill explain the main algorithm behind the controller Thegeneral state-space model can be written as in (8)

119909119896+1

= 119860119909119896+ 119861119906119896

119910119896= 119862119909119896+ 119863119906119896

(8)

For a prediction with a strictly proper system119863 = [0]

119909119896+2

= 119860119909119896+1

+ 119861119906119896+1

119910119896+2

= 119862119909119896+2

(9)

By substituting (8) into (9) the state-space model is writtenas follows

119909119896+2

= 1198602

119909119896+ 119860119861119906

119896+ 119861119906119896+1

119910119896+2

= 119862119909119896+2

119909119896+3

= 1198602

[119860119909119896+ 119861119906119896] + 119860119861119906

119896+1+ 119861119906119896+2

119910119896+3

= 119862119909119896+3

(10)

This process is simply an iteration of a one-step-ahead pre-diction and repeated substitution results can be generalizedto

119909119896+119899

= 119860119899

119909119896+ 119860119899minus1

119861119906119896+ 119860119899minus2

119861119906119896+1

+ sdot sdot sdot + 119861119906119896+119899minus1

119910119896+119899

= 119862 [119860119899

119909119896+ 119860119899minus1

119861119906119896+ 119860119899minus2

119861119906119896+1


]

(11)

It is clearly seen from (11) that it is possible to convert thestate-space model to state prediction equation

[[[[[[

[

119909119896+1

119909119896+2

119909119896+3

119909119896+119899

]]]]]]

]119909119896

=

=

=

=

[[[[[[

[

119860

1198602

1198603

119860119899

]]]]]]

]119875119909119909

119909119896+

[[[[[[

[

119861 0 0 sdot sdot sdot 0

119860119861 119861 0 sdot sdot sdot 0

1198602

119861 119860119861 119861 sdot sdot sdot 0

0

119860119899minus1

119861 119860119899minus2

119861 119860119899minus3

119861 sdot sdot sdot 119861

]]]]]]

]119867119909119909

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(12)


and output prediction equation

[[[[[[

[

119910119896+1

119910119896+2

119910119896+3

119910119896+119899

]]]]]]

]119910119896

=

=

=

=

[[[[[[

[

119862119860

1198621198602

1198621198603

119862119860119899

]]]]]]

]119875

119909119896

+

[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

119862119860119861 119862119861 0 sdot sdot sdot 0

1198621198602

119861 119862119860119861 119862119861 sdot sdot sdot 0

0

119862119860119899minus1

119861 119862119860119899minus2

119861 119862119860119899minus3

119861 sdot sdot sdot 119862119861

]]]]]]

]119867

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(13)

This can be achieved by introducing the prediction matrices119875 and 119867 Therefore the model used is a linear one that canbe obtained as shown in

119909119896= 119875119909119909119909119896+ 119867119909119909119906119896minus1

119910119896= 119875119909119896+ 119867119906119896minus1

(14)

where119909119896is the statemodel119906

119896is the inputmodel and119910

119896is the

measured output model 119875119909119909119867119909119909 119875 and119867 are matrices and

vectors of the right dimension respectivelyThe starting pointin formulating PFC control law is developing the referencetrajectory equation This can be done by placing the desiredclosed-loop dynamic into the reference trajectory Given theactual set point is 119903 and the loop set point 119908 is a first-orderlag

119908119896+119894119896

= 119903119896minus (119903119896minus 119910119896) 120595119894

(15)

where 119894 is value of 119899 119910119896is the most recent measured output

and Ψ (0 lt Ψ lt 1) is scalar time constant and a tuningparameter setting the desired closed-loop poles Equation(15) is the predictive essence of control strategy Indeed theaim is to have the set point trajectory closely follow thereference desired closed-loop behavior In addition it mustalso deal with the set of coincidence points This can beachieved by using the degree of freedom (DOF) to force theequality of the prediction and the reference trajectory at anumber of points Therefore solving the control moves suchthat

119910119896+119899

= 119908119896+119899

(16)

where 119899 = 1198991 1198992 These equalities are called coincidence

points In usual cases there are nomore than two coincidencepoints In this paper we will only focus on only one coinci-dence point 119899

1 Thus at a single coincidence point and using

(15) and (16) the control law is determined by

119910119896+119899

= 119908119896+119899

= 119903119896minus (119903119896minus 119910119896) 120595119894

(17)

Hence substituting (14) into (17)

119910119896+119899

= 119875119909119896+ 119867119906119896minus1

= 119903119896minus (119903119896minus 119910119896) 120595119894

(18)

Assuming that 119906119896+119894

= 119906119896 thus the control law can be

formulated by rewriting (18) and obtain

119906119896= minus119867

minus1

[119875119909119896+ (119903119896minus (119903119896minus 119910119896) 120595119894

)]

119906119896= minus119870119888119909119896+ 119875119888119903119896

(19)

where119870119888= minus119867

minus1

(119875minusΨ119894

119910119896) and 119875

119888= minus119867

minus1

(1minusΨ119894

) Now theprediction algorithm can easily be recognized from the fixedlinear feedback law Thus the typical posterior stability andsensitivity analysis can be easily achieved in a straightforwardmanner

As stated earlier there is only one coincidence pointAccording to [22] the typical procedurewith one coincidencepoint would be as follows

(1) Choose the desired time constant Ψ(2) Do a search for coincidence horizon 119899

1=

1 2 large and find the associated control lawfor each 119899

1

(3) Select the 1198991 which gives closed-loop dynamics

closest to the chosen Ψ(4) Simulate the proposed law Otherwise reselectΨ and

go to step 2Optimal parameter tuning is an optimization problem whichrequires implementation of global optimization strategy suchas particle swarm optimization (PSO)

32 Observer The model states are not related to physicalparameters In such cases and for the real implementation ofPFC an observer must be designed as the state variable 119909(119896

119894)

at time 119896119894is notmeasurable [23]The function of the observer

is to calculate the future state by using the values of thecurrent output of the plant 119910(119896

119894) and the current value of the

control signal 119906(119896119894) For the system in this study the observer

is designed using the pole-assignment method to calculatethe gain 119870ob The following equation is used to estimate thestate variable 119909(119896

119894) in each time instant

119909 (119896119894+ 1) = 119860119909 (119896

119894) + 119861119906 (119896

119894) + 119870ob (119910 (119896119894) minus 119862119909 (119896119894))

(20)

where 119906(119896119894) at time 119896

119894is as expressed in (19) The closed-loop

observer error equation is

119909 (119896 + 1) = (119860 minus 119870ob119862) 119909 (119896) (21)

where 119909(119896) = 119909(119896) minus 119909(119896) It is important to have alleigenvalues of Amatrix inside the unit circle for the observererror converge to zero Therefore the closed-loop observerpoles are selected to be inside the unit circle which givesthe observer the fast dynamic response required The closed-loop PFC system with state estimate has two independentcharacteristic equations

det (120582119868 minus (119860 minus 119870ob119862)) = 0 (22)

det (120582119868 minus (119860 minus 119861119870PFC)) = 0 (23)


Position model force model(state-space)

Observer design

PFC algorithm

u

Input r

Output positionoutput force X

x

x3

x1x2

Figure 3 Block diagram of PFC-O for plant model

Adding a sufficiently fast observer will not affect theperformance of the PFC controller (22) represents theeigenvalues of the PFC control loop while (23) representsthe eigenvalues of the observer loop This shows that twosets of eigenvalues are independent of each other Hencethe design of the observer will not affect the design of thePFC controller or vice versa The PFC-O design structure isillustrated in Figure 3The plantmodels are obtained by usingsystem identification technique (as discussed in Section 2)

The stability test method for this research is done bytesting the locations of the closed-loop poles The stabilityperformance of the closed-loop feedback system is deter-mined primarily by the location of the poles (eigenvalues) ofthe matrix (119860 minus 119861119870PFC) Since 119860 and 119861 lowast 119870PFC are both 3 by3 matrices there will be 3 poles for the closed-loop systemBy using the MATLAB function eig(119860 minus 119861119870PFC) the desiredpoles for position model and force model are stable becauseall the poles of the closed-loop system liewithin the unit circleof the z-plane

4 Stiffness Characteristic

The relationship between deflection and force is known as thestiffness or can be assumed as a spring rate The greater thestiffness the less the deflection for a given force 119865 and highstiffness springs are hard and low stiffness springs are softWith an ideal spring systemwith spring constant the stiffnesscharacteristic is achieved using compliance control as in

119865 = 119896119904119890 (119896) (24)

where 119865 119896119904 and 119890(119896) represent the force reference coefficient

of stiffness and position error from the optical sensorrespectively

Within its elastic (flexibility) limit the deflection 120575 ofa spring is linearly proportional to the force applied to thatspringThe coil spring phenomena are illustrated in Figure 4Stiffness coefficient of the spring can be calculated as

119865 = 120575119896119904 (25)

When weight119882 is the force exerted on a body by gravity

119865 = 119882 = 119898119892 (26)

Nat

ural

leng

th

F

F

120575

120575

Figure 4 Coil spring illustration

+r

X

OutPc

Kc

minus

Figure 5 PFC controller stage

the deflection is

120575 =119898119892

119896119904

(27)

where free gravitational acceleration 119892 is 98ms2

5 Embedded Controller Development

Before applying to embed algorithm in PSoC programmingall equations need specific data a simple equation andrewriting for easier coding Consider a PFC controller withthe following fundamental matrices

119860 =

[[[[

[

11988611

11988612

11988613

0 1 0

0 0 1

]]]]

]

119861 = [

[

1

0

0

]

]

119862 = [11988811

11988812

11988813]

(28)

where pole is 1 times 3 matrix of constantsFigure 5 shows the controller stage of a PFC controller

from (19) which can be represented by

Out = 119875119888119903 minus 119870119888119883 (29)


where 119903 is reference input 119883 is 3 times 1 matrix representing thesystem states Out is control signal 119875

119888is constant gain and

coincidence horizon and 1198991is 2 while the matrix 119870

119888is given

by

119870119888= [11989611988811

11989611988812

11989611988813] = [(119862119860119861 + 119862119861) (119862119860

2

minus 1198621205952

)]minus1

(30)

where Ψ is a given constant Expanding (29) yields

Out = 119875119888119903 minus [119896

1198881111989611988812

11989611988813] [

[

11990911

11990921

11990931

]

]

= 119875119888119903 minus (119896

1198881111990911+ 1198961198881211990921+ 1198961198881311990931)

(31)

Figure 6 shows the observer stage of a PFC controllerfrom (20) where the output signal of the rightmost summingjunction119872

119901 is represented by

119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= 119870(119884 minus 119862 sdot 119872119901(119896 minus 1)) + 119860119872

119901(119896 minus 1)

(32)

where matrix 119870 as 119870ob and derived using the MATLABfunction119870 = place(1198601015840 1198621015840 pole) yielding

119870 = [11989611

11989612

11989613] (33)

and 119884 and 119883 are the plant output signal and estimated stateoutput respectively The value of119883 is given by

119883 (119896) = [

[

11990911(119896)

11990921(119896)

11990931(119896)

]

]

= 119872119901(119896 minus 1) (34)

The value of119872119901(119896) is obtained by expanding (32) yielding

119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= [11989611

11989612

11989613]

times [

[

119884 (119896) minus 1198881111990111(119896 minus 1)

119884 (119896) minus 1198881211990121(119896 minus 1)

119884 (119896) minus 1198881311990131(119896 minus 1)

]

]

+ [

[

11988611

11988612

11988613

1 0 0

0 1 0

]

]

[

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= (11989611+ 11989612+ 11989613) 119884 (119896)

minus (119896111198881111990111(119896 minus 1) + 119896

121198881211990121(119896 minus 1)

+119896131198881311990131(119896 minus 1))

+ [

[

1198861111990111(119896 minus 1) + 119886

1211990121(119896 minus 1) + 119886

1311990131(119896 minus 1)

11990111(119896 minus 1)

11990112(119896 minus 1)

]

]

(35)

K +

A

C

Y XMx

Mp+minus

1

z

Figure 6 Observer stage

To rewrite the equations for easier coding the equationfor PFC controller and observer stage is now reduced to (31)(34) and (35) which are still in their matrix form To easecoding the equations are rewritten as single-line expressionsthus yielding the following equations The observer stage iswritten as

Out = 119875119888119903 (119896) minus (119896

1198881111990911(119896) + 119896

1198881211990921(119896) + 119896

1198881311990931(119896))

(36)

where Out(119896) and 119903(119896) are the controller output and con-troller reference signal respectively The value of 119909

1198991(119896) is

provided by the observer stage written as

11990911(119896) = 119901

11(119896 minus 1)

11990921(119896) = 119901

21(119896 minus 1)

11990931(119896) = 119901

31(119896 minus 1)

(37)

and the value of 1199011198991(119896) is provided by

11990111(119896) = 119867 + 119886

1111990111(119896 minus 1) + 119886

1211990121(119896 minus 1)

+ 1198861311990131(119896 minus 1)

11990121(119896) = 119867 + 119901

11(119896 minus 1)

11990131(119896) = 119867 + 119901

12(119896 minus 1)

(38)

The value of119867 is given by

119867 = 119868 minus 119869 (39)

where 119868 = (11989611+ 11989612+ 11989613)119884(119896) 119869 = (119896

111198881111990111(119896 minus 1) +

119896121198881211990121(119896 minus 1) + 119896

131198881311990131(119896 minus 1)) and 119884(119896) is the general

feedback signal from the plantIn this research the control methodology contains force

inner loop and position outer loop to obtain the stiffnesscharacteristic objective By controlling the difference of bothsides of the pneumatic actuator the inner loop enforcesthe natural stiffness characteristic of the pneumatic actuatorThe working function of stiffness characteristic is shown inFigure 7 where the system tried to achieve the target positionby giving the appropriate value of force The error in forcevalue reading will be eliminated using PFC-O control thatadjusts the duty cycle of PWMsignal for actuator stroke forceMeanwhile integral gain 119896

119868 as a compensator is added to

solve the problem of stretch-back not functioning with lowerstiffness parameter

The feedback of output force (signal inner loop) toobserver is

119884 (119896) = 119910119865(119896) = 1049074 minus 08437119899

119901 (40)


Controller

Observer

+ PositionPlant Force

Position (reference) (PFC)

u(k) e(k) F = r(k)

x(k)

z(k)

I(k)intkI

ks+

minus

yF(k)

Figure 7 Block diagram for control system with stiffness characteristic

where 119899119901is PSoC 11-bit delta-sigma ADC raw conversion

result by calculation and the PFC force controller referencesignal is

119903 (119896) = 119896119904119890 (119896) + 119868 (119896) (41)

where 119896119904is a coefficient of stiffness 119890(119896) is position error 119868(119896)

is compensator output and the equation for the compensatoris given by

119868 (119896) = 119896119868120591119890 (119896) + 119868 (119896 minus 1) (42)

where 119896119868is integral gain and 120591 is discrete integrator sampling

time

6 Experimental Setup

The experimental setup for these researches consists ofsimulation and real-time analysis The simulation data isacquired using MATLAB Simulink where (6) and (7) aredirectly applied and tested with the close-loop controllerdesign using MATLAB Simulink Meanwhile the real-timeexperimental data are acquired using national instrument(NI) devices and programmable system on chip (PSoC)microcontroller The experimental setup for the real-timeusing national instrument (NI) devices is the same as thatdescribed in Section 2 but the input-output connection isdirectly tested with the close-loop controller design usingMATLAB Simulink [4] Therefore the technical merit of thiswork consists of modified new wiring and communicationfigure with an online system in a real-time environment Thedata acquisition (DAQ) card PCIPXI-6221 (68-Pin) boardconnected is used for interfacing the plant with a computerFrom the communication diagram in Figure 8 the signalemitted from the circuit board consists of an analog signaloutput for valves an analog signal input for pressure and asignal counter input for the encoder Experiment for positioncontrol or compliance control is in normal movement of theactuator as in Figure 9(a) However experiments on forcecontrol will be in static position movement as in Figure 9(b)

Next experimental setup to implement the real-timeenvironment using embedded system is a continuationof previous work using the PSoC control board [16ndash19]There are 5 connectors attached on the board connectedto valves pressure sensor 2 for power supply and I2Ccommunication and 1 for reburning programs From thisboard other parts are controlled by reading pressure sensor

MATLAB

PC

PCIPXI-6221 (68-pin)board

SHC68-68-EPMcable

PlantSCB-68 M series

devices

Figure 8 National instrument (NI) devices connection

data and detecting actuator strokes from the optical sensorCY8C27443 chip and C programming were used for easierimplementation and fast execution PSoC represents a wholenew concept in microcontroller development By having aneasy-to-use development tool PSoC enables user to selectdesired peripherals including analogue function (amplifiersADCs DACs filters and comparators) and digital functions(timers counters PWMs SPI and UARTs) making PSoCdifferent from other microcontrollers Additionally a fastCPU of 24MHz 16 kb of Flash programmemory SRAMdatamemory with 256 bytes and configurable inputoutput (IO)is included in a range of pin outsThe distributed architectureapplying several PSoCs enables multitasking and parallelprocessing of themicrocontrollerThiswill increase efficiencyof the data processing and give shorter access time In thisdistributed approach the PSoC has its own private memoryand information is exchanged by passing data between themicrocontrollers

By applying this methodology the overall system willbe enhanced with the new controller coding such as PFC-O algorithm simpler connections and reduced numbersof wires between PC and the actuator Furthermore thecommunication protocol between PC and I2C communi-cation board applies USB to UART converter protocolFor better response the actuator will give different outputcharacteristics (position and stiffness parameter) from theinput given and monitor using MATLAB M-File (positionand force) as an online communication Figure 10 shows thePSoC control board and experiment setup to be applied tothe embedded system In addition the payload as a mass


(a) Position control or compliance control (b) Force control

Figure 9 Real experiment setup using NI devices

MATLAB

PCUSB to UART converter PSoC control board

Figure 10 Embedded system connection

Figure 11 Pneumatic actuator with mass

is attached to the pneumatic plant in vertical direction totest the system capability with fixed position and differentstiffness parameters The purpose of this experiment wasto compare the theoretical data analysis for mass-springmechanical system method and real-time experiment usingNI devices Figure 11 shows the real experiment setup forpneumatic actuator with mass

7 Result and Discussion

In this research a new model and a novel embedded pro-cess control strategy to design the controller for real-timepneumatic system have been proposed This section showsthe results of model validation and application to embedded

Table 1 Comparison of simulated and experimental performancefor position control

Specifications Simulation ExperimentSettling time (119879

119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s

Percent steady state error (119890ss) 001 003 percent s second

system are analyzed and discussed to further evaluate thecontroller

71 Model Validation Analysis Simulation and real-timeexperiment using national instrument (NI) device analysiswere carried out to validate the controller performance Thisanalysis of the actual situation pneumatic actuator whereforce maximum and without stiffness characteristics Theresults of position control and force control are analyzedbefore applying the PFC-O controller algorithm to embeddedsystem

711 Position Control Comparison between the simulationand the experiment result for position step and multistepresponses including control signals within 18 s is shown inFigures and 13 For this control position the PFC controllaw and the prediction model of the system are developedusing the following parameters desired time constant Ψis 095 and coincidence horizon 119899

1 is 2 while the closed-

loop observer poles are selected to be inside the unit circlethat is 005 004 and 0001 The performances index ofthe simulation and experiment for position step responses issummarized in Table 1

712 Force Control Figures 14 and 15 show the forceresponses of the system for step and multistep responsesincluding control signals within 18 s Force readings wereobtained from the mathematical derivation of the pressuresensor dataThe high negative force reading during the initial


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)

ReferenceSimulationReal-time

(b)

Figure 12 Force multistep responses

0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)

Figure 13 Position multistep responses

Table 2 Comparison of simulated and experimental performancefor force control


119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s


stage of the experiment is due to the double acting nature ofthe cylinder where one chamber is filled with compressedair driving the cylinder in the negative direction when theother chamber is emptied The parameters of PFC desiredtime constant Ψ are 092 coincidence horizon 119899

1 is 2

and closed-loop observer poles are 005 023 and 001 Theperformance index of the simulation and experiment forforce step responses is summarized in Table 2

The results for model validation analysis and the positioncontrol and force control analysis provide good performancein terms of no overshoot faster settling time (119879

119878) rise time

(119879119877) and smaller percent steady-state error (119890

119904119904) PFC-O

control signal for both models is stable because the signalamplitude is between 255 and minus255 Not to mention the zeroalso to force the valve to fully open in their periods an 8-bitPWM generator is used so the maximum value for the signalis 255 which forces the first valve to have a full open periodwhereas when the signal is minus255 it forces the second valve tohave a full open period instead The simulated result is betterbecause the transfer function used for simulation is linearwhich does not contain the nonlinearities found on actual

systems However due to the involvement of nonlinearitiesthe transient response experiment shows slower response butcan be considered fast enough for a pneumatic system

72 Embedded System Analysis The control analysis willbe done in the simulation and real-time experiment usingNational Instrument (NI) device environment Next allcoding in Section 5 is converted to C programming andburned to PSoCThe aim controller performances proceed toapply an embedded system and realized compliance controlfor stiffness characteristic Different stiffness coefficients willbe tested and the position value will be fixed based onexperimental work Two methods to get the position valueare examined first by controlling the pneumatic actuatorposition and sending the value for force control loop andsecond by getting the values frommass attached and sendingthem to the force control loop

721 Compliance Control without Mass The basic compli-ance control is presented in (24) In this control the targetposition was set to origin position at 100mm within 18 sThree different 119896

119904inputs of 2Nmm 1Nmm and 05Nmm

are plotted in Figure 16 From the results feedback forcefrom the actuator gives positive force In addition when thevalue of 119896

119904is small position during the experiment is slightly

different and rise time is slow to achieve the target comparedto the simulation This is because the actuator becomes softat low force This can be seen more clearly in Figure 17for position step response PFC parameters were not muchdifferent with force control where desired time constantΨ is


minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)

Figure 14 Force step responses

minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25

Figure 16 Stiffness characteristic responses

092 coincidence horizon 1198991 is 2 observer poles are 005 02

and 001 and integral gain 119896119868 is 01These parameters are also

the same as with simulations real-time experiments usingnational Instrument (NI) devices and real-time embeddedsystem

722 Compliance Control with Mass The second method forcompliance control was referred to in (27) The mass 3 kg isattached and raised at certain times to the pneumatic plant invertical direction to test the system capability In this control

0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

Referenceks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2ks(NI) = 05

ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05

Figure 17 Position step responses for difference stiffness

with fixed 100mm position and different stiffness parame-ters such as 119896

119904input of 2Nmm 1Nmm and 05Nmm

results of the analysis found that the deflection value inexperiment using NI devices is almost the same and betterthan embedded systems This is because embedded systemsfollow the behavior that has been set through MATLAB andtime taken to calculate the algorithm Furthermore when amass applied on the value of 119896

119904is small the time decreases

faster but rise time is slow to achieve the target because theactuator becomes soft A comparison between the theoretical


15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1

ks(NI) = 2ks(Emb) = 05

ks(Emb) = 1

ks(Emb) = 2

Figure 18 Deflection analysis responses

Table 3 Comparison of deflection results

Stiffnessparameters 119896

119904

Theory Real-timeNI devices

Real-timeembeddedsystem

05Nmm 5886mm 5823mm 5750mm1Nmm 2943mm 2901mm 2817mm2Nmm 1472mm 1680mm 1594mmN newton mm millimeter

calculations with both real-time results is shown in Figure 18and Table 3 where the controller parameters are set up ascontrol with mass

In the analysis of compliance control for an embeddedsystem stiffness characteristics were successfully applied togive the spring effectThe experimental 119896

119904data are identical to

the input data giving minimum errorThis is due to hardwarefriction inside the actuator Despite the observed differencesthe model is considered acceptable because of the similaritiesbetween simulation theoretical calculation and both real-time experiments except for rise time and target achieved

8 Conclusion

Considering the nonlinear characteristics of the pneumaticsystem for this research scope the results from the simulationand the both real-time experiments matched closely and thisis considered as a validation of the obtained mathematicalmodel Controller design for pneumatic actuator is doneusing PFC-O Stiffness characteristic is realized using thecompliance control To compare the performance of thePFC-O analysis several parameters have been identifiedThe results obtained from the simulation and experimentshow that the developed real-time model could be used forvarious research bases such as improvement of the controllerperformance and implementation on embedded systemsFurthermore this pneumatic system can work well as arobust system and that makes it a suitable controller withgood control performance This research will provide greateropportunities for future work such as development of graphic

user interface (GUI) to enhance online communication withmore than one actuator and to apply the pneumatic actuatorto related applications such as rehabilitation device

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 the Universiti TeknologiMa-laysia (UTM) Ministry of Higher Education (MOHE)Malaysia under Exploratory Research Grant Scheme(ERGS) no RJ13000078234L070 Universiti TeknikalMalaysia Melaka (UTeM) and the Okayama University fortheir support

References

[1] A C Valdiero C S Ritter C F Rios and M Rafikov ldquoNon-linear mathematical modeling in pneumatic servo positionapplicationsrdquo Mathematical Problems in Engineering vol 2011Article ID 472903 16 pages 2011

[2] L A Zadeh ldquoFrom circuit theory to system theoryrdquo Proceedingsof the IRE vol 50 no 5 pp 856ndash865 1962

[3] J A Corrales G J G Gomez F Torres and V PerdereauldquoCooperative tasks between humans and robots in industrialenvironmentsrdquo International Journal of Advanced Robotic Sys-tems vol 9 article 92 2012

[4] A A M Faudzi K Osman M F Rahmat K Suzumori ND Mustafa and M A Azman ldquoReal-time position controlof intelligent pneumatic actuator (IPA) system using opticalencoder and pressure sensorrdquo Sensor Review vol 33 no 4Article ID 17094939 pp 341ndash351 2013

[5] A Saleem S Abdrabbo and T Tutunji ldquoOn-line identificationand control of pneumatic servo drives via a mixed-realityenvironmentrdquo International Journal of AdvancedManufacturingTechnology vol 40 no 5-6 pp 518ndash530 2009

[6] P Matousek ldquoAdaptive control of pneumatic servomechanismrdquoANNALS of Faculty Engineering Hunedoara vol 2 pp 73ndash782011

[7] M F Rahmat N H Sunar S N S Salim M S Z Abidin A AM Fauzi and Z H Ismail ldquoReview onmodeling and controllerdesign in pneumatic actuator control systemrdquo InternationalJournal on Smart Sensing and Intelligent Systems vol 4 no 4pp 630ndash661 2011

[8] M F Rahmat S N S Salim N H Sunar A A M Faudzi ZH Ismail and K Huda ldquoIdentification and non-linear controlstrategy for industrial pneumatic actuatorrdquo International Jour-nal of the Physical Sciences vol 7 no 17 pp 2565ndash2579 2012

[9] B Huyck H J Ferreau M Diehl et al ldquoTowards online modelpredictive control on a programmable logic controller practicalconsiderationsrdquo Mathematical Problems in Engineering vol2012 Article ID 912603 20 pages 2012

[10] J A Rossiter Model-Based Predictive Control A PracticalApproach CRC Press 2003

[11] A I Maalouf ldquoImproving the robustness of a parallel robotusing Predictive Functional Control (PFC) toolsrdquo inProceedingsof the 45th IEEE Conference on Decision and Control (CDC 06)pp 6468ndash6473 December 2006


[12] M Aliff S Dohtaa T Akagi and H Li ldquoDevelopment of asimple-structured pneumatic robot arm and its control usinglow-cost embedded controllerrdquo in Proceedings of the Interna-tional Symposium on Robotics and Intelligent Sensors (IRIS 12)vol 41 of Procedia Engineering pp 134ndash142 2012

[13] R Isermann ldquoMechatronic systemsmdashinnovative products withembedded controlrdquo Control Engineering Practice vol 16 no 1pp 14ndash29 2008

[14] JWangHHu JWang Z Li andZGong ldquoDevelopment of anembedded control system for magnetorheological fluid damperunder impact loadrdquo in Proceedings of the 9th InternationalConference on Electronic Measurement and Instruments (ICEMI09) pp 717ndash722 August 2009

[15] K-P Kang M Moallem and R V Patel ldquoEmbedded controllerdesign for an active damper systemrdquo in Proceedings of IEEEConference on Control Applications (CCA 03) pp 526ndash531 June2003

[16] A A M Faudzi K Suzumori and SWakimoto ldquoDevelopmentof an intelligent pneumatic cylinder for distributed physicalhuman-machine interactionrdquo Advanced Robotics vol 23 no 1-2 pp 203ndash225 2009

[17] A A M Faudzi K Suzumori and SWakimoto ldquoDevelopmentof an intelligent chair tool system applying new intelligentpneumatic actuatorsrdquo Advanced Robotics vol 24 no 10 pp1503ndash1528 2010

[18] A A M Faudzi and K Suzumori ldquoProgrammable systemon chip distributed communication and control approachfor human adaptive mechanical systemrdquo Journal of ComputerScience vol 6 no 8 pp 852ndash861 2010

[19] A A M Faudzi K Suzumori and SWakimoto ldquoDevelopmentof pneumatic actuated seating system to aid chair designrdquoin Proceedings of the IEEEASME International Conference onAdvanced IntelligentMechatronics (AIM 10) pp 1035ndash1040 July2010

[20] L Ljung Identification Toolbox for Use with MATLAB TheMathWorks 2002 httpwwwmathworkscomproductssysid

[21] K Osman A A M Faudzi M F Rahmat N D Mustafa MA Azman and K Suzumori ldquoSystem identification model foran Intelligent Pneumatic Actuator (IPA) systemrdquo in Proceedingsof the 25th IEEERSJ International Conference on Robotics andIntelligent Systems (IROS 12) pp 628ndash633 October 2012

[22] J A Rossiter and J Richalet ldquoHandling constraints with pre-dictive functional control of unstable processesrdquo in Proceedingsof the American Control Conference (ACC 02) vol 6 pp 4746ndash4751 May 2002

[23] LWangModel Predictive Control SystemDesign and Implemen-tation Using MATLAB Springer 2009

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Algebra

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Discrete MathematicsJournal of


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Stochastic AnalysisInternational Journal of


Online system identification can be conducted effectively andefficiently using the proposed method Next the researchrealized online identification of the pneumatic positionalservomechanism necessary to determine the order of thenumerator and denominator of the system transfer [6] Thisresearch briefly describes two main parts that constitutean adaptive control The first part describes the design ofan optimal structure of mathematical model that allowsfor continuous identification The second part describes thedesign of an adaptive state-space controller whereby theadaptive control is implemented Another review on model-ing controller design and implement system identification topneumatic actuator has been proposed by various researchersas presented in [7 8] The implication of this research isto further improve the performance of existing pneumaticactuators

Controller design for pneumatic system to control theposition force compliance viscosity and so forth is a chal-lenging issue for improving its tracking performance Manycontroller designs were proposed to control pneumatic sys-tem such as proportional-integral-derivative (PID) artificialintelligence and robust controller Model predictive control(MPC) is one of the controllers that have been successfullyused in both industry and academia for the control of large-scale installations which are typically described by large-scale models with relatively slow dynamics The key elementin MPC is to repeatedly solve an optimization problembased on available measurements of the current state of theprocess The advantages of MPC over classic PID controlare its ability to steer the process in an optimal approachwhile taking proactively desired future behavior into accountto tackle multiple inputs and outputs simultaneously andto incorporate constraints Among the most popular MPCalgorithms are dynamic matrix control (DMC) model algo-rithm control (MAC) generalized predictive control (GPC)predictive functional control (PFC) and so forth [9] Eachcontroller has their own strategies advantages and theirspecific applications which assured good results UsuallyGPC is widely used in pneumatic systems However thesystem suffers from instability and it is difficult to beimplemented on this research real-time embedded systemIndustrial applications of PFC can be found in the defensesector automotive metallurgical industries miscellaneousprocess (chemical reactors and distillation excluded) andso forth [10] PFC is based on the same approach as allMPC strategies that is prediction of the future outputsand calculation of the manipulated variables for optimalcontrol using a simple algorithm Therefore PFC is alsobased on the same principle which uses an internal modelspecification of a reference trajectory and determination ofthe control law [11] The research is motivated by the PFCrsquoshigh-quality control performance with improved rise timeprecise tracking robust stabilization fast response and analgorithm that is easy to understand for implementation ona real-time embedded system

In recent years interest in exploiting several controllerdesigns on embedded systems has grown Examples ofimplementing the controller design for embedded system andtheir advantage were presented by [9 12 13] The embedded

Valves

Pressure sensor

Optical sensor

PSoC control board

Figure 1 Pneumatic system and its parts

system has been widely applied to manufacturing industryprocessing control communication instrumentation vehi-cle weapon system and so forth In addition the embeddedsystem is referred to as a dedicated computer applicationsystem which can be adapted into some specialized rigorousrequirements to function and power the application systemforward That is to say it can be centered on the engineeringapplication system based on computer technology and itshardware and software can be easily clippedThis allows real-time application by using a chip microprocessor dSPACEPC DSP and so forth In these cases the controller designsare not a supervisory controller anymore but directly steerthe actuators and as such also the process itself [14 15]

The related development of the pneumatic system usedin this research is presented in [16ndash19] Pneumatic systemcan be further divided into two types of actuator specificallywith position accuracy of 0169mm and position accuracyof 001mm The design of actuator with position accuracy of001mm was enhanced from position accuracy of 0169mmfor better performance during experimentation on the appli-cations but the system operation for both actuators is still thesame Design with position accuracy of 001mm will havea new position sensor with higher accuracy new tape typestripe code for better durability and new enhanced circuitdesign and will not have been implemented as yet in anyapplication Figure 1 shows all the parts of the pneumaticactuator at position accuracy of 001mmused in this researchThe actuator has 200mm stroke and can deliver maximumforce up to 120N KOGANEI-ZMAIR optical sensor isused where smaller pitch of 001mm can be detected Thepneumatic system presents the next generation of actuatordevelopment with new features that provide better controlhigher position and speed force accuracy communicationability and all-in-onemechanism for compact system designThe pneumatic actuator is equipped with programmablesystem on chip (PSoC) microcontroller which acts as thebrain for the system and performs the local control to suitthe requirements of any related applications Contractionand extension movements depend on the algorithm todrive the valve using pulse width modulation (PWM) dutycycle In addition the pneumatic actuator is able to analyzeposition force stiffness and viscosity However the existingsystem implements only a simple proportional-integral (PI)










119899119886119910 (119896 minus 119899119886)

= 1198871119906 (119896 minus 119889) + 119887

2119906 (119896 minus 119889 minus 1)


119884 (119911minus1

)


)

119860 (119911minus1)

(1)


FPE = 119881 sdot(1 + 119899

119886119873)

(1 minus 119899119886119873)

(2)

where

119881 =1198902

(119896)

119873=119890119879

(119896) sdot 119890 (119896)

119873

119890 (119896) = [119890119896119890119896minus1


]119879

(3)



AIC = log [119881 (1 +2119899119886

119873)] (4)



norm (119910 minus 119910)] (5)




minus05

0

05

1

Real part

Imag

inar

y pa

rt

Pole and zero


ForceForce




)


=0001269119911

minus1

+ 00004517119911minus2

minus 00003498119911minus3

1 minus 1932119911minus1+ 109119911


minus3

(6)


)

119860Force (119911minus1)

=004097119911

minus1

+ 004577119911minus2

+ 001379119911minus3



minus3

(7)


3 Control Strategy




119909119896+1

= 119860119909119896+ 119861119906119896

119910119896= 119862119909119896+ 119863119906119896

(8)


119909119896+2

= 119860119909119896+1

+ 119861119906119896+1

119910119896+2

= 119862119909119896+2

(9)


119909119896+2

= 1198602

119909119896+ 119860119861119906

119896+ 119861119906119896+1

119910119896+2

= 119862119909119896+2

119909119896+3

= 1198602

[119860119909119896+ 119861119906119896] + 119860119861119906

119896+1+ 119861119906119896+2

119910119896+3

= 119862119909119896+3

(10)


119909119896+119899

= 119860119899

119909119896+ 119860119899minus1

119861119906119896+ 119860119899minus2

119861119906119896+1


119910119896+119899

= 119862 [119860119899

119909119896+ 119860119899minus1

119861119906119896+ 119860119899minus2

119861119906119896+1


]

(11)


[[[[[[

[

119909119896+1

119909119896+2

119909119896+3

119909119896+119899

]]]]]]

]119909119896

=

=

=

=

[[[[[[

[

119860

1198602

1198603

119860119899

]]]]]]

]119875119909119909

119909119896+

[[[[[[

[


119860119861 119861 0 sdot sdot sdot 0

1198602

119861 119860119861 119861 sdot sdot sdot 0

0

119860119899minus1

119861 119860119899minus2

119861 119860119899minus3


]]]]]]

]119867119909119909

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(12)



[[[[[[

[

119910119896+1

119910119896+2

119910119896+3

119910119896+119899

]]]]]]

]119910119896

=

=

=

=

[[[[[[

[

119862119860

1198621198602

1198621198603

119862119860119899

]]]]]]

]119875

119909119896

+

[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

119862119860119861 119862119861 0 sdot sdot sdot 0

1198621198602

119861 119862119860119861 119862119861 sdot sdot sdot 0

0

119862119860119899minus1

119861 119862119860119899minus2

119861 119862119860119899minus3

119861 sdot sdot sdot 119862119861

]]]]]]

]119867

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(13)


119909119896= 119875119909119909119909119896+ 119867119909119909119906119896minus1

119910119896= 119875119909119896+ 119867119906119896minus1

(14)



119896is the



119908119896+119894119896

= 119903119896minus (119903119896minus 119910119896) 120595119894

(15)



119910119896+119899

= 119908119896+119899

(16)





119910119896+119899

= 119908119896+119899

= 119903119896minus (119903119896minus 119910119896) 120595119894

(17)


119910119896+119899

= 119875119909119896+ 119867119906119896minus1

= 119903119896minus (119903119896minus 119910119896) 120595119894

(18)

Assuming that 119906119896+119894



119906119896= minus119867

minus1

[119875119909119896+ (119903119896minus (119903119896minus 119910119896) 120595119894

)]

119906119896= minus119870119888119909119896+ 119875119888119903119896

(19)

where119870119888= minus119867

minus1

(119875minusΨ119894

119910119896) and 119875

119888= minus119867

minus1

(1minusΨ119894




1=


1





119894)







119909 (119896119894+ 1) = 119860119909 (119896

119894) + 119861119906 (119896

119894) + 119870ob (119910 (119896119894) minus 119862119909 (119896119894))

(20)

where 119906(119896119894) at time 119896



119909 (119896 + 1) = (119860 minus 119870ob119862) 119909 (119896) (21)






Observer design

PFC algorithm

u

Input r


x

x3

x1x2






119865 = 119896119904119890 (119896) (24)




119865 = 120575119896119904 (25)


119865 = 119882 = 119898119892 (26)

Nat

ural

leng

th

F

F

120575

120575


+r

X

OutPc

Kc

minus


the deflection is

120575 =119898119892

119896119904

(27)




119860 =

[[[[

[

11988611

11988612

11988613

0 1 0

0 0 1

]]]]

]

119861 = [

[

1

0

0

]

]

119862 = [11988811

11988812

11988813]

(28)



Out = 119875119888119903 minus 119870119888119883 (29)





119888is given

by

119870119888= [11989611988811

11989611988812

11989611988813] = [(119862119860119861 + 119862119861) (119862119860

2

minus 1198621205952

)]minus1

(30)


Out = 119875119888119903 minus [119896

1198881111989611988812

11989611988813] [

[

11990911

11990921

11990931

]

]

= 119875119888119903 minus (119896

1198881111990911+ 1198961198881211990921+ 1198961198881311990931)

(31)



119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= 119870(119884 minus 119862 sdot 119872119901(119896 minus 1)) + 119860119872

119901(119896 minus 1)

(32)


119870 = [11989611

11989612

11989613] (33)


119883 (119896) = [

[

11990911(119896)

11990921(119896)

11990931(119896)

]

]

= 119872119901(119896 minus 1) (34)


119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= [11989611

11989612

11989613]

times [

[

119884 (119896) minus 1198881111990111(119896 minus 1)

119884 (119896) minus 1198881211990121(119896 minus 1)

119884 (119896) minus 1198881311990131(119896 minus 1)

]

]

+ [

[

11988611

11988612

11988613

1 0 0

0 1 0

]

]

[

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= (11989611+ 11989612+ 11989613) 119884 (119896)

minus (119896111198881111990111(119896 minus 1) + 119896

121198881211990121(119896 minus 1)

+119896131198881311990131(119896 minus 1))

+ [

[

1198861111990111(119896 minus 1) + 119886

1211990121(119896 minus 1) + 119886

1311990131(119896 minus 1)

11990111(119896 minus 1)

11990112(119896 minus 1)

]

]

(35)

K +

A

C

Y XMx

Mp+minus

1

z



Out = 119875119888119903 (119896) minus (119896

1198881111990911(119896) + 119896

1198881211990921(119896) + 119896

1198881311990931(119896))

(36)


1198991(119896) is


11990911(119896) = 119901

11(119896 minus 1)

11990921(119896) = 119901

21(119896 minus 1)

11990931(119896) = 119901

31(119896 minus 1)

(37)


11990111(119896) = 119867 + 119886

1111990111(119896 minus 1) + 119886

1211990121(119896 minus 1)

+ 1198861311990131(119896 minus 1)

11990121(119896) = 119867 + 119901

11(119896 minus 1)

11990131(119896) = 119867 + 119901

12(119896 minus 1)

(38)


119867 = 119868 minus 119869 (39)

where 119868 = (11989611+ 11989612+ 11989613)119884(119896) 119869 = (119896

111198881111990111(119896 minus 1) +

119896121198881211990121(119896 minus 1) + 119896







119884 (119896) = 119910119865(119896) = 1049074 minus 08437119899

119901 (40)


Controller

Observer



u(k) e(k) F = r(k)

x(k)

z(k)

I(k)intkI

ks+

minus

yF(k)




119903 (119896) = 119896119904119890 (119896) + 119868 (119896) (41)



119868 (119896) = 119896119868120591119890 (119896) + 119868 (119896 minus 1) (42)


time




MATLAB

PC


SHC68-68-EPMcable


devices







MATLAB









119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s









minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra


















119899119886119910 (119896 minus 119899119886)

= 1198871119906 (119896 minus 119889) + 119887

2119906 (119896 minus 119889 minus 1)


119884 (119911minus1

)


)

119860 (119911minus1)

(1)


FPE = 119881 sdot(1 + 119899

119886119873)

(1 minus 119899119886119873)

(2)

where

119881 =1198902

(119896)

119873=119890119879

(119896) sdot 119890 (119896)

119873

119890 (119896) = [119890119896119890119896minus1


]119879

(3)



AIC = log [119881 (1 +2119899119886

119873)] (4)



norm (119910 minus 119910)] (5)




minus05

0

05

1

Real part

Imag

inar

y pa

rt

Pole and zero


ForceForce




)


=0001269119911

minus1

+ 00004517119911minus2

minus 00003498119911minus3

1 minus 1932119911minus1+ 109119911


minus3

(6)


)

119860Force (119911minus1)

=004097119911

minus1

+ 004577119911minus2

+ 001379119911minus3



minus3

(7)


3 Control Strategy




119909119896+1

= 119860119909119896+ 119861119906119896

119910119896= 119862119909119896+ 119863119906119896

(8)


119909119896+2

= 119860119909119896+1

+ 119861119906119896+1

119910119896+2

= 119862119909119896+2

(9)


119909119896+2

= 1198602

119909119896+ 119860119861119906

119896+ 119861119906119896+1

119910119896+2

= 119862119909119896+2

119909119896+3

= 1198602

[119860119909119896+ 119861119906119896] + 119860119861119906

119896+1+ 119861119906119896+2

119910119896+3

= 119862119909119896+3

(10)


119909119896+119899

= 119860119899

119909119896+ 119860119899minus1

119861119906119896+ 119860119899minus2

119861119906119896+1


119910119896+119899

= 119862 [119860119899

119909119896+ 119860119899minus1

119861119906119896+ 119860119899minus2

119861119906119896+1


]

(11)


[[[[[[

[

119909119896+1

119909119896+2

119909119896+3

119909119896+119899

]]]]]]

]119909119896

=

=

=

=

[[[[[[

[

119860

1198602

1198603

119860119899

]]]]]]

]119875119909119909

119909119896+

[[[[[[

[


119860119861 119861 0 sdot sdot sdot 0

1198602

119861 119860119861 119861 sdot sdot sdot 0

0

119860119899minus1

119861 119860119899minus2

119861 119860119899minus3


]]]]]]

]119867119909119909

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(12)



[[[[[[

[

119910119896+1

119910119896+2

119910119896+3

119910119896+119899

]]]]]]

]119910119896

=

=

=

=

[[[[[[

[

119862119860

1198621198602

1198621198603

119862119860119899

]]]]]]

]119875

119909119896

+

[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

119862119860119861 119862119861 0 sdot sdot sdot 0

1198621198602

119861 119862119860119861 119862119861 sdot sdot sdot 0

0

119862119860119899minus1

119861 119862119860119899minus2

119861 119862119860119899minus3

119861 sdot sdot sdot 119862119861

]]]]]]

]119867

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(13)


119909119896= 119875119909119909119909119896+ 119867119909119909119906119896minus1

119910119896= 119875119909119896+ 119867119906119896minus1

(14)



119896is the



119908119896+119894119896

= 119903119896minus (119903119896minus 119910119896) 120595119894

(15)



119910119896+119899

= 119908119896+119899

(16)





119910119896+119899

= 119908119896+119899

= 119903119896minus (119903119896minus 119910119896) 120595119894

(17)


119910119896+119899

= 119875119909119896+ 119867119906119896minus1

= 119903119896minus (119903119896minus 119910119896) 120595119894

(18)

Assuming that 119906119896+119894



119906119896= minus119867

minus1

[119875119909119896+ (119903119896minus (119903119896minus 119910119896) 120595119894

)]

119906119896= minus119870119888119909119896+ 119875119888119903119896

(19)

where119870119888= minus119867

minus1

(119875minusΨ119894

119910119896) and 119875

119888= minus119867

minus1

(1minusΨ119894




1=


1





119894)







119909 (119896119894+ 1) = 119860119909 (119896

119894) + 119861119906 (119896

119894) + 119870ob (119910 (119896119894) minus 119862119909 (119896119894))

(20)

where 119906(119896119894) at time 119896



119909 (119896 + 1) = (119860 minus 119870ob119862) 119909 (119896) (21)






Observer design

PFC algorithm

u

Input r


x

x3

x1x2






119865 = 119896119904119890 (119896) (24)




119865 = 120575119896119904 (25)


119865 = 119882 = 119898119892 (26)

Nat

ural

leng

th

F

F

120575

120575


+r

X

OutPc

Kc

minus


the deflection is

120575 =119898119892

119896119904

(27)




119860 =

[[[[

[

11988611

11988612

11988613

0 1 0

0 0 1

]]]]

]

119861 = [

[

1

0

0

]

]

119862 = [11988811

11988812

11988813]

(28)



Out = 119875119888119903 minus 119870119888119883 (29)





119888is given

by

119870119888= [11989611988811

11989611988812

11989611988813] = [(119862119860119861 + 119862119861) (119862119860

2

minus 1198621205952

)]minus1

(30)


Out = 119875119888119903 minus [119896

1198881111989611988812

11989611988813] [

[

11990911

11990921

11990931

]

]

= 119875119888119903 minus (119896

1198881111990911+ 1198961198881211990921+ 1198961198881311990931)

(31)



119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= 119870(119884 minus 119862 sdot 119872119901(119896 minus 1)) + 119860119872

119901(119896 minus 1)

(32)


119870 = [11989611

11989612

11989613] (33)


119883 (119896) = [

[

11990911(119896)

11990921(119896)

11990931(119896)

]

]

= 119872119901(119896 minus 1) (34)


119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= [11989611

11989612

11989613]

times [

[

119884 (119896) minus 1198881111990111(119896 minus 1)

119884 (119896) minus 1198881211990121(119896 minus 1)

119884 (119896) minus 1198881311990131(119896 minus 1)

]

]

+ [

[

11988611

11988612

11988613

1 0 0

0 1 0

]

]

[

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= (11989611+ 11989612+ 11989613) 119884 (119896)

minus (119896111198881111990111(119896 minus 1) + 119896

121198881211990121(119896 minus 1)

+119896131198881311990131(119896 minus 1))

+ [

[

1198861111990111(119896 minus 1) + 119886

1211990121(119896 minus 1) + 119886

1311990131(119896 minus 1)

11990111(119896 minus 1)

11990112(119896 minus 1)

]

]

(35)

K +

A

C

Y XMx

Mp+minus

1

z



Out = 119875119888119903 (119896) minus (119896

1198881111990911(119896) + 119896

1198881211990921(119896) + 119896

1198881311990931(119896))

(36)


1198991(119896) is


11990911(119896) = 119901

11(119896 minus 1)

11990921(119896) = 119901

21(119896 minus 1)

11990931(119896) = 119901

31(119896 minus 1)

(37)


11990111(119896) = 119867 + 119886

1111990111(119896 minus 1) + 119886

1211990121(119896 minus 1)

+ 1198861311990131(119896 minus 1)

11990121(119896) = 119867 + 119901

11(119896 minus 1)

11990131(119896) = 119867 + 119901

12(119896 minus 1)

(38)


119867 = 119868 minus 119869 (39)

where 119868 = (11989611+ 11989612+ 11989613)119884(119896) 119869 = (119896

111198881111990111(119896 minus 1) +

119896121198881211990121(119896 minus 1) + 119896







119884 (119896) = 119910119865(119896) = 1049074 minus 08437119899

119901 (40)


Controller

Observer



u(k) e(k) F = r(k)

x(k)

z(k)

I(k)intkI

ks+

minus

yF(k)




119903 (119896) = 119896119904119890 (119896) + 119868 (119896) (41)



119868 (119896) = 119896119868120591119890 (119896) + 119868 (119896 minus 1) (42)


time




MATLAB

PC


SHC68-68-EPMcable


devices







MATLAB









119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s









minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











minus05

0

05

1

Real part

Imag

inar

y pa

rt

Pole and zero


ForceForce




)


=0001269119911

minus1

+ 00004517119911minus2

minus 00003498119911minus3

1 minus 1932119911minus1+ 109119911


minus3

(6)


)

119860Force (119911minus1)

=004097119911

minus1

+ 004577119911minus2

+ 001379119911minus3



minus3

(7)


3 Control Strategy




119909119896+1

= 119860119909119896+ 119861119906119896

119910119896= 119862119909119896+ 119863119906119896

(8)


119909119896+2

= 119860119909119896+1

+ 119861119906119896+1

119910119896+2

= 119862119909119896+2

(9)


119909119896+2

= 1198602

119909119896+ 119860119861119906

119896+ 119861119906119896+1

119910119896+2

= 119862119909119896+2

119909119896+3

= 1198602

[119860119909119896+ 119861119906119896] + 119860119861119906

119896+1+ 119861119906119896+2

119910119896+3

= 119862119909119896+3

(10)


119909119896+119899

= 119860119899

119909119896+ 119860119899minus1

119861119906119896+ 119860119899minus2

119861119906119896+1


119910119896+119899

= 119862 [119860119899

119909119896+ 119860119899minus1

119861119906119896+ 119860119899minus2

119861119906119896+1


]

(11)


[[[[[[

[

119909119896+1

119909119896+2

119909119896+3

119909119896+119899

]]]]]]

]119909119896

=

=

=

=

[[[[[[

[

119860

1198602

1198603

119860119899

]]]]]]

]119875119909119909

119909119896+

[[[[[[

[


119860119861 119861 0 sdot sdot sdot 0

1198602

119861 119860119861 119861 sdot sdot sdot 0

0

119860119899minus1

119861 119860119899minus2

119861 119860119899minus3


]]]]]]

]119867119909119909

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(12)



[[[[[[

[

119910119896+1

119910119896+2

119910119896+3

119910119896+119899

]]]]]]

]119910119896

=

=

=

=

[[[[[[

[

119862119860

1198621198602

1198621198603

119862119860119899

]]]]]]

]119875

119909119896

+

[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

119862119860119861 119862119861 0 sdot sdot sdot 0

1198621198602

119861 119862119860119861 119862119861 sdot sdot sdot 0

0

119862119860119899minus1

119861 119862119860119899minus2

119861 119862119860119899minus3

119861 sdot sdot sdot 119862119861

]]]]]]

]119867

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(13)


119909119896= 119875119909119909119909119896+ 119867119909119909119906119896minus1

119910119896= 119875119909119896+ 119867119906119896minus1

(14)



119896is the



119908119896+119894119896

= 119903119896minus (119903119896minus 119910119896) 120595119894

(15)



119910119896+119899

= 119908119896+119899

(16)





119910119896+119899

= 119908119896+119899

= 119903119896minus (119903119896minus 119910119896) 120595119894

(17)


119910119896+119899

= 119875119909119896+ 119867119906119896minus1

= 119903119896minus (119903119896minus 119910119896) 120595119894

(18)

Assuming that 119906119896+119894



119906119896= minus119867

minus1

[119875119909119896+ (119903119896minus (119903119896minus 119910119896) 120595119894

)]

119906119896= minus119870119888119909119896+ 119875119888119903119896

(19)

where119870119888= minus119867

minus1

(119875minusΨ119894

119910119896) and 119875

119888= minus119867

minus1

(1minusΨ119894




1=


1





119894)







119909 (119896119894+ 1) = 119860119909 (119896

119894) + 119861119906 (119896

119894) + 119870ob (119910 (119896119894) minus 119862119909 (119896119894))

(20)

where 119906(119896119894) at time 119896



119909 (119896 + 1) = (119860 minus 119870ob119862) 119909 (119896) (21)






Observer design

PFC algorithm

u

Input r


x

x3

x1x2






119865 = 119896119904119890 (119896) (24)




119865 = 120575119896119904 (25)


119865 = 119882 = 119898119892 (26)

Nat

ural

leng

th

F

F

120575

120575


+r

X

OutPc

Kc

minus


the deflection is

120575 =119898119892

119896119904

(27)




119860 =

[[[[

[

11988611

11988612

11988613

0 1 0

0 0 1

]]]]

]

119861 = [

[

1

0

0

]

]

119862 = [11988811

11988812

11988813]

(28)



Out = 119875119888119903 minus 119870119888119883 (29)





119888is given

by

119870119888= [11989611988811

11989611988812

11989611988813] = [(119862119860119861 + 119862119861) (119862119860

2

minus 1198621205952

)]minus1

(30)


Out = 119875119888119903 minus [119896

1198881111989611988812

11989611988813] [

[

11990911

11990921

11990931

]

]

= 119875119888119903 minus (119896

1198881111990911+ 1198961198881211990921+ 1198961198881311990931)

(31)



119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= 119870(119884 minus 119862 sdot 119872119901(119896 minus 1)) + 119860119872

119901(119896 minus 1)

(32)


119870 = [11989611

11989612

11989613] (33)


119883 (119896) = [

[

11990911(119896)

11990921(119896)

11990931(119896)

]

]

= 119872119901(119896 minus 1) (34)


119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= [11989611

11989612

11989613]

times [

[

119884 (119896) minus 1198881111990111(119896 minus 1)

119884 (119896) minus 1198881211990121(119896 minus 1)

119884 (119896) minus 1198881311990131(119896 minus 1)

]

]

+ [

[

11988611

11988612

11988613

1 0 0

0 1 0

]

]

[

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= (11989611+ 11989612+ 11989613) 119884 (119896)

minus (119896111198881111990111(119896 minus 1) + 119896

121198881211990121(119896 minus 1)

+119896131198881311990131(119896 minus 1))

+ [

[

1198861111990111(119896 minus 1) + 119886

1211990121(119896 minus 1) + 119886

1311990131(119896 minus 1)

11990111(119896 minus 1)

11990112(119896 minus 1)

]

]

(35)

K +

A

C

Y XMx

Mp+minus

1

z



Out = 119875119888119903 (119896) minus (119896

1198881111990911(119896) + 119896

1198881211990921(119896) + 119896

1198881311990931(119896))

(36)


1198991(119896) is


11990911(119896) = 119901

11(119896 minus 1)

11990921(119896) = 119901

21(119896 minus 1)

11990931(119896) = 119901

31(119896 minus 1)

(37)


11990111(119896) = 119867 + 119886

1111990111(119896 minus 1) + 119886

1211990121(119896 minus 1)

+ 1198861311990131(119896 minus 1)

11990121(119896) = 119867 + 119901

11(119896 minus 1)

11990131(119896) = 119867 + 119901

12(119896 minus 1)

(38)


119867 = 119868 minus 119869 (39)

where 119868 = (11989611+ 11989612+ 11989613)119884(119896) 119869 = (119896

111198881111990111(119896 minus 1) +

119896121198881211990121(119896 minus 1) + 119896







119884 (119896) = 119910119865(119896) = 1049074 minus 08437119899

119901 (40)


Controller

Observer



u(k) e(k) F = r(k)

x(k)

z(k)

I(k)intkI

ks+

minus

yF(k)




119903 (119896) = 119896119904119890 (119896) + 119868 (119896) (41)



119868 (119896) = 119896119868120591119890 (119896) + 119868 (119896 minus 1) (42)


time




MATLAB

PC


SHC68-68-EPMcable


devices







MATLAB









119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s









minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











[[[[[[

[

119910119896+1

119910119896+2

119910119896+3

119910119896+119899

]]]]]]

]119910119896

=

=

=

=

[[[[[[

[

119862119860

1198621198602

1198621198603

119862119860119899

]]]]]]

]119875

119909119896

+

[[[[[[

[

119862119861 0 0 sdot sdot sdot 0

119862119860119861 119862119861 0 sdot sdot sdot 0

1198621198602

119861 119862119860119861 119862119861 sdot sdot sdot 0

0

119862119860119899minus1

119861 119862119860119899minus2

119861 119862119860119899minus3

119861 sdot sdot sdot 119862119861

]]]]]]

]119867

times

[[[[[[

[

119906119896

119906119896+1

119906119896+2

119906119896+119899minus1

]]]]]]

]119906119896minus1

(13)


119909119896= 119875119909119909119909119896+ 119867119909119909119906119896minus1

119910119896= 119875119909119896+ 119867119906119896minus1

(14)



119896is the



119908119896+119894119896

= 119903119896minus (119903119896minus 119910119896) 120595119894

(15)



119910119896+119899

= 119908119896+119899

(16)





119910119896+119899

= 119908119896+119899

= 119903119896minus (119903119896minus 119910119896) 120595119894

(17)


119910119896+119899

= 119875119909119896+ 119867119906119896minus1

= 119903119896minus (119903119896minus 119910119896) 120595119894

(18)

Assuming that 119906119896+119894



119906119896= minus119867

minus1

[119875119909119896+ (119903119896minus (119903119896minus 119910119896) 120595119894

)]

119906119896= minus119870119888119909119896+ 119875119888119903119896

(19)

where119870119888= minus119867

minus1

(119875minusΨ119894

119910119896) and 119875

119888= minus119867

minus1

(1minusΨ119894




1=


1





119894)







119909 (119896119894+ 1) = 119860119909 (119896

119894) + 119861119906 (119896

119894) + 119870ob (119910 (119896119894) minus 119862119909 (119896119894))

(20)

where 119906(119896119894) at time 119896



119909 (119896 + 1) = (119860 minus 119870ob119862) 119909 (119896) (21)






Observer design

PFC algorithm

u

Input r


x

x3

x1x2






119865 = 119896119904119890 (119896) (24)




119865 = 120575119896119904 (25)


119865 = 119882 = 119898119892 (26)

Nat

ural

leng

th

F

F

120575

120575


+r

X

OutPc

Kc

minus


the deflection is

120575 =119898119892

119896119904

(27)




119860 =

[[[[

[

11988611

11988612

11988613

0 1 0

0 0 1

]]]]

]

119861 = [

[

1

0

0

]

]

119862 = [11988811

11988812

11988813]

(28)



Out = 119875119888119903 minus 119870119888119883 (29)





119888is given

by

119870119888= [11989611988811

11989611988812

11989611988813] = [(119862119860119861 + 119862119861) (119862119860

2

minus 1198621205952

)]minus1

(30)


Out = 119875119888119903 minus [119896

1198881111989611988812

11989611988813] [

[

11990911

11990921

11990931

]

]

= 119875119888119903 minus (119896

1198881111990911+ 1198961198881211990921+ 1198961198881311990931)

(31)



119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= 119870(119884 minus 119862 sdot 119872119901(119896 minus 1)) + 119860119872

119901(119896 minus 1)

(32)


119870 = [11989611

11989612

11989613] (33)


119883 (119896) = [

[

11990911(119896)

11990921(119896)

11990931(119896)

]

]

= 119872119901(119896 minus 1) (34)


119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= [11989611

11989612

11989613]

times [

[

119884 (119896) minus 1198881111990111(119896 minus 1)

119884 (119896) minus 1198881211990121(119896 minus 1)

119884 (119896) minus 1198881311990131(119896 minus 1)

]

]

+ [

[

11988611

11988612

11988613

1 0 0

0 1 0

]

]

[

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= (11989611+ 11989612+ 11989613) 119884 (119896)

minus (119896111198881111990111(119896 minus 1) + 119896

121198881211990121(119896 minus 1)

+119896131198881311990131(119896 minus 1))

+ [

[

1198861111990111(119896 minus 1) + 119886

1211990121(119896 minus 1) + 119886

1311990131(119896 minus 1)

11990111(119896 minus 1)

11990112(119896 minus 1)

]

]

(35)

K +

A

C

Y XMx

Mp+minus

1

z



Out = 119875119888119903 (119896) minus (119896

1198881111990911(119896) + 119896

1198881211990921(119896) + 119896

1198881311990931(119896))

(36)


1198991(119896) is


11990911(119896) = 119901

11(119896 minus 1)

11990921(119896) = 119901

21(119896 minus 1)

11990931(119896) = 119901

31(119896 minus 1)

(37)


11990111(119896) = 119867 + 119886

1111990111(119896 minus 1) + 119886

1211990121(119896 minus 1)

+ 1198861311990131(119896 minus 1)

11990121(119896) = 119867 + 119901

11(119896 minus 1)

11990131(119896) = 119867 + 119901

12(119896 minus 1)

(38)


119867 = 119868 minus 119869 (39)

where 119868 = (11989611+ 11989612+ 11989613)119884(119896) 119869 = (119896

111198881111990111(119896 minus 1) +

119896121198881211990121(119896 minus 1) + 119896







119884 (119896) = 119910119865(119896) = 1049074 minus 08437119899

119901 (40)


Controller

Observer



u(k) e(k) F = r(k)

x(k)

z(k)

I(k)intkI

ks+

minus

yF(k)




119903 (119896) = 119896119904119890 (119896) + 119868 (119896) (41)



119868 (119896) = 119896119868120591119890 (119896) + 119868 (119896 minus 1) (42)


time




MATLAB

PC


SHC68-68-EPMcable


devices







MATLAB









119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s









minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra











Observer design

PFC algorithm

u

Input r


x

x3

x1x2






119865 = 119896119904119890 (119896) (24)




119865 = 120575119896119904 (25)


119865 = 119882 = 119898119892 (26)

Nat

ural

leng

th

F

F

120575

120575


+r

X

OutPc

Kc

minus


the deflection is

120575 =119898119892

119896119904

(27)




119860 =

[[[[

[

11988611

11988612

11988613

0 1 0

0 0 1

]]]]

]

119861 = [

[

1

0

0

]

]

119862 = [11988811

11988812

11988813]

(28)



Out = 119875119888119903 minus 119870119888119883 (29)





119888is given

by

119870119888= [11989611988811

11989611988812

11989611988813] = [(119862119860119861 + 119862119861) (119862119860

2

minus 1198621205952

)]minus1

(30)


Out = 119875119888119903 minus [119896

1198881111989611988812

11989611988813] [

[

11990911

11990921

11990931

]

]

= 119875119888119903 minus (119896

1198881111990911+ 1198961198881211990921+ 1198961198881311990931)

(31)



119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= 119870(119884 minus 119862 sdot 119872119901(119896 minus 1)) + 119860119872

119901(119896 minus 1)

(32)


119870 = [11989611

11989612

11989613] (33)


119883 (119896) = [

[

11990911(119896)

11990921(119896)

11990931(119896)

]

]

= 119872119901(119896 minus 1) (34)


119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= [11989611

11989612

11989613]

times [

[

119884 (119896) minus 1198881111990111(119896 minus 1)

119884 (119896) minus 1198881211990121(119896 minus 1)

119884 (119896) minus 1198881311990131(119896 minus 1)

]

]

+ [

[

11988611

11988612

11988613

1 0 0

0 1 0

]

]

[

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= (11989611+ 11989612+ 11989613) 119884 (119896)

minus (119896111198881111990111(119896 minus 1) + 119896

121198881211990121(119896 minus 1)

+119896131198881311990131(119896 minus 1))

+ [

[

1198861111990111(119896 minus 1) + 119886

1211990121(119896 minus 1) + 119886

1311990131(119896 minus 1)

11990111(119896 minus 1)

11990112(119896 minus 1)

]

]

(35)

K +

A

C

Y XMx

Mp+minus

1

z



Out = 119875119888119903 (119896) minus (119896

1198881111990911(119896) + 119896

1198881211990921(119896) + 119896

1198881311990931(119896))

(36)


1198991(119896) is


11990911(119896) = 119901

11(119896 minus 1)

11990921(119896) = 119901

21(119896 minus 1)

11990931(119896) = 119901

31(119896 minus 1)

(37)


11990111(119896) = 119867 + 119886

1111990111(119896 minus 1) + 119886

1211990121(119896 minus 1)

+ 1198861311990131(119896 minus 1)

11990121(119896) = 119867 + 119901

11(119896 minus 1)

11990131(119896) = 119867 + 119901

12(119896 minus 1)

(38)


119867 = 119868 minus 119869 (39)

where 119868 = (11989611+ 11989612+ 11989613)119884(119896) 119869 = (119896

111198881111990111(119896 minus 1) +

119896121198881211990121(119896 minus 1) + 119896







119884 (119896) = 119910119865(119896) = 1049074 minus 08437119899

119901 (40)


Controller

Observer



u(k) e(k) F = r(k)

x(k)

z(k)

I(k)intkI

ks+

minus

yF(k)




119903 (119896) = 119896119904119890 (119896) + 119868 (119896) (41)



119868 (119896) = 119896119868120591119890 (119896) + 119868 (119896 minus 1) (42)


time




MATLAB

PC


SHC68-68-EPMcable


devices







MATLAB









119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s









minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra













119888is given

by

119870119888= [11989611988811

11989611988812

11989611988813] = [(119862119860119861 + 119862119861) (119862119860

2

minus 1198621205952

)]minus1

(30)


Out = 119875119888119903 minus [119896

1198881111989611988812

11989611988813] [

[

11990911

11990921

11990931

]

]

= 119875119888119903 minus (119896

1198881111990911+ 1198961198881211990921+ 1198961198881311990931)

(31)



119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= 119870(119884 minus 119862 sdot 119872119901(119896 minus 1)) + 119860119872

119901(119896 minus 1)

(32)


119870 = [11989611

11989612

11989613] (33)


119883 (119896) = [

[

11990911(119896)

11990921(119896)

11990931(119896)

]

]

= 119872119901(119896 minus 1) (34)


119872119901(119896)

= [

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= [11989611

11989612

11989613]

times [

[

119884 (119896) minus 1198881111990111(119896 minus 1)

119884 (119896) minus 1198881211990121(119896 minus 1)

119884 (119896) minus 1198881311990131(119896 minus 1)

]

]

+ [

[

11988611

11988612

11988613

1 0 0

0 1 0

]

]

[

[

11990111(119896)

11990121(119896)

11990131(119896)

]

]

= (11989611+ 11989612+ 11989613) 119884 (119896)

minus (119896111198881111990111(119896 minus 1) + 119896

121198881211990121(119896 minus 1)

+119896131198881311990131(119896 minus 1))

+ [

[

1198861111990111(119896 minus 1) + 119886

1211990121(119896 minus 1) + 119886

1311990131(119896 minus 1)

11990111(119896 minus 1)

11990112(119896 minus 1)

]

]

(35)

K +

A

C

Y XMx

Mp+minus

1

z



Out = 119875119888119903 (119896) minus (119896

1198881111990911(119896) + 119896

1198881211990921(119896) + 119896

1198881311990931(119896))

(36)


1198991(119896) is


11990911(119896) = 119901

11(119896 minus 1)

11990921(119896) = 119901

21(119896 minus 1)

11990931(119896) = 119901

31(119896 minus 1)

(37)


11990111(119896) = 119867 + 119886

1111990111(119896 minus 1) + 119886

1211990121(119896 minus 1)

+ 1198861311990131(119896 minus 1)

11990121(119896) = 119867 + 119901

11(119896 minus 1)

11990131(119896) = 119867 + 119901

12(119896 minus 1)

(38)


119867 = 119868 minus 119869 (39)

where 119868 = (11989611+ 11989612+ 11989613)119884(119896) 119869 = (119896

111198881111990111(119896 minus 1) +

119896121198881211990121(119896 minus 1) + 119896







119884 (119896) = 119910119865(119896) = 1049074 minus 08437119899

119901 (40)


Controller

Observer



u(k) e(k) F = r(k)

x(k)

z(k)

I(k)intkI

ks+

minus

yF(k)




119903 (119896) = 119896119904119890 (119896) + 119868 (119896) (41)



119868 (119896) = 119896119868120591119890 (119896) + 119868 (119896 minus 1) (42)


time




MATLAB

PC


SHC68-68-EPMcable


devices







MATLAB









119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s









minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










Controller

Observer



u(k) e(k) F = r(k)

x(k)

z(k)

I(k)intkI

ks+

minus

yF(k)




119903 (119896) = 119896119904119890 (119896) + 119868 (119896) (41)



119868 (119896) = 119896119868120591119890 (119896) + 119868 (119896 minus 1) (42)


time




MATLAB

PC


SHC68-68-EPMcable


devices







MATLAB









119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s









minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra












MATLAB









119878) 079 s 112 s

Rise time (119879119877) 057 s 080 s









minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0

100

200

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus2000

200

Cont

rol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)




119878) 02788 s 0935 s

Rise time (119879119877) 01601 s 03616 s



1 is 2



119878) rise time


119904119904) PFC-O










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










minus200

0

200Fo

rce (

N)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

0

100200

300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


minus400minus200

0200

Forc

e (N

)

0 2 4 6 8 10 12 14 16 18Time (s)

(a)

minus1000

100200300

Con

trol s

igna

ls

0 2 4 6 8 10 12 14 16 18Time (s)


(b)


0 20 40 60 80 100 1200

20

40

60

80

100

120

Position (mm)

Forc

e (N

)

ks(Sim) = 05

ks(Sim) = 1

ks(Sim) = 2

ks(NI)= 05

ks(NI) = 1

ks(NI) = 2

ks(Emb) = 1

ks(Emb) = 2

ks(Emb) = 25






0

20

40

60

80

100

120

Posit

ion

(mm

)

0 2 4 6 8 10 12 14 16 18Time (s)


ks(Sim) = 1


ks (Sim) = 2

ks(NI) = 2

ks(NI) = 1

ks(Emb) = 2

ks(Emb) = 1

ks(Emb) = 05








15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra










15 20 25 3040

50

60

70

80

90

100

110

Time (s)

Posit

ion

(mm

)

ks(NI) = 05

ks(NI) = 1


ks(Emb) = 1

ks(Emb) = 2




119904








8 Conclusion





Acknowledgments


References
































Volume 2014




Journal of











Journal of


Function Spaces






Algebra





























Volume 2014




Journal of











Journal of


Function Spaces






Algebra









research article system identification and embedded controller design for pneumatic ... · 2019. 7....

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