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14
BC
[1] W.K. Lai, M.F. Rahmat and N. Abdul Wahab, Modeling and Controller Design of Pneumatic Actuator
System with Control Valve, International Journal of Smart Systems, VOL. 5, NO. 3, 2012.
[2] R. B. Varseveld, et al., Accurate Position Control of a Pneumatic Actuator Using On/Off Solenoid Valves,
IEEE/ASME Trans On Mechatronics, Vol. 2, No 3, pp. 195-204, 1997.
[3] J. L. Shearer, Study of Pneumatic Process in the Continuous Control of Motion With Compressed Air,
Transactions of the ASME, pp. 233-249, 1956.
[4] J.E. Bobrow, F. Jabbari, Adaptive Pneumatic Force Actuation and Position Control, ASME Journal of
Dynamic Systems, Measurement, and Control, Vol. 113, pp. 267-272, 1991.
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1387
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[6] X. Shen, J. Zhang, E. J. Barth, M. Goldfarb, Nonlinear Averaging Applied to the Control of Pulse Width
Modulated (PWM) Pneumatic Systems, American Control Conference, FrA16.3, 2004.
[7] C. L. Chen, P. C. Chen, C. K. Chen, A Pneumatic Model-Following Control System using a Fuzzy
Adaptive Controller, Automatica, Volume 29, Issue 4, Pages 1101-1105, 1993.
[8] C. Ying al. et, Design and Hybrid Control of the Pneumatic Force-Feedback Systems for Arm-Exoskeleton
by using On/Off Valve, Mechatronics, Vol. 17, Issue 6, Pages 325-335, 2007.
[9] H. Schulte, H. Hahn, Fuzzy State Feedback Gain Scheduling Control of Servo-Pneumatic Actuators,
Control Engineering Practice, Vol. 12, Issue 5, Pages 639-650, 2004
[10] M. Taghizadeh, A. Ghaffari, F. Najafi, Modeling and identification of a solenoid valve for PWM control
applications, C. R. Mecanique, 337 131–140, 2009.
[11] Najafi, F., Fathi, M., Saadat, M., Dynamic Modelling of Servo Pneumatic Actuators with Cushioning,
International Journal of Advanced Manufacture Technology 42:757–765, 2009.
[12] J. J. Slotine, W. Li, Applied Nonlinear Control, Prentice Hall, 1991.
[13] Liu, J., Wang, X, Advanced Sliding Mode Control for Mechanical Systems, Tsinghua University
Press Beijing, 2012.
15
Fuzzy-Sliding Mode Controller is Designed to Control the Servo Actuator Pneumatic Solenoid
Valves using a Genetic Algorithm
M.Siavash1
, M.Hasanlou2
, F.Najafi3
, A.Bagheri4
MS Student Mechanical Engineering, University of Guilan, Iran
MS Student Mechanical Engineering, University of Guilan, Iran
Associate Professor of Mechanical Engineering, University of Guilan, Iran
Professor of Mechanical Engineering, University of Guilan, Iran
In this study, position control servo-pneumatic system is done by on/off solenoid valves. Nonlinear
behavior of air in pneumatic systems leads to difficulties in controlling these systems. Therefore, in
order to control the position of the pneumatic model, Sliding Mod nonlinear controller is considered.
First, using pulse width modulation algorithm, control command converts into pulses for on/off
solenoid valves. Then, Sliding Mod controller is designed to trace an optimal situation. Due to
environmental disturbances for robustness of the controller, coefficients are considered as fuzzy.
Moreover, setting fuzzy membership functions and controller coefficients for performance
improvement have been obtained by using genetic algorithm. Finally, the designed controller was
tested with fuzzy controller under different standard inputs and the results were revealed.

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Fuzzy-Sliding Mode Controller is Designed to Control the Servo Actuator Pneumatic Solenoid Valves using a Genetic Algorithm

  • 1. 1 Fuzzy-Sliding Mod ! " # $ % & ' ( )* + !, - # +./ 1 1 2 3 4 2 +3 ,' 6 4 3 ! , 4 4 1 ,# # ! 39 * MostaphaSiavashi@gmail.com 2 ,# # ! 39 * M.Hasanlou@aol.com 3 4 ), : ! " # $% & ' () * +" , - . /0 /23% 4 5 ) 4 6 7 7 .# 9 3: ! 6 4 6 ! +" & ' 6 4 7 , ( : (; " 6 # +" # $% & ' 4 , <) . & 9 ) ' 3: Sliding Mod 7 ( = #!> .# ) ? @ , 4 A B " C) A (, ) ' C) A . 7 /" D /0 /23% 4 5 ) 4 6 7 4 , " 6 ) ' CE Sliding Mod , " 4 , % 7 F G H I3 # $ .# - * = J, 3 K L 7 9 ; #IM (, = 4? L N, O" P ) ' , 7 ( . + QJ6 ' O" P 4? #" RM 2, = , ) 4 # , S " ) 4 , , IJM D , .# T 7 F G ) ' #" 4 #K U" ?T VI > 4 6 (!" * (5 W" ( % 7 .# )% , " # $% & ' Fuzzy Sliding Mod C) A 4 A B ,; 7 >, 4 J , ? 4 (Q 6 DNM LB : 6 , I 4 .# L X . ? @ (, 4 6 IJM 4 J$ / M & , Y 4X J B , !, ? (, #D! / ) 6 L , #: # ; D L + " A ( "X @ ! , Z RM , / $ 4 , " 6 >, ? . 7 , [" " 4 6 IJM , ' O; (' " 6 >, ' # 0 : ." / M & 4 "<A @ (, +" , , .# 4 6 ' / ) 7XA ( ? 6 IJM +" [" # J6 " (' B , J" ]3 ^ % & ' I; 4 P -?B , Z RM " O T _M , +" +" ? . ' ^ *K (, , IJM & D & ' -X #: , (' !6 B , #% ' # ; VI > 4 6 4 6 "T . 7 ( , >,
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  • 3. 3 / 7 1 : ! , =>* " LB $ OJ) ' l 30 + = , ( G I u : (, (; , IJM ! A #' F - # " /0 F D!i c , ? !" "T #M , B , / ) (, X I " 4 6 "T 7 w , " T f K , X i 4S & D I /: .# / 7 2 : IJM ?T - " / 7 ^, 3 2 M " LB $ , IJ LB $ L N 1 4 7 , ] 5 [ . ) 1 ( ) 2 ( ) 3 ( ) 4 ( !, - ! " #
  • 4. 4 7 4 6 ) 4 5 !* B ! G ) ! "? ( (, 7 ] 10 , - " .[ 7 ' I ) !* +" , 4 5 4 4 , ; : 6 T + , U ' 6 / 7 3 7 .# / 7 3 4 5 I 7 ' I, - " : ! "? H !K " ! ! G ) 4 6 z A 4 / ) + J6 (, 7 < 4 6 , 6 : (, ! "? . /JM 3: 9 E - ; " L 0 QJ6 (' X B ! "? . ' & ( 7 ( , + ,) C @" " 7 " ; 4 , C @" I' LB $ , 6 4 6 1 . ' & , 1 ? & 1 '( !( " ? ! "? +" 7 / ! G ) # , ! "? +" 4 , (' ) .# ( (, " , "T 4 (, (' ' /" D ; : ! G ) 4 " (, 4 S ) (' 7 , ! "? . 7 ! G ) / 7 4 7 .# / 7 4 ) ! "? : ! G ! G +" 4 , :#7 ) 5 ( 1 Turbulent Flow
  • 5. 5 T (' 4 6 $ { A (, ! G L 7 . !6 " 6 (I0 ( !6 O " 6 (I0 ( !6 ! G & G .# ! G & $ & G # , "? (3, ? : "T ) 6 ( T (' (, , 6 ( !6 4 "<A| @ O" P O .# ( !6 D! 4 "<A| @ O" P (I0 (' , /' " 6 6 (I0 * ? 7 / #, c " .# () $ ? 5 (, ! G C ' "? 4 , f, (, # $% ? $, L 0 # : "T ) 7 ( ) 8 ( T (' ! G 7 7 ) i c 23* ]3 .# 7 ! : , , 6 : , , ! G C ' ) 9 ( ! "? +" #) F () $ b . V 7 ' S ) % & JM , 1 , : T # ) 10 ( T (' 4 S ) .# " ) " ; ? 4 ^ , : " ) 11 ( LB $ ? 10 11 } > "? / 7 (, ! 3: 9 #) F () $ + ) : 7 ) 12 ( 1 Kirchhoff’s Voltage Law
  • 6. 6 , & 1 '( !( ! "? " & $ - ; - - E % 4 4 ! G 4 6 c #K (' # Y , . % ? @ + - :#7 ) 13 ( T (' - ; E O" P ( ) & G 4 4 .# 4 4 : ? O" * "? (3, , ) 14 ( T (' (Q" 7 ; : 2D 4 6 23* ]3 4 c VI > 4 6 #F ! = 7 . 4 6 , , D" * / ) + J6 (, . c 4 " .# + = , & F () $ !" ? , #) F 4 6 $, 13 , #) F LB $ "? L N : "T ) 15 ( , > & 1 '( !( , " () $ ? 7 6 " ; , = J @ 6 " ; 4 , C @ 2, ? () $ +" . 7 ^ > 0 "? " ; "S 4 , VI > 7 / ! 7 " ; (' " . T ? .# ' ( = "<A + " A #D! % . 7 ) # ) ("< 2D (, ( K, * ? J' ( " ; "S 7 (, , " ; , ^ > L 0 ( !, 6 (, 3: 9 L N #D! +" % . 7 j X, 7 , K, * ? , L 0 "? #M (, " ; D # B , (, f* 3: L N f . 7 () $ ]# "? / 7 (, C @" " ? ; " ; ~ 4 , 11 :[ ) 16 (
  • 7. 7 T (' # B , 7 ( I> O" P 3 (=K) 6 7 C @" 23* ] ' 4 . 7 , + QJ6 :# # B , (, # + " A #D! ) 17 ( * b :( 7 !, & [" 4 #D! (, ) 18 ( T 7 ( !, ? , #M (, !, 6 7 C @" 23* ]3 * (D K "? f, ? (' . 6 ] 7 11 .[ ) 19 ( ) 20 ( (' (, 7 7 ( !, 7? , 4 , -?B ? O . 7 , Fuzzy-Sliding Mod 7X) ) ' QJ6 3: 9 4 6 ) ' = ! LB $ , 3: 9 #IM (, D H > (, #M # $% ) ' 4 M (, + = , . 7 , / 7 (, ! LB $ #) F 4 6 M (5 /, % "? : 7 , ) 21 ( T (' .# * u + $ ) ' % f (=K) 6 + $ 4 , . 7 u `X) ]3 , 1 V" $ "? L N, 7 ] 12 [ ) 22 ( T (' , .# H I3 # $% " J6 #M , (' # #D• #, c A " X . € D (3, u E I #: ? L N, ! & $ & ' (3, 23 # , "T ] 12 [ : 1 Sliding Surface
  • 8. 8 ) 23 ( , `X) € 7 4 P = (, #" # M Y , ( A - " ' ( P s L N, ) ' & (3, 14 , 6 : ] 12 [ : ) 24 ( (3, 24 O" P ( (, " , ' @" ) ' , U* ? } : 4 , ! 4 " A (' 7 H > 4 ]3 s , = +" (, . 7 , % , + = " u A ) 2, M (, ] 13 [ : ) 25 ( (3, 4 % , 4 , 25 #! ' 7 , #D• % 3 K L 7 9 #K # + J ! ( " (, (; , (' $% 4 3: ^ 3: #" RM 2, Y , 4? L N, A +" , 4 $, ! A # .# 7 ( = ; : $, 3: ^ 3: 4 , 4? #" RM 2, 4 ? , + , (' # $% [0,1] 7 #7 ? , + , (' ; : [0,120] * 4 , / 7 5 7 .# 7 / 7 5 # $% 4 3: #" RM 2, :
  • 9. 9 Degree of Membership / 7 6 # $% 4 3: ^ #" RM 2, : / 7 7 ) ' , #" RM 2, : , • 0 "? L N, T # , ) ' % `X) ]3 " X B , C ' L 2 = J : 7 ) 26 ( (' S " ) f ) ' 4 O" P " J6 T * # `X) ]3 & F 4? ("B # >P .# 7 + $ @' ! "# MATLAB/Simulink $ %& .( )* + & , - & . 1 *0 . )* + 1 : , & 2 345& , - ! & 6 160[mm] 7 # 60[Hz]
  • 10. 10 8 9: 16[mm] 7 ;$ * <9%& =9 10 [mm2 ] > - . & 9: 6[mm] ? 5# 600 [kPa] > @ * > & 1.7[msec.] A B;C& * 5# 100 [kPa] > D & 8 > & 2[msec.] B;C& * & A 293 [K] ( O 7 (IA 4 i #K # $% 4 3: # $% J / 7 4 4 6 8 15 .# 7 / 7 8 4 O *$ : / 7 9 4 O *$ 4 3: :
  • 11. 11 / 7 10 (IA 4 O *$ : / 7 11 (IA 4 O *$ 4 3: :
  • 12. 12 / 7 12 O 7 4 O *$ : / 7 13 O 7 4 O *$ 4 3: :
  • 13. 13 / 7 14 ( 4 O *$ : 4 / 7 15 ( 4 O *$ 4 3: : 4 3 ! A G = J, ^ *K +" L #: F IJM " # $% & ' >, % u 6 (IJM (" A T 4 ) 3: #' F (' # +" u 6 $, IJM +" H > / ) .# + QJ6 .# 6 IJM " 4 , 4 -X ." 4 , 4 6 IJM & ' #: ' # ; " 6 4 6 "T (, J (' J , >, 7 ' F / i M > L $" P c ? , ! "? LB $ Y , , +" , , . " J 4 6 ) ' F G (, CE T # , ) Fuzzy-Sliding Mod ( , 4? 7 ( : A T 4 6 A = (; , . 7 (5 W" (, . J ^" N ) ' ! 4 IJM #K0
  • 14. 14 BC [1] W.K. Lai, M.F. Rahmat and N. Abdul Wahab, Modeling and Controller Design of Pneumatic Actuator System with Control Valve, International Journal of Smart Systems, VOL. 5, NO. 3, 2012. [2] R. B. Varseveld, et al., Accurate Position Control of a Pneumatic Actuator Using On/Off Solenoid Valves, IEEE/ASME Trans On Mechatronics, Vol. 2, No 3, pp. 195-204, 1997. [3] J. L. Shearer, Study of Pneumatic Process in the Continuous Control of Motion With Compressed Air, Transactions of the ASME, pp. 233-249, 1956. [4] J.E. Bobrow, F. Jabbari, Adaptive Pneumatic Force Actuation and Position Control, ASME Journal of Dynamic Systems, Measurement, and Control, Vol. 113, pp. 267-272, 1991. ] 5 [ D 6 .F 4)* ( ,2 .F 4& G' ( . 4 +3 .H " ) ? @ , ! " # $% 4? & ' ( IIJ) + ,) ( B C @ ' + J6 X 7 C) A 4 A B 1387 . [6] X. Shen, J. Zhang, E. J. Barth, M. Goldfarb, Nonlinear Averaging Applied to the Control of Pulse Width Modulated (PWM) Pneumatic Systems, American Control Conference, FrA16.3, 2004. [7] C. L. Chen, P. C. Chen, C. K. Chen, A Pneumatic Model-Following Control System using a Fuzzy Adaptive Controller, Automatica, Volume 29, Issue 4, Pages 1101-1105, 1993. [8] C. Ying al. et, Design and Hybrid Control of the Pneumatic Force-Feedback Systems for Arm-Exoskeleton by using On/Off Valve, Mechatronics, Vol. 17, Issue 6, Pages 325-335, 2007. [9] H. Schulte, H. Hahn, Fuzzy State Feedback Gain Scheduling Control of Servo-Pneumatic Actuators, Control Engineering Practice, Vol. 12, Issue 5, Pages 639-650, 2004 [10] M. Taghizadeh, A. Ghaffari, F. Najafi, Modeling and identification of a solenoid valve for PWM control applications, C. R. Mecanique, 337 131–140, 2009. [11] Najafi, F., Fathi, M., Saadat, M., Dynamic Modelling of Servo Pneumatic Actuators with Cushioning, International Journal of Advanced Manufacture Technology 42:757–765, 2009. [12] J. J. Slotine, W. Li, Applied Nonlinear Control, Prentice Hall, 1991. [13] Liu, J., Wang, X, Advanced Sliding Mode Control for Mechanical Systems, Tsinghua University Press Beijing, 2012.
  • 15. 15 Fuzzy-Sliding Mode Controller is Designed to Control the Servo Actuator Pneumatic Solenoid Valves using a Genetic Algorithm M.Siavash1 , M.Hasanlou2 , F.Najafi3 , A.Bagheri4 MS Student Mechanical Engineering, University of Guilan, Iran MS Student Mechanical Engineering, University of Guilan, Iran Associate Professor of Mechanical Engineering, University of Guilan, Iran Professor of Mechanical Engineering, University of Guilan, Iran In this study, position control servo-pneumatic system is done by on/off solenoid valves. Nonlinear behavior of air in pneumatic systems leads to difficulties in controlling these systems. Therefore, in order to control the position of the pneumatic model, Sliding Mod nonlinear controller is considered. First, using pulse width modulation algorithm, control command converts into pulses for on/off solenoid valves. Then, Sliding Mod controller is designed to trace an optimal situation. Due to environmental disturbances for robustness of the controller, coefficients are considered as fuzzy. Moreover, setting fuzzy membership functions and controller coefficients for performance improvement have been obtained by using genetic algorithm. Finally, the designed controller was tested with fuzzy controller under different standard inputs and the results were revealed.