Robust Control of DC Motor Using Fuzzy Sliding Mode Control with Fractional PID Compensator

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1 Y. heidri, A. R. Noee, H. Ali Shynfr,S. Slehi / TJMCS Vol.1 No.4 (21) The Journl of Mthemtic nd Computer Science Avilble online t The Journl of Mthemtic nd Computer Science Vol.1 No.4 (21) Robut Control of DC Motor Uing Fuzzy Sliding Mode Control with Frctionl PID Compentor Yghoub heidri 1,*, Abolfzl Rnjbr Noee 2, Heydr Ali Shynfr 3,Soheil Slehi 4 Deprtment of Electricl, Nour Brnch, Ilmic Azd Univerity, Nour, Irn Bbol Nohirvny Univerity of Technology,.rnjbr@nit.c.ir Irn Univerity of Science nd Technology, Hhynfr@ut.c.ir Bbol Nohirvny Univerity of Technology, oheillehy@yhoo.com Received: July 21, Revied: September 21 Online Publiction: December 21 Abtrct Thi pper preent robut fuzzy liding mode control cheme nd the dditionl compentor. The dditionl compentor relying on the lidingmode theory i ued to improve the dynmicl chrcteritic of the drive ytem. Sliding mode control method i tudied for controlling DC motor becue of it robutne gint model uncertintie nd externl diturbnce. In thi method, uing high control gin to overcome uncertintie led to occur chttering phenomen in control lw which cn excite unmodeled dynmic nd mybe hrm the plnt. In order to enhncement the liding mode controller performnce, we hve ued fuzzy logic. For thi purpoe, we hve ued Frctionl PID outer loop in the control lw then the gin of the liding term nd Frctionl PID term re tuned on-line by fuzzy ytem, o the chttering i voided nd repone of the ytem i improved gint externl lod torque here. Preented implementtion reult on DC motor confirm the bove clim nd demontrte the performnce improvement in thi ce. Keyword: Fuzzy logic, Frctionl PID, liding mode, DC motor. 1,* Correponding Author: E-mil ddre: mudheidri@yhoo.com (Phone: ) 238

2 Y. heidri, A. R. Noee, H. Ali Shynfr,S. Slehi / TJMCS Vol.1 No.4 (21) Introduction The PID controller i by fr the mot dominting form of feedbck in ue tody. Due to it functionl implicity nd performnce robutne, the proportionl-integrl-derivtive controller h been widely ued in the proce indutrie [1]. For deign nd tuning of PID controller prmeter we ue optimiztion method. Specifiction, tbility, deign, ppliction nd performnce of the PID controller hve been widely treted, but generliztion of the PID controller, nmely the PI D controller, involving n integrtor of order λ nd differentitor of order µ h the better repone in comprion with the clicl PID controller. The form of frctionl PID followed by: k i C ( ) K P K d S (1) S The interet of thi kind of controller i jutified by better flexibility, ince it exhibit frctionl power (, ) of the integrl nd derivtive prt, repectively. Thu, five prmeter cn be tuned in thi tructure (,, k, k, k p i d ), tht i, two more prmeter thn in the ce of conventionl PID controller ( 1, 1). They re widely ue in indutry [2,3]. A genetic lgorithm w ued to find the optimum tuning prmeter of the Frctionl PID controller by tking integrl bolute error fitting function [4]. Sliding mode control (SMC) i one of the populr trtegie to del with uncertin control ytem [5-7]. The min feture of SMC i the robutne gint prmeter vrition nd externl diturbnce. Vriou ppliction of SMC hve been conducted, uch robotic mnipultor, ircrft, DC motor, chotic ytem, nd o on [8-1]. The liding mode control i robut to plnt uncertintie nd inenitive to externl diturbnce. It i widely ued to obtin good dynmic performnce of controlled ytem. However, the chttering phenomen due to the finite peed of the witching device cn ffect the ytem behvior ignificntly. Additionlly, the liding control require the knowledge of mthemticl model of the ytem with bounded uncertintie. Reduced chttering my be chieved without crificing robut performnce by combining the ttrctive feture of fuzzy control with SMC. Fuzzy logic i potent tool for controlling ill-defined or prmeter-vrint plnt. By generlizing Fuzzy rule, Fuzzy logic controller cn cope well with evere uncertintie. Fuzzy cheme with explicit expreion for tuning cn void the hevy computtionl burden [11-14]. It i necery to know ytem mthemticl model or to mke ome experiment for tuning PID prmeter. However, it h been known tht conventionl PID controller generlly do not work well for non-liner ytem, nd prticulrly complex nd vgue ytem tht hve no precie mthemticl model. To overcome thee difficultie, vriou type of modified conventionl PID controller uch uto-tuning nd dptive PID Controller were developed ltely. Alo Fuzzy Logic Controller (FLC) cn be ued for thi kind of problem. When compred to the conventionl controller, the min dvntge of Fuzzy logic i tht no mthemticl modeling i required [15-17] In thi pper the combined olution we hve propoed nd deigned robut controller. We hve ued Frctionl PID outer loop in the control lw then the gin of the liding term nd Frctionl PID term re tuned on-line by Fuzzy ytem. 2. Model of DC Motor DC motor re widely ued in indutril nd dometic equipment. The control of the poition of motor with high ccurcy i required. The electric circuit of the rmture nd the free body digrm of the rotor re hown in fig

3 Y. heidri, A. R. Noee, H. Ali Shynfr,S. Slehi / TJMCS Vol.1 No.4 (21) Fig. 1: The tructure of DC motor A deired peed my be trcked when deired hft poition i lo required. In fct, ingle controller my be required to control both the poition nd the peed. The reference ignl determine the deired poition nd/or peed. The controller i elected o tht the error between the ytem output nd reference ignl eventully tend to it minimum vlue, idelly zero. There re vriou DC motor type. Depending on type, DC motor my be controlled by vrying the input voltge whilt nother motor only by chnging the current input. In thi pper DC motor i controlled vi the input voltge. The control deign nd theory for controlling DC motor vi current i nerly the me. For implicity, contnt vlue reference ignl i injected to the ytem to obtin deired poition. However, the method work uccefully for ny reference ignl, prticulrly for ny tepwie time-continuou function. Thi ignl my be periodic ignl or ny ignl to get deired hft poition, i.e. deired ngle between nd 36 degree from virtul horizontl line. The dynmic of DC motor my be expreed : di V t RI L E dt d T J B T l dt (2) T K I E T K d dt With the following phyicl prmeter: E : The input terminl voltge (ource), (v); E b : The bck emf, (v); R : The rmture reitnce, (ohm); I : The rmture current (Amp); L : The rmture inductnce, (H); J :The moment inertil of the motor rotor nd lod, (Kg.m 2 / 2 ); T : The motor torque, (Nm) : The peed of the hft nd the lod (ngulr velocity), (Rd/); : The hft poition, (rd); B : The dmping rtio of the mechnicl ytem, (Nm); T k : The torque fctor contnt, (Nm/Amp); B : The motor contnt (v-/ rd). k 24

4 Y. heidri, A. R. Noee, H. Ali Shynfr,S. Slehi / TJMCS Vol.1 No.4 (21) Block digrm of DC motor i hown in fig. 2. Fig. 2: The block digrm of DC motor 3. Sliding mode controller A Sliding Mode Controller i Vrible Structure Controller (VSC). Biclly, VSC include everl different continuou function tht cn mp plnt tte to control. Surfce nd the witching mong different function re determined by plnt tte tht i repreented by witching function. Without lot of generlity, conider the deign of liding mode controller for the following econd order ytem: Here ut () i the input to the ytem: u u u (3) eq Where u k t nd contnt fctor define the thickne of the boundry lyer. St i turtion function tht i defined : if 1 t gn if 1 The function between u nd i hown: (4) Fig3: Switching urfce in the phe plne The control trtegy dopted here will gurntee the ytem trjectorie move towrd nd ty on the liding urfce from ny initil condition if the following condition meet: (5) Where i poitive contnt tht gurntee the ytem trjectorie hit the liding urfce in 241

5 Y. heidri, A. R. Noee, H. Ali Shynfr,S. Slehi / TJMCS Vol.1 No.4 (21) finite time.uing ign function often cue chttering in prctice. One olution i to introduce boundry lyer round the witch urfce. Thi controller i ctully continuou pproximtion of the idel rely control. The conequence of thi control cheme i tht invrince of liding mode control i lot. The ytem robutne i function of the width of the boundry lyer. The principle of deigning liding mode control lw for rbitrry-order plnt i to mke the error nd derivtive of error of vrible i forced to zero. In the DC motor ytem the poition error nd it derivtive re the elected coordinte vrible thoe re forced to zero. Switching urfce deign conit of the contruction of the witching function. The trnient repone of the ytem i determined by thi witching urfce if the liding mode exit. Firt, the poition error i introduced: e k k k (6) ref Where ref k, k, re the repective repone of the deired reference trck nd ctul rotor poition, t the K the mpling intervl nd ek i the poition error. The liding urfce () i defined with the trcking error (e) nd it integrl ( e dt ) nd rte of chnge ( e ) e 1e 2e dt (7) Where 1, 2 re trictly poitive rel contnt. The bic control lw of Sliding Mode Controller i given by: U k (8) gn Where K i contnt prmeter, ign ( ) i the ign function nd S i the witching function. 4. Deign of Fuzzy Frctionl PID Sliding Mode Controller In thi ection, fuzzy liding urfce i introduced to develop liding mode controller. Which the expreion k t i replced by n inference fuzzy ytem for eliminte the chttering phenomenon. In ddition, to improve the repone of ytem gint externl lod torque, the liding mode controller deign with Frctionl PID out loop. The deigned fuzzy logic controller h two input nd n output. The input re liding urfce () nd the chnge of the liding urfce in mple time, nd output i the fuzzy gin ( k ).The fuzzy controller conit of three tge: Fuzzyfiction, inference engine nd Defuzzyfiction. Then, 7*7 rule be w defined (Tble 1) to develop the inference ytem. Both Fuzzyfiction nd inference ytem were tuned experimentlly. The memberhip function of input vrible re depicted in Fig. 4, 5. fuzz u Tble 1. Fuzzy Frctionl PID Sliding Mode Rule Tble PB PM PS ZE NS NM NB PB NB NB NB NB NM NS ZE PM NB NB NB NM NS ZE PS PS NB NB NM NS ZE PS PM ZE NB NM NS ZE PS PM PB NS NM NS ZE PS PM PB PB NM NS ZE PS PM PB PB PB NB ZE PS PM PB PB PB PB 242

6 Y. heidri, A. R. Noee, H. Ali Shynfr,S. Slehi / TJMCS Vol.1 No.4 (21) Where NB=Negtive big; NS: Negtive Smll; Z: Zero; PS: Poitive Smll; PB: Poitive Big; M: Medium. The liding function i defined : e 1e 2edt (9) Where 1, 2 re trictly poitive rel contnt. The control lw i defining : u k k gn (1) Where k k e k e k edt, k N k, k Nk function. Trcking loop for out frctionl PID nd, v fuzz fuzz k k re gin to enure for tbility nd gn i ign Fig. 4: Memberhip function for () normlized input Fig. 5: Memberhip function for ( ) normlized input 5. Simultion reult In thi ection, the overll model of DC motor with liding mode controller nd fuzzy logic nd PID i implemented in MATLAB/Simulink. The imulink model of the FPIDSMC with Fuzzy urfce i hown in fig

7 Y. heidri, A. R. Noee, H. Ali Shynfr,S. Slehi / TJMCS Vol.1 No.4 (21) Fig.6: Simulink block digrm of FPIDSMC Fig, 7 how the controller repone of ytem gint uncertintie in the ytem, when the implemented controller repectively re Frctionl PID with ignum function, PID liding mode with Fuzzy urfce, Frctionl PID liding mod with Fuzzy urfce. 3 FPID liding mode control with Signum function PID liding mode control with Fuzzy urfce FPID liding mode control with Fuzzy urfce Time () Fig. 7: Simulted reult comprion between the Frctionl PID with ignum function, PID liding mode with Fuzzy urfce, Frctionl PID liding mod with Fuzzy urfce gint uncertintie 244

8 u(t) u(t) u(t) Y. heidri, A. R. Noee, H. Ali Shynfr,S. Slehi / TJMCS Vol.1 No.4 (21) FPID liding mode control with Signum function PID liding mode control with Fuzzy urfce FPID liding mode control with Fuzzy urfce Time () Fig. 8: Control ignl comprion between the Frctionl PID with ignum function, PID liding mode with Fuzzy urfce, Frctionl PID liding mod with Fuzzy urfce gint uncertintie 6. Concluion In thi pper, robut control ytem with the fuzzy liding mode controller nd the dditionl compentor i preented for DC motor poition control. According to the imultion reult, the Frctionl PIDSMC with Fuzzy urfce nd PIDSMC with Fuzzy urfce controller cn provide the propertie of inenitivity nd robutne to uncertintie nd externl diturbnce, nd repone of the DC motor for the Frctionl PIDSMC with Fuzzy urfcecontroller gint uncertintie nd externl diturbnce i the very better nd moother thn of the repone of PIDSMC with Fuzzy urfce nd Frctionl PID with ignum function. Alo, comprion between the poition control of the DC motor by Frctionl PIDSMC with Fuzzy urfce nd PIDSMC with Fuzzy urfce how clerly tht the FPIDSMC give better performnce thn PIDSMC gint externl lod torque. So propoed controller i robut controller, nd the chttering i voided nd repone of the ytem i improved gint externl lod torque. Reference [1]A. Lev, PID utotuning lgorithm bed on rely feedbck, IEE Porc-Control Theory Appl., vol. 14, 1993, pp [2] Tuning of frctionl PID controller with Ziegler Nichol-type rule, Durte Vle rio, Joe S d Cot, Technicl Univerity of Libon, Signl Proceing 86 (26) [3] Tuning of Frctionl PID Controller by Uing QFT, Joquin Cerver, Alfono Bño, Univerity of Murci, Conch A. Monje, Bl M. Vingre, Univerity of Extremdur. [4]A. Altinten, S. Erdogn, F. Alioglu, H. Hpoglu, nd M. Alpbz, Appliction of dptive PID with genetic lgorithm to polymeriztion rector, Chemicl Eng. Comm., vol. 191, 24, pp [5] J. Y. Hung, W. Go, nd J. C. Hung, Vrible tructure control: urvey, IEEE Trn. Ind. Electr., vol. 4, 1993, pp [6] K. D. Young, V. I. Utkin, nd Ü. Özgüner, A control engineer' guide to liding mode control, IEEE Trn. Control Sy. Tech., vol. 7, 1999, pp

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