RULES REDUCTION AND OPTIMIZATION OF FUZZY LOGIC MEMBERSHIP FUNCTIONS FOR INDUCTION MOTOR SPEED CONTROLLER

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1 RULES REDUCTION AND OPTIMIZATION OF FUZZY LOGIC MEMBERSHIP FUNCTIONS FOR INDUCTION MOTOR SPEED CONTROLLER 1 ZULHISYAM SALLEH, 2 MARIZAN SULAIMAN, 3 FIZATUL AINI PATAKOR, 4 ROSLI OMAR 1 Snior Lcturr. Dpt. of Elctrical Enginring, Politknik Mlaka, Plaza Pandan Malim, 75250, Mlaka, Malaysia 2 Profssor. Faculty of Elctrical Enginring, Univrsiti Tknikal Malaysia Mlaka (UTM) Hang Tuah Jaya, Durian Tunggal, Mlaka, Malaysia 3 Snior Lcturr. Dpt. of Elctrical Enginring Politknik Mrlimau, Mlaka, Malaysia 4 Associat Profssor. Faculty of Elctrical Enginring, Univrsiti Tknikal Malaysia Mlaka (UTM) Hang Tuah Jaya, Durian Tunggal, Mlaka, Malaysia 1 zulhisyam@polimlaka.du.my, 2 marizan@utm.du.my ABSTRACT Fuzzy logic controllrs ar widly usd in induction motor drivs systms for thir robust prformanc. Svral tchniqus hav bn promotd to lssn th computational burdn and mmory constraint for implmntation of fuzzy logic controllr in softwar and hardwar. Ruls rduction and optimization of fuzzy logic mmbrship functions hav bn tstd with full, mdium and low spd undr forward and rvrs opration of induction motor using Matlab/Simulink. Th simplifid fuzzy ruls and mmbrship functions wr analyzd on th dsign and simulation of th controllr for vctor control induction motor. Th drivs systm was simulatd with standard mmbrship functions through 25 ruls and simplifid ruls such 9 ruls, 7 ruls and proposd 5 ruls for ovrviw comparison. Th simplifid ruls wr simulatd using optimization mmbrship functions. Th rsults of this invstigation show that Optimizd5 giv xcptional prformanc for both forward and rvrs opration at ratd spd with no load condition. Thr wr lss than 1% ovrshoot ascnd for Optimizd5 whil tstd in mdium and low spd nvironmnt. Ths invstigations confirmd that Optimiz5 firmly rjctd load disturbancs with sam short priod for diffrnt spd. As a rsult, th considration of optimiz mmbrship functions is significant whn apply ruls rduction for robust spd controllr. Kywords: Fuzzy Logic, Induction Motor, Mmbrship Functions, Ruls, Spd Controllr, Optimization 1. INTRODUCTION Nowadays, fuzzy logic controllr (FLC) has shown grat rcognition controllr bcaus of its ability to control th plant that tough to rprsnt mathmatically du to its difficulty, nonlinarity, and inaccuracy [1]. Authors [2]and [3] suggstd that Fuzzy logic controllr (FLC) should b usd for induction motor spd control in vctor control induction motor drivs. By using FLC, rsarchrs provd that good dynamic and robustnss of drivs prformanc can b achivd[4][5]. Howvr, th implmntation of FLC in motor drivs has som limitation du to high computational burdn and larg mmory rquirmnt ithr in th hardwar or softwar[6]. To solv this limitation and improv prformanc of FLC, rsarchrs hav bn usd svral tchniqus such as scaling factor tuning, rul sts adaptation, and tuning mmbrship function[1][7][8]. Som rsarchrs proposd diffrnt tchniqus of rducing ruls for vctor control induction motor drivs. Th most common tchniqu is to rduc rul st by rducing mmbrship function (MF) numbrs. Rsarchrs oftn dsignd rul st using MF matrics to dtrmin th output of controllr basd on th rlationships of input or output of MFs [8]. Th rfrncs[7][8][9] hav studid th FLC s with rducd th numbr of MF for instanc 7x7, 5x5 and 3x3, and producd 49, 25 and 9 ruls rspctivly. Howvr, authors in [8][10] rportd that rducing 4922

2 numbr of MFs and ruls caus th prformanc of driv systm diffring compar to mor MFs and ruls. But, ths contributd to lss computational tim and mmory. Thrfor rsarchrs in [11][12][13] ar only usd slctd significant ruls and activatd in th FLC. Authors in [11] provd that by using clustring tchniqus nabld to rduc rul bas from 64 to 16 without dgrading driv prformanc. In addition, simplification of fuzzy ruls has bn implmntd in [12] which only usd 5 ruls from 5 by 5 MFs matrics. Though, th work only considrs for forward spd opration. Th rduction of ruls in [13] usd 5x5 MF matrics and mployd 7 ruls du to 25 and nabld oprat for wid rang opration includd forward and rvrs spd control. Som rsarchrs usd phas plan mthod to rduc ruls for FLC dsign[1][13][14]. Th usful of this mthod is to analyz th stadinss of nonlinar systm[15]. Prvious rsarchrs hav bn usd 49 ruls and 25 ruls for ruls rduction and simplifid until 7 ruls. Howvr, th paprs wr not considrd to optimiz th MFs for robust spd controllr. Thrfor, this papr invstigats th succssful implmntation of simplifid 5 ruls and optimization of FLC MFs for spd controllr[16] rlatd with full, mdium and low spd undr forward and rvrs opration of induction motor. 5 ruls ar gnratd from rduction ruls mthod basd on 3x3 mmbrship functions. Th optimization of FLC MFs can b achivd by tuning th position of pak valu of th MFs. Th prformancs of th proposd tchniqu wr compard to 25 ruls, 9 ruls and 7 ruls of FLC. Th robustnss of drivs prformanc has bn valuatd undr load disturbanc condition. Th prformanc critria, such as transint rspons, undrshoot and rcovry tim du to load disturbanc has bn considrd for prformanc valuation. 2. INDUCTION MOTOR DRIVE Th illustration of th control systm is shown in Figur 1. Th FLC procssd th rsulting rror of masurd rotor spd to produc q-axis rfrnc currnt. Th rfrnc currnt and ar convrtd through Invrs Park s Transform to thr phas form and corrsponding to th currnt from th fdback of th motor. Thn hystrsis currnt band rcivd th currnt rrors and gnrat switching signal for th invrtr [17][18]. Figur 1: Indirct Vctor Control With Hystrsis Currnt Band Th mathmatical modl of th induction d qs (1) Vqs Rsiqs ds dt d ds Vds Rsids (2) qs dt motor rfr to [19] [20] can b rprsnt as (1) (8): V V dr R r i R i r dr d dt d dt dr ( ) ( ) r r dr (3) (4) 4923

3 qs LLs iqs Lm ( iqs i ) (5) L i L i i ) (6) lr m ( qs L i L i i ) (7) ds ls ds m ( ds dr L i L i i ) (8) dr lr dr m ( ds dr All diffrnt symbols in this quations dnot th following: V qs, V ds voltags apply to th stator; ids, iqs, idr, and i- d and q axis stator currnts and rotor currnts rspctivly; φ qs, φ, φ ds, φ dr - th stator and rotor flux componnt; Rs, Rr - th stator and rotor rsistancs; Lls, Llr indicats slf-inductancs stator and rotor rspctivly, Lm - th mutual inductanc. Th lctromagntic torqu quation of th induction motor is givn by T 3 2 P L 2 L m r ( i dr qs i ds ) (9) P, rprsnts th motor s pol numbr. If th vctor control is satisfid, th φ would b zro. Thn th lctromagntic torqu is controlld only by φ qs and bcoms: 3 P Lm T ( dr i ) (10) qs 2 2 Lr Th rotor flux ar masurd using rotor tim constant, rotor angular vlocity and stator currnt as in (11). d dt i qs 1 (11) r Tr ids Th modl of simulation for vctor control of induction motor is shown in Figur 2. Figur 2: Simulation Modl Of Induction Motor Drivs Systm 3. DESIGN OF FUZZY LOGIC CONTROL Th structurs of FLC is shown in Figur 3. Th structurs contain of fuzzification, infrnc ngin, rul bas and dfuzzification. Th proposd FLC has two input linguistic variabls; th spd rror, and chang in spd rror, c and on output linguistic variabl; th torqu producing currnt componnt, or cu. Hnc, th function can b statd as [6] (12), chang in spd rror, 1 (13) spd rror is (14) is ral spd, is rfrnc spd and rprsnts th nonlinar function. Figur 3: Structur Of Fuzzy Logic Controllr 4924

4 3.1 Scaling Factors Thr scaling factors ar st to fit th inputs and th output of th FLC [6]. Th factors G and G c ar slctd to rgulat th two inputs rmain within th limit of -1 to +1. Factor G cu is chosn so that on can gt th ratd currnt for ratd condition. By using mthod in[19][8][21][22], G and G c ar calculatd using known motor data. Th motor ratd spd, 184.3rad/s is assum as th maximum spd rror, of th motor. Thus, th scaling factor G for forward-rvrs motor is dtrmind using (15) as: 1 (15) Th scaling factor for G c is dtrmind basd on ratd inrtia and maximum torqu givn by manufacturr. Sampling tim is 20µs. G 1 1 Givn that Thrfor, G (16) (17) G cu = 2. In ordr to acquir th optimum driv prformancs, fin tuning of th G c is chosn bcaus it gav mor influnc on th dynamic rspons [10]. In ordr to tun G c, th cofficint of th G c can b xprssd as; Whr β dnots th tuning factor in a rang 0 β 1. As a rsult, β= and from (18) Tund G c = Rul Bas Dsign Tund G βg (18) Rul bas is basically a matrics that to dtrmin th controllr output from thir input(s) as it holds th input/output rlationships [8]. As to provid a natural structur to convrt th human data into fuzzy IF THEN ruls, Mamdani s typ rul has bn usd in this work. In this stag th input variabls and c ar procssd by th infrnc ngin that implmnts th rul bas. Th linguistic trms usd for inputs and output variabls ar dfind as: NL is Ngativ Larg, NM is Ngativ Mdium, NS is Ngativ Small, ZE is Zro Error, PS is Positiv Small, PM is Positiv Mdium and PL is Positiv Larg. In this papr, FLCs with diffrnt sizs of ruls bas ar dsignd basd on prvious studis[8][13] for spd control of induction motor driv to compar th prformanc of th controllrs. Th ruls usd in th comparison ar 25 ruls, 9 ruls and 7 ruls as shown in Tabl 1, Tabl 2 and Tabl 3 rspctivly. Tabl 1: Rul Bas 25 Ruls c NL NS ZE PS PL NL NL NL NL NS ZE NS NL NS NS ZE PS ZE NL NS ZE PS PL PS NS ZE PS PS PL PL ZE PS PL PL PL Tabl 2: Rul Bas 9 Ruls c NS ZE PS NS NS NS ZE ZE NS ZE PS PS ZE PS PS Tabl 3. Rul Bas 7 Ruls c NL NS ZE PS PL NL NL NS NS ZE NS ZE PS PS PS PL PL 3.3 Ruls Rduction Th ruls rduction mthod is mad bas on 3x3 mmbrship functions. Th most dominant ruls ar slctd by sing virtuous covrag for input/output variabls to mak sur that th schm maintain good prformanc or bttr than prvious. By rfrring phas plan mthod, only 5 ruls ar slctd in ruls rduction as follows: 1. Rul 1: If is NS and c is ZE thn cu is NS 2. Rul 2: If is ZE and c is NS thn cu is NS 4925

5 3. Rul 3: If is ZE and c is ZE thn cu is ZE 4. Rul 4: If is ZE and c is PS thn cu is PS 5. Rul 5: If is PS and c is ZE thn cu is PS Thrfor, NS, ZE and PS ar th most important MFs to b usd in th proposd dsign. ZE is usd in chang of rror, c to maintain th stabilization of th systm during stady stat condition. In th mantim, NS and PS ar applid for th duration of transint rspons and cop with load. Tabl 4 shows 5 ruls tabl. \ Tabl 5. Rul Bas 5 Ruls c NL NS ZE PS PL NL NS NS ZE NS ZE PS PS PS PL 3.4 Standard Mmbrship Functions Figur 4 illustrats th standard MFs for 25 ruls, 9 ruls, 7 ruls and 5 ruls. Th trapzoid and triangular shaps ar usd for th input and output of FLC variabls. Th triangular MFs ar dsignd to b symmtrical and idntical in trms of width and pak position. (A) (B) (C) (D) Figur 4: Standard Mfs For (A) Rul Bas 25 Ruls (B) 9 Ruls (C) 7 Ruls And (D) 5 Ruls 3.5 Optimization of Mmbrship Functions MFs can b optimiz by altring th position of pak valu of th MFs for FLC in th drivs systm can incras th robustnss of th systm [16]. Th optimal rspons of th driv systm can b achivd whn convrgnt and c of MFs but divrgnt for cu [23]. Tuning th width and moving th pak valu positions of ths MFs towards th ZE valu will caus th spd controllr to b mor snsitiv to a small chang in spd rror and produc a larg control. But, to nsur th drivs covr varid spd opration from forward to rvrs opration, th valu of third paramtrs of NS/PS must lss than th valu of first paramtrs of ZE. Thr diffrnt simplifid ruls 5, 7 and 9 will b usd for this mthod. Thr diffrnt simplifid ruls 5, 7 and 9 will b usd for this mthod. Figur 5, 4926

6 (A) (B) Figur 6 and Figur 7 show th optimizd MFs of 9 Ruls, 7 Ruls and 5 ruls rspctivly (C). (A) (B) (C) Figur 5. Optimizd Mfs Of 9 Ruls For (A) Spd Error (B) Chang In Spd Error And (C) Chang In Q-Axis Rfrnc Currnt, Cu 4927

7 (A) (B) (C) Figur 6. Optimizd Mfs Of 7 Ruls For (A) Spd Error, (B) Chang In Spd Error And (C) Chang In Q-Axis Rfrnc Currnt, Cu (a) (b) (c) Figur 7. Optimizd MFs of 5 Ruls for (a) spd rror, (b) chang in spd rror and (c) chang in q-axis rfrnc currnt, cu 4. RESULTS AND DISCUSSION Svral simulation tsts of standard MFs and optimizd MFs with diffrnt siz of ruls of basd vctor control of induction motor wr prsntd using MATLAB/ SIMULINK. Th motor usd in th simulation is 415V, 3 phas, and 1.5hp squirrl cag induction motor. Th paramtrs of th motor ar givn in Tabl 6. Th rfrnc flux is Wb and starting torqu is limit to 15Nm. Th hystrsis currnt band is st constant and qual to ±0.5 A. DC Voltag supply limit to 400V. Tabl 6: Induction Motor Paramtrs Paramtr Stator rsistanc, Rs 4.3 Ω Valu Rotor rsistanc, Rr Stator inductanc, Ls Rotor inductanc, Lr Mutual inductanc, Lm 2.9 Ω 0.3 H 0.3 H 0.29 H Momnt of inrtia, J Kgm 2 Numbr of pols 4 Figur 8 provids an ovrviw of spd rspons at ratd spd 1760rpm for standard MFs of ruls 25 (standard25), 9 (standard9),7 (standard7) and 5 (standard5) opratd in forward and rvrs opration. It can b sn from th graph in Figur 8 that standard25, standard7 and standard5 rportd significantly similar compar to standard9 in trm of 4928

8 rising and sttling tims. Howvr, th spd rspons for load disturbanc in Figur 9 shown that standard9 is th last ffct for th load disturbanc. Thus, thr diffrnt simplifid ruls ar usd for comparison of optimization MFs. Th prformancs of th proposd tchniqu using 5 ruls wr compard with simplifid 9 and 7 ruls Standard25 Standard 9 Standard7 Standard5 Spd (rpm) Standard25 Standard 9 Standard7 Standard Tim (s) Tim (s) Figur 8. Spd rspons for Standard MFs of 25, 9, 7 and 5 ruls at spd ratd 1760 rpm (a) forward opration (b) rvrs opration Spd (rpm) Standard25 Standard9 Standard7 Standard Tim (s) Figur 9. Standard Mfs Of 25, 9, 7 And 5 Ruls With Load 6Nm At Ratd Spd 1760 Rpm 4929

9 Spd (rpm) Journal of Thortical and Applid Information Tchnology Optimiz 9 Optimiz 7 Optimiz Tims (s) Tim (s) Figur 10. Spd Rspons For Optimizd Mfs Of 9, 7 And 5 Ruls At Ratd Spd 1760 Rpm Spd (rpm) Optimiz 9 Optimiz 7 Optimiz 5 Figur 10 shows spd rspons for optimizd MFs of 9 ruls (Optimizd9), 7 ruls (Optimizd7) and 5 ruls (Optimizd5) at ratd spd 1760 rpm during forward and rvrs opration. It clarly shows that in forward condition, Optimizd5 and Optimizd9 hav paralll fastr spd rspons which obtaind th stady stat at t=0.2s whil Optimizd7 at t=0.21s. For rvrs opration, Optimizd5 rach th rfrnc point at th sam tim with Optimizd7 but Optimizd9 has dlayd 0.03s. It is vidnc from ths figurs that show th prformanc of Optimiz5 is xcllnt for both forward and rvrs opration at ratd spd 1760rpm undr no load condition. Ths thr optimizd ruls also tstd in half ratd spd 880rpm as shown in Figur 11. Optimizd5 and Optimizd7 qually hav fastr spd rspons which obtaind th stady stat at t=0.13 compard to at t=0.15. Thr wr microscopic ovrshoot occurrd for Optimiz5 and Optimiz9. It is only 0.1% that can b accptabl for motor control spd. In contrast with, thr is no ovrshoot but th ris tim is vry slow. Th sttling tim in rvrs opration, optimizd 5 and optimiz9 acquird 115ms to achiv rfrnc point thn optimizd7 took 130ms to complt Optimiz 9 Optimiz Figur 11. Spd Rspons For Optimizd Mfs Of 9, 7 And 5 Ruls At Ratd Spd 880 Rpm Optimiz 9 Optimiz5 4930

10 0 Spd (rpm) Optimiz9 Optimiz5 Spd (rpm) Optimiz9 Optimiz Tim (s) Tim (s) Figur 12. Spd Rspons For Optimizd Mfs Of 9, 7 And 5 Ruls At Ratd Spd 220 Rpm Figur 12 shows th rsults of optimizd MFs for low spd stting at 220 rpm. Th ris tim of spd rspons vry fast for Optimiz5 and Optimiz9 compard to Optimizd7. Ths fast rsponss contributd ovrshoot lss than 1% which is tolrabl for this systm. Optimizd5 and Optimizd9 achivd stady stat at 0.06s manwhil Optimizd7 rachd stady stat at 0.8s. For rvrs opration, dfrrd 0.04s than Optimizd5 and Optimizd9. To tst robustnss of th drivs systm, th capability of load disturbanc rjction of ths thr optimizd ruls ar invstigatd undr two diffrnt load for half ratd, 3Nm and full ratd load, 10Nm. Th systm ar tstd for full (1760rpm), mdium (880rpm) and low (220rpm) spd as dpictd in Figur 13, Figur 14 and Figur 15 rspctivly Optimiz9 Optimiz (a) (b) Figur 13. Load Disturbanc Rjction Of Optimizd5, Optimizd7 And Optimizd9 At Ratd Spd 1760rpm (A) Half Ratd Load, 3Nm (B) Full Ratd Load 6Nm optimiz Optimiz From Figur 13 and Figur 14, th rjction tim of load disturbanc for Optimizd5, Optimizd7 and Optimizd9 ar 10ms, 30ms and 5ms, rspctivly. It sms that th rcovris tim for full and mdium spd with full and half ratd load ar consistnt for ach Optimizd rul. But, for low spd as shown in Figur 15, th Optimizd9 acquird 10ms sam as Optimizd5 thn Optimizd7 took 26ms to rjct th load disturbancs for 5Nm and 10Nm. Th Optimizd9 shows th fastst rspons to rjct disturbanc among thr optimizd ruls. Howvr, Optimizd5 maintain sam rjction tim for thos thr-spd rfrnc. 4931

11 optimiz9 optimiz (a) (b) Figur 14.. Load Disturbanc Rjction Of Optimizd5, Optimizd7 And Optimizd9 At Half Ratd Spd 880rpm (A) Half Ratd Load, 3Nm (B) Full Ratd Load 6Nm Optimiz9 optimiz Optimiz9 optimiz Optimiz9 optimiz (a) (b) Figur 15. Load Disturbanc Rjction Of Optimizd5, Optimizd7 And Optimizd9 At Ratd Spd 220rpm (A) Half Ratd Load, 3Nm (B) Full Ratd Load 6Nm Tabl 7: Comparison Rjction Prformanc for Load Disturbanc 5 ruls 10ms 10ms 10ms 10ms 10ms 10ms Howvr, th proposd mthod show xcptional rsult in trm of diffrnt spd rspond and load disturbancs. It is found that simplifid optimiz MF with 5 ruls prformanc is consistnt whn tstd with diffrnt load. This proof that this mthod achiv th objctiv to rduc computational tim at th sam yild bttr prformanc for induction motor. Tabl 7, summarizd th prformanc of th thr tchniqus in trm of sttling tim of spd whn th load is givn. It is obvious that Optimizd5 prform consistntly for half and full ratd load givn. In addition, for low spd, th Optimizd5 sttling tim for both load is sam as Optimizd9. From th simulation tst, it is found that th simplifid 5 ruls has bttr rsult compar to standard 25 ruls. Furthrmor, in forward and rvrs opration, th 5 ruls prform good rspond and compnsat th load in avrag 0.6 scond Optimizd Sttling Tim Aftr load 3Nm Sttling Tim Aftr load 6Nm Spd (rpm) Spd (rpm) ruls 5ms 5ms 10ms 5ms 5ms 10ms 7 ruls 30ms 30ms 25ms 30ms 30ms 25ms 5. CONCLUSIONS In this invstigation, th aims wr to assss simplifid ruls and optimizd MFs of FLC for spd

12 controllr and tstd in full, mdium and low spd with half and full ratd load undr forward and rvrs opration of induction motor. Thus, th prformancs of simplifid ruls and optimizd ruls such Optimizd7 and Optimizd9 wr compard with proposd Optimizd5. Th rsults of this invstigation show that Optimizd5 giv xcptional prformanc for both forward and rvrs opration at ratd spd with no load condition. Th scond major finding was that vry small ovrshoot ascnd for Optimizd5 whil tstd in mdium and low spd nvironmnt but th prformanc is accptabl compar to Optimizd7 and Optimizd9. Ths invstigations confirmd that Optimiz5 consistntly firm in rjction of load disturbancs for diffrnt spd. Th rsult of this study indicats that optimization of FLC MFs ar should b considrd whil apply ruls rduction for robust spd controllr. Furthr study might invstigat how to fix th ovrshoot by tuning th scaling factors of th motor. 6. ACKNOWLEDGEMENT Th authors would lik to acknowldg th funding givn by Univrsiti Tknikal Malaysia Mlaka (UTM) through th grant FRGS/2/2014/TK03/FKE/01/F00238, Politknik Mrlimau and Politknik Mlaka through th grant FRGS/1/2015/TK04/JPP/03/1 and Ministry of Highr Education Malaysia for thir support. REFRENCES: [1] S.-C. Wang and Y.-H. Liu, A Modifid PI- Lik Fuzzy Logic Controllr for Switchd Rluctanc Motor Drivs, IEEE Trans. Ind. Elctron., vol. 58, no. May, pp , [2] R. Kumar, R. a. Gupta, and S. V. Bhangal, Indirct Vctor Controlld Induction Motor Driv with Fuzzy Logic Basd Intllignt Controllr, in IET-UK Intrnational Confrnc on Information and Communication Tchnology in Elctrical Scincs (ICTES 2007), 2007, no. Icts, pp [3] A. Kaltsanos, F. Xpapas, and S. N. Manias, A Novl Nonlinar and Intllignt Control Tchniqu for Induction Motor Driv Systms, in Confrnc Rcord of th 2004 IEEE Industry Applications Confrnc, th IAS Annual Mting., 2004, vol. 2, no. 8, pp [4] A. Rafa, S., Larabi, A., Barazan, L., Mancur, M., Essounbouli, N., & Hamzaoui, Fuzzy vctor control of induction motor, in In Ntworking, Snsing and Control (ICNSC), th IEEE Intrnational Confrnc, 2013, pp [5] M. Zrikat, A. Mchrnn, and S. Chkroun, High-prformanc snsorlss vctor control of induction motor drivs using artificial intllignt tchniqu, Eur. Trans. Elctr. Powr, vol. 21, no. 1, pp , [6] M. N. Uddin, T. S. Radwan, and M. A. Rahman, Prformancs of Fuzzy-Logic- Basd Indirct Vctor Control for Induction Motor Driv, IEEE Trans. Ind. Appl., vol. 38, no. 5, pp , [7] S. Chopra, R. Mitra, and V. Kumar, Fuzzy Controllr : Choosing an Appropriat and Smallst Rul St, Int. J. Comput. Cogn., vol. 3, no. 4, pp , [8] B. Kumar, Y. K. Chauhan, and V. Shrivastava, Efficacy of Diffrnt Rul Basd Fuzzy Logic Controllrs for Induction Motor Driv, Int. J. Mach. Larn. Comput., vol. 2, no. 2, pp , [9] J. Gayathri Monicka, D. N.O.Guna Skhar, and K. Ramash Kumar, Prformanc Evaluation of Mmbrship Functions on Fuzzy Logic Controlld AC Voltag Controllr for Spd Control of Induction Motor Driv, Int. J. Comput. Appl., vol. 13, no. 5, pp. 8 12, [10] S. Chopra, R. Mitra, and V. Kumar, A robust schm for tuning of fuzzy PI typ controllr, in 3rd Intrnational IEEE Confrnc Intllignt Systms, Sptmbr 2006, 2006, no. Sptmbr, pp [11] P. Vas, M. Nuroth, and A. F. Stronach, Full fuzzy control of a DSP-basd high prformanc induction motor driv, in IEE Procdings - Control Thory and Applications, 1997, vol. 144, no. 5, pp [12] M. J. Hossain, M. A. Hoqu, and K. K. Islam, Simplifid fuzzy control for flux-wakning spd control of IPMSM driv, Adv. Fuzzy Syst., vol. 2011, [13] M. H. N. Talib, Z. Ibrahim, N. A. Rahim, A. S. A. Hasim, and H. Zainuddin, Prformanc Improvmnt of Induction Motor Driv Using Simplifid FLC Mthod, Powr Elctron. Motion Control Conf. Expo. (PEMC),

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