A Parameter Varying PD Control for Fuzzy Servo Mechanism

Transcription

1 Intellgent Control and Automaton, 204, 5, Publshed Onlne August 204 n ScRes. A Parameter Varyng PD Control for Fuzzy Servo Mechansm Nader Jamal Souf, Mohsen Kabr Moghaddam 2, Saeed Sfandarpour Borouen 3, Alreza Vahdfar Sama Techncal and Vocatonal Tranng College, Islamc Azad Unversty, Islamshahr Branch, Tehran, Iran 2 Department of Electrcal and Electronc Engneerng, K. N. Toos Unversty of Technology, Tehran, Iran 3 Department of Electrcal and Electronc Engneerng, Unversty of Shraz, Shraz, Iran Emal: Jamal.tabrzu@yahoo.com, m.kabr77@yahoo.com, saeed.controleng@gmal.com, alreza.vahdfar@gmal.com Receved 2 May 204; revsed 27 June 204; accepted July 204 Copyrght 204 by authors and Scentfc Research Publshng Inc. Ths work s lcensed under the Creatve Commons Attrbuton Internatonal Lcense (CC BY. Abstract Ths paper presents the formulaton of novel mplementaton method based on parameter varyng PD controller for fuzzy servo controllers. Ths formulaton uses the appromaton of fuzzy nonlnear functon ncludng error and error dervaton n operaton pont. Obtaned fuzzy control law has been employed to control angular poston of servo usng dgtal control technque appled to a typcal mcrocontroller lke AVR. The performance and robustness of modfed fuzzy controller n comparson wth PID controller evaluated n no load, appled eternal dsturbance wth dfferent magntude condtons has been studed. The smulaton results showed that the proposed fuzzy controller has a consderable advantage n rse tme, settlng tme and overshoot respect to PID controller when the servo system encounters wth nonlnear features lke saturaton and frcton. Keywords Parameter Varyng PD Controller, Fuzzy Poston Control (FPC System, FLC, Servo Motor. Introducton All control systems suffer from problems related to undesrable overshoot, longer settlng tmes, vbratons and stablty whle gong from one state to another state. Real-world systems are nonlnear, accurate modelng s dffcult, costly and even mpossble n most cases. On other sde, a servo control system s one of the most mportant and wdely used n control systems. The role of the control system may nclude: mantanng the poston of a motor wthn certan lmts, even when the load on the output of the motor mght vary that ths s called regula- How to cte ths paper: Souf, N.J., Moghaddam, M.K., Borouen, S.S. and Vahdfar, A. (204 A Parameter Varyng PD Control for Fuzzy Servo Mechansm. Intellgent Control and Automaton, 5,

2 N. J. Souf et al. ton or varyng the poston of the motor and load accordng to an eternally set program of values that ths called set pont trackng []. Today, applcatons of servomechansms nclude ther use n automatc machne tools, satellte-trackng antennas, celestal-trackng systems on telescopes, automatc navgaton systems, manufacturng ndustry, transportaton, computers, communcaton networks and antarcraft-gun control systems. In many applcatons, servomechansms allow hgh-powered devces to be controlled by sgnals from devces of much lower power. The operaton of the hgh-powered devce results from a sgnal (called the error, or dfference, sgnal generated from a comparson of the desred poston of the hgh-powered devce wth ts actual poston. A servomotor s a specfc type of motor and rotary encoder combnaton, usually wth a dedcated, that forms a servomechansm. Ths assembly may n turn form part of another servomechansm. The encoder provdes poston and usually speed feedback, whch by the use of a PID controller allow more precse control of poston and thus faster achevement of a stable poston (for a gven motor power. However, the conventonal dgtal control systems lke classc PID solve the above problems appromately and generally do not work well for non-lnear systems, and partcularly comple and vague systems that have no precse mathematcal models [2]. Therefore, we need to ntellgent and precse control systems to acqurng desred response. Moreover, t has been known that mentoned controllers produce more nose. Therefore, more advanced control technques need to be used, whch wll mnmze the nose effects [3]. To overcome these dffcultes, varous types of modfed conventonal PID controllers such as auto-tunng and adaptve controllers have been developed lately [4]-[6]. Here we suggest ntellgent control approach. There are three basc approaches to ntellgent control: knowledge-based epert systems, fuzzy logc, and neural networks. All three approaches are nterestng and very promsng areas of research and development. In ths paper, we present only the fuzzy logc approach. Fuzzy logc proposed by Lotf A. Zadeh n 973. Zadeh ntroduced the concept of lngustc varables [7] that can be descrbed smply as computng wth words rather than numbers or control wth sentences rather than equatons [8]. Fuzzy Logc s a multvalued logc that allows ntermedate values to be defned between conventonal evaluatons lke true/false, yes/no, hgh/low and emerged as a tool to deal wth uncertan, mprecse, or qualtatve decson-makng problems. Fuzzy logc control (FLC s a control method based on fuzzy logc. Today, fuzzy control applcatons cover a varety of practcal systems, such as the control of cement klns [9], tran operaton [0], parkng control of a car [], heat echanger, robots, and also n many other systems, such as home applances, vdeo cameras, elevators, aerospace and etc. Many dfferent approaches are used for fuzzy controller mplementaton whch they can be cted to hybrdmethods such as neuro-fuzzy [2] [3], PI-lke fuzzy [4], multvarate regresson [5], non-lnear bond graphs (BG [6]. In neuro-fuzzy approach, controller learns fuzzy rules ncrementally or decrementally and the learnng algorthm uses a lngustc error measure that s epressed by fuzzy rules. In PI-lke fuzzy approach, frst, the proposed fuzzy controller adopts the step response of phase traectores to derve the correspondng lngustc control rules of such a system, and then apples the relatonshp between nput and output sgnals n a proportonal ntegral controller to convert the relatonshp of lngustc control rules to a decson table. Multvarate regresson analyss attempts to determne a formula that can descrbe how elements n a vector of varables respond smultaneously to changes n others. For lnear relatons, regresson analyses here are based on forms of the general lnear model. Also, a bond graph s a graphcal representaton of a physcal dynamc system. It s smlar to the better-known block dagram and sgnal-flow graph, wth the maor dfference that the arcs n bond graphs represent the b-drectonal echange of physcal energy, whle those n block dagrams and sgnal-flow graphs represent un-drectonal flow of nformaton. Furthermore, bond graphs are mult doman and doman neutral. Ths means a bond graph can ncorporate multple domans seamlessly. In partcular, for servo system, fuzzy logc PID [7], Taguch-method [8], DSP-based fuzzy logc [9] and neuro-fuzzy controller [20] are used n lteratures. In ths paper, we proposed a novel method based on parameter varyng PD controller for fuzzy servo controllers that uses the appromaton of fuzzy nonlnear functon ncludng error and ts dervaton n operaton pont. Ths paper s organzed as follows: frstly, the overall framework of the theory of fuzzy control and ts defuzzfcaton methods are presented. Then fuzzy control algorthm based on PD controller has been appromated. Then the dynamc modelng of servo motor system and ts epermental mplementaton usng the proposed algorthm s done. Fnally, smulaton results of the proposed controller are compared wth PID controller. 57

3 N. J. Souf et al. 2. Motvaton for Fuzzy Control Classcal mathematcs and conventonal control theory are qute lmted n modelng and controllng comple nonlnear dynamcal systems, partcularly ll-formulated and partally descrbed physcal systems. The motvaton for usng fuzzy logc technology n control systems stems from the fact that t allows desgners to buld a controller even when ther understandng of the system s stll n a vague, ncomplete, and developng phase. Moreover, t can be noted that the servo controller desgn does not requre to eplct knowledge of the motor and load characterstcs [2]. Snce the fuzzy controllers are desgned drectly from the propertes of the process, the development tme s often shorter than for conventonal controllers [22]. The overall procedure for developng a fuzzy control system for a model servo system s shown n Fgure. The system uses measured varables as nputs to descrbe the error or dervaton of error from the servo. These nputs are then fuzzfed usng membershp functons suppled by an epert operator to determne the degree of membershp n each nput class. The resultng fuzzy nputs are evaluated usng a lngustc rule base and fuzzy logc operatons to yeld an approprate output and an assocated degree of membershp. Ths fuzzy output s then defuzzfed to gve a crsp output response that can be appled to the drve servo. Accordng to real-world requrements, the lngustc varables have to be transformed to crsp output. There are many defuzzfcaton methods (e.g. Center of gravty, bsector of area, mean of area and center of average that are n followng [23] [24]. 2.. Center of Gravty (COG For dscrete sets, COG s called center of gravty for sngletons (COGS where the crsp control value s the abscssa of the center of gravty of the fuzzy set, where ( =, 2, s a pont n the unverse of the concluson and µ c( s the membershp value of the resultng concluson set. For contnuous sets, summatons are replaced by ntegrals Bsector of Area (BOA Where (, 2, u COGS µ c( = µ ( c = s a pont n the unverse (U of the concluson. There may be several solutons ths method s a comple method computatonally. For dscrete sets, the presented formula. Here ma s the nde of the largest abscssa value of the resultng concluson set. ma (, thus u BOA s the abscssa that mnmzes µ s membershp. Moreover ( µ c( µ c(, < < (2 ma = = + ma c Fgure. General structure of the fuzzy part. 58

4 N. J. Souf et al Mean of Mamum (MOM In ths method the crsp value s chosen by pont wth the hghest membershp. There may be several ponts n the overall mpled fuzzy set whch have mamum membershp value. Therefore, t s a common practce to calculate the mean value of these ponts. Here I s the (crsp set of ndces where µ c( reaches ts mamum µ ma. I umom =, I = { µ c ( = µ ma} (3 I 2.4. Center of Average (COA ( Where u lm s a sngle value of the fuzzy set of control output, mnlm = mn µ c A ( e, µ c B ( e, A ( e and B ( e are membershp functon for error and dervaton of error, respectvely. It must be mentoned that n ths paper, the chosen defuzzfcaton method for mplementaton s COA. u COA = l=, + lm lm m=, + l=, + m=, + mn 3. Problem Descrpton and Methodology 3.. Fuzzy Controller Based on PD Controller mn A fuzzy logc controller has four man components as shown n Fgure : fuzzfcaton, nference, rule base and defuzzfcaton. Implementaton of an FLC requres the choce of four key factors [25]: number of fuzzy sets that consttute lngustc varables, mappng of the measurements onto the support sets, control protocol that determnes the controller behavor and shape of membershp functons. Thus, FLCs can be tuned not ust by adustng controller parameters but also by changng control rules, membershp functons. Rule bases, nference mechansm and defuzzfcaton methods are the sources of nonlneartes n FLCs but t s possble to construct a rule base wth lnear nput-output characterstc for FLC to become a lnear controller wth a control sgnal [26]. It s constructve to apply a smlar analyss to Fuzzy PID control n order to accommodate ntegral acton but the ntegrator creates problems by ncreasng the order of the closed loop system. Here, output sgnal s a functon wth two varables: error and dervaton of error. Control sgnal U(n s a nonlnear functon of error and dervaton of error as shown n Fgure 2. The smplest membershp functons are formed usng straght lnes. In most lteratures, because of the smplcty of the theory and mplementaton of trangular membershp functons n desgn of fuzzy controller, these functons are used. In ths study, the trangular membershp functon s chosen for each fuzzy lngustc value of the error and the dervaton of error as shown n Fgure 3 and Fgure 4, respectvely. When e [, + ], e [, + ], we have u lm (4 Fgure 2. Fuzzy PD controller. 59

5 N. J. Souf et al. Fgure 3. Membershp functon for error (e. Fgure 4. Membershp functon fordervaton ( e. µ c( =, µ ( = Z µ c P + + ( = 0 for [, ] c + + µ c( =, µ ( = Z µ c P + + ( = 0 for [, ] c + When dscussng t, consderng the Equaton (4 there are eght condtons as mentoned n [24]. (5 Condton Descrpton µ ( µ c c( µ c( µ c( P P Z Z 2 µ ( µ c c( µ c( µ c( P Z P Z 3 µ ( µ ( c c µ c( µ c( Z Z P P 4 µ ( µ ( c c µ c( µ c( Z P Z P 5 µ ( µ ( c c µ c( µ c( P P Z Z 6 µ ( µ ( c c µ c( µ c( P Z P Z 7 µ ( µ c c( µ c( µ c( Z Z P P 8 µ ( µ c c( µ c( µ c( Z P Z P For desgn FPC, we consder to the ffth condton, arbtrary: (, ( (, ( (, ( (, ( ( ( ( ( µ c µ Z c µ Z c Z µ c µ Z c P µ c Z mn = µ c µ P c µ Z c Z µ c µ P c µ P c P 60

6 N. J. Souf et al. Thus ( + ( + ( + ( µ ( + µ ( + µ ( + µ ( µ u µ u µ u µ u u = c Z Z, Z c Z Z, P c Z P, Z c P P, P c Z c Z c Z c P In later equaton, uzz, refers to the mappng of membershp functon (Z for error to output and also refers to a mappng of membershp functon ( Z for dervaton of error to output and etc. Substtutng (5 n (6, we have: + ( u,,? ZZ + uzp + upz, + upp, u = ( We denote the nput-output relaton of the controller u n the followng model: δ u perturbatons, the Equaton (8 can be appromated by the follow- For suffcently small ng lnear equaton: (, (, ( ( ( ( ( + ( ( ZZ, ZP, 3 2 u = f E CE f = u + u + ( ( upz, + upp, δ e, δ e and δ f δ f δu = δ δ δ + δ where δ =, δ =, δu = u u. ZZ, ( ( Note. The operatng pont (OP that we consder t for lnearzaton here s Also ( ( ( ( + ( 2 ( + + u 2 PP, ( ( 3 2 ( + =. = δ f 2 u u u δ = ( 2 ZZ, ZP, 2 P,? Z δ f = u + u + u ( ( ( ZZ, ZP, ZP, δ OP ( ( ( ( δ f δ = upz, upp, δ f Consderng Equaton (8, we have: = u + ( ( PZ ( (, PP, δ OP u = u + u + u + u u ( ( ( ( ZZ, ZZ, ZP, PZ, PP, Proportonal Gan Addtve Term ( ( ( uzz, uzp, + up, u P PZ, 3 + 3( + u ( ( Dervatve Gan (6 (8 (9 (0 ( (2 6

7 N. J. Souf et al. Then after some algebra operatons the Equaton (2 become u = Addtve Term + Proportonal Gan + Dervate Gan Thus ( ( Addtve Term Fuzzy Controller wth Proportonal Gan Varyng Parameter PD controller Dervate Gan We can see that the above controller behaves lke a parameter varyng PD controller thus the FLC performs lke PID controller when we have not any eternal load or dsturbance. Takag-Sugeno or Mamdan [27] fuzzy nference system can be used to desgn the fuzzy controller. In ths paper, Mamdan fuzzy nference system s used. The nputs of FPD are Error (E and Dervate of Error (DE whle the output s control. Input and output varables of FPD consst of three fuzzy sets namely N (negatve, Z (zero, P (postve as shown n Fgures 5-7, respectvely. The fuzzy rule bases used n desgn of controller for the servo system are followng: Rule If e s N and de s N then control s N. Rule 2 If e s Z and de s N then control s N. Rule 3 If e s P and de s N then control s Z. Rule 4 If e s N and de s Z then control s N. Rule 5 If e s Z and de s Z then control s Z. Rule 6 If e s P and de s Z then control s P. Rule 7 If e s N and de s P then control s Z. Rule 8 If e s Z and de s P then control s P. Rule 9 If e s P and de s P then control s P. Fgure 5. Fuzzy nput varable error. Fgure 6. Fuzzy nput varable dervaton of error. Fgure 7. Fuzzy output varable control. 62

8 N. J. Souf et al Flowchart for Real-Tme Implementaton of FPC Fgure 8 shows the flow chart for the herarchcal fuzzy control algorthm, where θ d and θ denotes the desred poston and dsplacement date that reported from the poston sensor lke encoder and potentometer, respectvely PID Controller When the dgtal controller s used, one could replace the dervatve term wth a backward dfference and the ntegral term may be replaced wth a sum. For a small constant samplng tme, u( t can be appromated as: ( ( ( ( n e n e n un = KP en+ e( T s + TD (3 T = Ts PID controllers can be set usng the rules of Zegler Nchols (ZN or manually. Hand-tunng s generally used by eperenced control engneers based on the specal rules but these rules are not always vald. In recent years, many studes have been performed for optmzaton of PID coeffcents whch can be ponted to an etremum seekng [4], stochastc algorthm [5], genetc algorthm [6] and so on. Then the dervatve gan T D and the ntegral gan T are adusted to mprove and optmze the response of the system. In ths paper, acheved coeffcents of PID controller usng (ZN tunng method are as follows: K P =.43, T = and T D = Modellng and Implementaton The heart of the system that ntegrates the system components, control operatons and defnes features functonalty usng related technques and methods s software. The total schematc dagram of ths system ncludng controller, actuator, process, and poston sensor s shown n Fgure 9. Desgned prnted crcut board (PCB n Altum Desgner Summer (ADS envronment and photograph of the mplemented poston trackng control system usng fuzzy Logc are shown n Fgure 0 and Fgure respectvely. The system dynamcs are represented as follows: The state space equatons for a typcal servo motor as follows: Fgure 8. Flow chart for the poston fuzzy control system. 63

9 N. J. Souf et al. Fgure 9. Schematc dagram of control system. Fgure 0. Crcut of FLC n ADS envronment. Fgure. A vew of the mplemented system n lab. 64

10 N. J. Souf et al. where t ( s state vector, ( ( ( ( = ( + ( t = At+ But+ w y C t Du t u t s nput control sgnal and w s eternal dsturbance. System matr A, vectors B and C of the lnearzed benchmark problem are gven by: 0 0 A = 0 0 ( KT Kb + Ra Bm ( Ra Jm + La Bm 0 La Jm La J m (5 0 B = 0, C = [ 0 0 ], D = 0, w= sn ( t Va La J m where V a = armature voltage (v, R a = armature resstance (Ω, L a = armature nductance (H, J m = rotor nerta (kg m 2, B m = vscous frcton coeffcent (N ms/rad, K T = torque constant (N m/a and K b = backemf constant(v s/rad. Remark. For applcatons where the load s to be rapdly accelerated or decelerated frequently, the electrcal and mechancal tme constants of the motor play an mportant role. The mechancal tme constants n these motors are reduced by reducng the rotor nerta. In ths study, a DC motor wth these specfcatons was used: (moment of nerta of the rotor: e-3, rated motor voltage: 6 v DC, armature nductance: 0.0 H, armature resstance: Ω, Electromotve force constant: 0.22, Back E.M.F. Constant:.5, Dampng rato:.9 N s/m. 5. Smulaton Results In ths paper, frst PID classc controller s desgned for system control of servo mechansm usng Secton 3.3. Note that chosen gans for PID controller are gven n ths secton. Then fuzzy controller usng nne rules and trangular membershp functons desgned n Matlab/Smulnk envronment by Mamdan approach n Secton 3.. The output response of both the PID and fuzzy logc controllers were presented. Fgure 2 shows the result of the comparson between the output response (.e. Poston of servo for the PID and Fuzzy logc controller under (4 Fgure 2. Output response n no load condton. 65

11 N. J. Souf et al. no-load condton. Fgure 3 and Fgure 4 show the obtaned result from comparson between PID controller and FLC for appled eternal dsturbance (η wth dfferent ampltudes η = 0. + sn(t, η = sn(t, respectvely. Smulaton results shows that the FLC performs lke PID controller when we have not any load or changed parameters or dsturbance [23] but when comparng both controllers under nected load or changed parameters or dsturbance, the FLC performs better than PID controller [28]. However, the performance of PID controllers depends heavly on the operatng parameters of the system. Also, f there s any change n the system, a sgnfcant amount of tme s requred to reset the controllers. Consderng proposed method, output responses usng dfferent defuzzfcaton methods such as center of gravty (COG, bsector of area (BOA, mean of mamum (MOM, center of average (COA under no load condton, load and eternal dsturbance (η condtons were shown n Fgures 5-7, respectvely. One can result that center of average (COA method has an acceptable result than other methods (.e. COG, BOA and MOM. PID controller s desgned on operatng pont and when t encountered wth uncertanty or unmodeled dynamcs n the system, t cannot compensate these changes enough effectvely. Besdes, fuzzy controller can cover these changes and handles them. Fgure 3. Output wth eternal dsturbance η = 0. + sn(t. Fgure 4. Output wth eternal dsturbance η = sn(t. 66

12 N. J. Souf et al. Fgure 5. Output response n no load condton. Fgure 6. Output response wth constant load. Fgure 7. Output response wth eternal dsturbance. 67

13 N. J. Souf et al. 6. Concluson The formulaton of a novel mplementaton method based on parameter varyng PD controller for the fuzzy logc servo controller s presented. Then obtaned results from the comparson between PID controller and FLC wth proposed method are presented. Smulaton results show that FLC performs lke PID controller for when we have not any load or changed parameters or dsturbance but when comparng both controllers wth consderng nected load or changed parameters or dsturbance, the fuzzy logc controller performs better. References [] Hedar, Y., Noee, A.R., Shayanfar, H.A. and Saleh, S. (200 Robust Control of DC Motor Usng Fuzzy Sldng Mode Control wth Fractonal PID Compensator. The Journal of Mathematcs and Computer Scence,, [2] Vkas, S.W., Mthun, M.B., Tulas, R.D. and Kumar, A.D. (200 A New Fuzzy Logc Based Modellng and Smulaton of a Swtched Reluctance Motor. Journal of Electrcal Engneerng & Technology, 5, [3] Kllngsworth, N.J. and Krstc, M. (2006 PID Tunng Usng Etremum Seekng. IEEE Control Systems Magazne, 26, [4] Karthkraa, A. (2009 Stochastc Algorthm for PID Tunng of Bus Suspenson System. Internatonal Conference on Control Automaton Communcaton and Energy Conservaton, Perundura, 4-6 June 2009, -6. [5] Altnten, A., Karakurt, S., Erdogan, S. and Alpbaz, M. (200 Applcaton of Self-Tunng PID Control wth Genetc Algorthm to a Sem-Batch Polystyrene Reactor. Indan Journal of Chemcal Technology (IJCT, 7, [6] Zadeh, L.A. (973 Outlne of a New Approach to the Analyss of Comple Systems and Decson Processes. IEEE Transactons Systems Man and Cybernetcs, SMC-3, [7] Natsheh, E. and Buragga, K.A. (200 Comparson between Conventonal and Fuzzy Logc PID Controllers for Controllng DC Motors. Internatonal Journal of Computer Scence Issues (IJCSI, 7, [8] Wang, X., Meng, Q., Yu, H., Yuan, Z. and Xu, X. (2005 Dstrbuted Control for Cement Producton of Vertcal Shaft Kln. Internatonal Journal for Informaton & Systems Scences (IJISS,, [9] Bng, G., Harong, D. and Yann, Z. (2009 Speed Adustment Brakng of Automatc Tran Operaton System Based on Fuzzy-PID Swtchng Control. Sth Internatonal Conference on Fuzzy Systems and Knowledge Dscovery, Tann, 4-6 August 2009, [0] Hanafy, M., Gomaa, M.M., Taher, M. and Wahba, A. (20 Path Generaton and Trackng for Car Automatc Parkng Employng Swarm Algorthm. IEEE Internatonal Conference on Computer Engneerng Systems, Caro, 29 November 20- December 20, [] Mud, R.K., Dey, C. and Lee, T.T. (2006 Neuro-Fuzzy Implementaton of a Self-Tunng Fuzzy Controller. IEEE Internatonal Conference on Systems, Man and Cybernetcs, 6, [2] Akcayol, M.A. and Sagroglu, S. (2007 Neuro Fuzzy Controller Implementaton for an Adaptve Cathodc Protecton on Iraq-Turkey Crude Ol Ppelne. Appled Artfcal Intellgence: An Internatonal Journal, 2, [3] Azzouna, A., Sakly, A., Trmeche, A., Mtbaa, A. and Benreeb, M. (200 PI-Lke Fuzzy Control Implementaton Usng FPGA Technology. 5th Internatonal Conference on Desgn and Technology of Integrated Systems n Nanoscale Era (DTIS, Hammamet, March 200, [4] Baleghy, A.N. and Mashhad, M.S.K. (202 Desgn and Implementaton Fuzzy Controller n the Frost-Free Refrgerator by Usng Multvarate Regresson. 20th Iranan Conference on Electrcal Engneerng (ICEE, Tehran, 5-7 May 202, [5] Lnkens, D.A., Wang, H., Bennett, S. and Xa, S. (992 Usng Qualtatve Bond Graph Reasonng to Derve Look-Up Tables for Fuzzy Logc Controllers. Frst Internatonal Conference on Intellgent Systems Engneerng, Ednburgh, 9-2 August 992, [6] Yu, J.Z., Hu, X.L. and Dng, R. (2009 Fuzzy Logc PID Based Control Desgn for Permanent Magnet Synchronous Motor Servo System. Second Internatonal Conference on Intellgent Computaton Technology and Automaton, 2, [7] Tzeng, C.B., Lu, Y.C. and Young, M.S. (995 A Prelmnary Study of Fuzzy Control Parameters and Taguch- Method on DC Servo Motor Control. IEEE/IAS Internatonal Conference on Industral Automaton and Control: Emergng Technologes, Tape, May 995, [8] Hao, Y. (202 DSP-Based Fuzzy Logc Servo Motor Control. Internatonal Conference on Control Engneerng and Communcaton Technology (ICCECT, Laonng, 7-9 December 202,

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