Proceedings of the 6th WSEAS International Conference on Applications of Electrical Engineering, Istanbul, Turkey, May 27-29,

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1 Proceedngs o the 6th WSEAS Internatonal Conerence on Applcatons o Electrcal Engneerng, Istanbul, Turkey, May 27-29, THE SPEED CONTROL OF DC SERVO MOTOR WITH PROPORTIONAL INTEGRAL, FUZZY LOGIC AND ADAPTIVE NEURO-FUZZY INFERENCE SYSTEMS ISMAIL TEMIZ Electrcal Department Marmara Unversty Techncal Educaton aculty Goztepe Campus, Kadkoy/Istanbul/Turkey MEHMET AKAR Electrc Programme Gazosmanpaşa Unversty Taşlıçtlk Campus/Tokat/Turkey Abstract In ths study DC servo motor s mathematcal model and equatons were extracted or solvng the speed control problem. There were three derent methods used or controllng the speed. It was created smulaton model at the Matlab programme and mplemented proportonal-ntegral, uzzy and adaptve neuro uzzy nerence system controllers respectvely whle t was workng varable condtons. At the servo motor applcaton t s expected that no overshoot, settlng reerence value quckly and mnmum nluence on the system stablty. Key-Words: DC Servo Motor, Proportonal-Integral, Fuzzy, Adaptve Neuro Fuzzy Inerence System 1. Introducton DC servo motors have been used generally at the computers, numerc control machnes, ndustral equpments, weapon ndustry, speed control o alternators, control mechansm o ull automatc regulators as the rst starter, startng systems quckly and correctly. Whle some propertes o DC servo motors are the same, lke nerta, physcal structure, shat resonance and shat characterstcs, ther electrcal and physcal constants are varable. The velocty and poston tolerance o servo motors whch are used at the control systems are nearly the same. So they must be controlled accordng to the control system needs. For ths am; t has mplemented proportonalntegral, uzzy logc and adaptve neuro uzzy nerence system respectvely at the varable workng stuatons to the smulaton model whch has prepared at the Matlab programme or mprovement the servo motor perormance. 2. Control Methods 2.1. Proportonal-Integral Control (PI) PI control whch uses requently at the ndustral applcaton s math total o ntegraton error and multplyng o error wth constant. Ths stuaton depcted n equaton 1. t u( t) = Kp. e( t) + Kı e( t). dt (1) 0 Kp, Kı, u(t) and e(t) are proportonal gan, ntegral gan, controller output and error sgnal, respectvely. Steady state error whch occurs wth proportonal control can be reset manually or automatcally. For automatc reset, electronc ntegrator crcuts are used at the controller. The derence between measured and reerence value whch s called error sgnal s beng ntegrated accordng to tme. System s settled the reerence value by ncreasng or decreasng the energy whch has gven by ntegrator crcut to the system. I workng stuatons changes and response value s derent rom the reerence value, error sgnal occurs as a result. Then ntegrator crcut repars output. PI controller block dagram as llustrated n gure 1. Fgure 1: PI controller block dagram

2 Proceedngs o the 6th WSEAS Internatonal Conerence on Applcatons o Electrcal Engneerng, Istanbul, Turkey, May 27-29, Fuzzy Logc Control Frst o all mathematcal model s necessary whle makng expermentaton or control systems but t may not be always possble n practce. Sometmes n spte o creatng true model, usng o ths model makes some complcated problems at the mplementaton. When conronted wth lke these problems, knowledge and experence o expert people s utlzed. These people develop lexble control mechansm by usng the words requently n our le,lke sutable, not very sutable, hgh, a lttle hgh, more, very more whch are dened specal varable. Fuzz logc control whch has expermentaton o uzzy cluster theores and uzzy logc, has been set up lke logcal relatves. A uzzy logc system s based on 4 man parts whch are llustrated n gure ) Input unts whch has been known uzzer 2- ) Rule base 3- ) Inerence mechansm 4- ) Output unts whch has been known deuzzer Layer 1: Ths s membershp uncton layer where membershp uncton degree has been calculated or every nput varable. (A 1 (x1) and A 2 (x1); B 1 (x2) and B 2 (x2)) Layer 2: Second layer consttutes rule base o algorthm and uzzy rules are dened n ths layer. Nod nputs are degree o rules and outputs are normalzed weghtness degrees. As a result, ths layer s msson s normalzaton o rule weghtness. w = A x1 B x2 (2) ( ) ( ) Fgure 3: Structure o Ans wth 2 nputs, 1 output Fgure 2: Block dagram o the uzzy logc controller 2.3. Adaptve -Neuro Fuzzy Inerence System Ans algorthm s composed o uzzy logc and neural networks wth 5 layers. Structure o Sugeno model wth 2 nputs and 1 output s shown at table 1. Inputs x1 x2 Membershp unctons A 1, A 2 B 1, B 2 Rules IF x1 IS A 1 AND x2 IS B 1 THEN 1 = p1( x1) + q1( x2) + r1 IF x1 IS A 2 AND x2 IS B 2 THEN 2 = p2( x1) + q2( x2) + r2 Table 1: Fuzzy-Sugeno model Propertes o layer descrbed or x1, x2 as an nput varables. Layer 3: Ths layer s called as normalzaton layer and t calculates degree decsveness o uzzy rules. The normalzaton process or. node s dvson o degree decsveness o. uzzy rules to sum o degree decsveness o uzzy rules. Model parameters are called as deuzzer or result parameters. w w = (3) w Layer 4: Fourth layer o ans s called as dmenson degree o gnton o a rule. In ths layer; uzzy rule s process s mplemented by multplyng the gntons degree o normalzed rules wth lnear uncton w = w ( p x1 + q x2+ r ) (4) Layer 5: Ths s output node o ans and conssts o only one node. Ths layer s output s arthmetcal average o 4 nodes ormer tsel. w = w = (5) w

3 Proceedngs o the 6th WSEAS Internatonal Conerence on Applcatons o Electrcal Engneerng, Istanbul, Turkey, May 27-29, DC Servo Motor Mathematcal Model The velocty o the D C servo motor s controlled by changng the supply voltage. Accordng to ths theory rewrtes voltage and moment equatons; d V = R. I + L (6) dt V = R. ( t) + L d(t) + e(t) dt (7) dϖ ( t) M e = j + B. ϖ ( t) + M y ( t) dt (8) e( t) = K. ϖ ( t) (9) V=240 V I=15 A n=3000 rpm M y =5 Nm B=0.02 Nms J=0.05 kg m 2 K=5/15,3Nm/A Ra=0,5 Ω La=0,01 Table 2: Servo Motor Paramete rs H In orde r to create the block dagram o system; ntal condtons are acquescence zero and laplace transorm s mplemented to the equatons.. ( s)( Ls + R) = V ( s) Kϖ ( s) (10) V ( s) K. ϖ ( s) ( s) = (11) R + Ls K B M y (s) s. ϖ ( s) = ( s) ϖ (s) (12) j j j K. ( s) M y ( s) ϖ ( s) = (13) B + sj V(s), M y (s), ω(s) mot or voltage, load moment and angular velocty, respectvely. Accordng to these varable DC servo motor s closed loop block dagram s shown n gure 4. Fgure 4: DC servo motor block dagram 4. Applcaton Proportonal-ntegral controller whch s known as a classcal controller s created or DC servo motor. DC servo motor s current (I a), angular velocty (ω m ) s smulated or constant and varable velocty poston under the load at the Matlab programme. Then or the same workng stuatons uzzy and ans based controllers are created or DC servo motor. Fgure 5: Servo Motor Smulaton Model In ths smulaton t s amed to control motor velocty wth the motor current and armature s voltage. Z ω = ω - ω re whch s called angular velocty error s used as an nput varable. Armature current must be lmt or sot start and protect the motor rom hgh current. So that armature current was used as a second nput varable. Output uzzy cluster s created as an output varable whch regulates PWM duty perod accordng to error between motor velocty normaton and reerence value. Membershp unctons represents the motor velocty normaton wth the words "very small", "small", "ok", "much", "very much" and people experence s relected to the system. Rules used at the controllers whch are based on human experence and normaton are:

4 Proceedngs o the 6th WSEAS Internatonal Conerence on Applcatons o Electrcal Engneerng, Istanbul, Turkey, May 27-29, I ω err = Very small => output= ncrease 2- I ω err = Small => output= a lttle ncrease 3- I ω err = Ok => output = Ok 4- I ω err = More =>output = a lttle decrease 5- I ω err = Most => output = decrease Fgure 6: Membershp unctons relatng to ω nputs In gure 6 sgnal angular velocty error ( ω range s lmted between [-30, 30] values. Negatve zone denes motor velocty slower than the reerence and postve zone denes aster. Fgure 8: Controller output under the 3 Nm load and 100 radan/s reerence velocty At ths reerence velocty and load, although rsng response o PI, uzzy and ans controller are nearly the same, overshoot s occurred or PI control. Ans controller settlng tme s better than the others. Also there s no steady-state error or three methods. Fgure 7: Membershp unctons belong to PWM Duty output Output membershp uncton represents how much the perod o pwm duty shall ncrease or decrease. It ncludes 5 membershp unctons between [-5, 5] n range. Fuzzy clusters are dened as "decrease", "a lttle decrease", "ok", "a lttle ncrease" and "ncrease" Fgure 9: PI controller output under varable load and reerence velocty.

5 Proceedngs o the 6th WSEAS Internatonal Conerence on Applcatons o Electrcal Engneerng, Istanbul, Turkey, May 27-29, Fgure 10: Fuzzy controller output under the varable load and reerence velocty. Fgure 12: All controller output under the varable load and velocty. Fgure 11: Ans controller output under the varable load and reerence velocty. Fgure 13: Fuzzy controller velocty-tme, currenttme response under the 3 Nm load and 100 radan/s reerence velocty. At gure 9, 10, 11 varable reerence velocty and load response are llustrated or three controllers. When studed careully these gures accordng to rsng tme, settlng tme, postve and negatve overshoot best perormance s belong to ans. Fgure 14: Ans controller velocty-tme, currenttme response under the 3 Nm load and 100 radan/s reerence velocty.

6 Proceedngs o the 6th WSEAS Internatonal Conerence on Applcatons o Electrcal Engneerng, Istanbul, Turkey, May 27-29, Concluson In ths study, 3 and 5 Nm load under the varable and reerence speed s mplemented to the DC servo motor whch s used as a model. At the 3 Nm load, although PI controller s stablzed poston at 0.4 second overshoot s observed at response o system. At the same workng condtons, t s observed no overshoot or uzzy and ans controllers, settlng tme or uzzy and ans controller s 0.38 and 0.33 seconds respectvely. When the load moment on DC servo motor s shat ncreased 5 Nm and system response tested or varable velocty t s observed that the response o ans controller s better than the others. Current s responses are between reasonable values or three controllers at the test stuaton whch s descrbed above. Because o learnng characterstc o error the perormance o ans controller s better than the others under varable load and velocty. But uzzy and ans controller s response are nearly the same because o the current lmt. The control operaton s not perormed n the lmted zone. Reerences [1]Temz,İ., Tunçalp, K. ve Oğuz, Y., Fuzzy Logc Controller For Constant Out Voltage O A Three Phase Synchronous Generator At Varous Load Levels MS 2000 Internatonal Conerence On Modellng And Smulaton, Las Palmas de Gran Canara, Span, September 25-27, [2]F.Barrero,A.Gonzalez,A.Torralba,E.Galvan, and L.G. ranquelo, Speed Control o Inducton motor usng a naval uzzy sldng-mode structure IEEE Transacton on Fuzzy Systems, Vol.10,No:3,June,2002 [3]Temz,İ.,Akuner,C.,Brbr,Y. Bulanık Mantık Yöntemyle Asenkron Motorun Stator Akımın Smülasyonu,GAP V. Mühendslk kongres, Nsan 2006 Şanlıura, Türkye [4] Åström K.J., Hägglund T.," PID Controllers", 2nd Edton, Instrument Socety o Amerca,1995 [5] Zadeh,L.A.: Bulanık Sets,Conormaton and Control 8, [6] Paytra M.J., Mlynek D.M.,1996, Fuzzy logc mplementaton and Applcatons, John Wley pres, New York, 317p. [7] Jang, J. S. R ANFIS: Adaptve-Network Based Fuzzy Inerence Systems.IEEE Trans. on Systems, Man, and Cybernetcs, 23 (03): [8] Neuro-Fuzzy and Sot Computng: A Computatonal Approach to Learnng and Machne Intellgence, nbj. R. Jang & C. Sun &E. Mzutan, Prentce Hall 1997, ISBN: [9] Vardar K.: DC Motorun Hızının Bulanık Logc le kontrolü, Dumlupınar Ünv. Elektrk-Elektronk Mühendslğ Bölüm Semner (2002)