Optimization of PID Parameter for Position Control of DC-Motor using Multi-Objective Genetic Algorithm

Transcription

1 ISSN (Online) Vol. 2, Issue 6, June 214 Opimizaion of PID Parameer for Posiion Conrol of DC-Moor using Muli-Objecive Geneic Algorihm MD Amanullah 1, Mohi Jain 2, Praibha Tiwari 3, Sidharh Gupa 4, Geea Kumari 5 M.Tech Scholar, EEE Deparmen, SHIATS, Allahabad, INDIA 1,4,5 Assisan Professor, EEE Deparmen, GLA Universiy, Mahura, INDIA 2 Assisan Professor, EEE Deparmen, SHIATS, Allahabad, INDIA 3 Absrac: The ambiion of his paper is o design a posiion conroller of a DC moor by selecion of a PID parameer using geneic algorihm. The Proporional plus Inegral plus Derivaive (PID), conrollers are mos widely used in conrol heory as well as indusrial plans due o heir ease of execuion and robusness performance. The aspiraion of his deed represenaion capable and apace uning approach using Geneic Algorihm (GA) o obain he opimized crierion of he PID conroller so as o appropriae he essenial appearance designaion of he echnique below consideraion. This scheme is a simulaion and experimenal analysis ino he developmen of PID conroller using MATLAB/SIMULINK sofware. There are several echniques which are used for uning of PID conroller o conrol he speed conrol of DC moor. Tuning of PID parameers is considerable because hese parameers have a admirable effec on he sabiliy and performance of he conrol sysem. Using geneic algorihms o perform he uning of he conroller resuls in he opimum conroller being appraise for he sysem every ime. Keywords: PID Conroller, DC-Moor, Tuning Mehods, Geneic Algorihm, Opimizaion Technique I. INTRODUCTION DC moor is a power acuaor which ransforms elecrical energy ino mechanical energy. DC moor is widely used in various indusrial applicaions where wide speed ranges are required. The advanage of DC moors may be speed conrol. The erm speed conrol sand for inenional speed variaion carried ou auomaically and manually. DC moors are mos suiable for wide range speed conrol and are herefore used in many adjusable speed drives. Since speed is direcly proporional o armaure volage and inversely proporional o magneic flux produced by he poles and adjusing he armaure volage and/or he field curren will change he roor speed. DC moors have been widely used in many indusrial applicaions such as elecric cranes, elecric vehicles, and roboic manipulaors due o wide, simple, and coninuous conrol characerisics. Due o is excellen speed conrol characerisics, he DC moor has been widely used in indusry even hough is mainenance coss are higher han he inducion moor. As a resul, posiion conrol of DC moor has araced considerable research and several mehods have evolved. Proporional-Inegral Derivaive (PID) conrollers have been widely used for speed and posiion conrol of DC moor. Now a day s world wide PID conroller sweepingly used for an opimum soluion gives a superior efficiency. For obaining he beer efficiency he absolue oupu needed o mach se oupu. For his aspiraion requiremen of a conroller. PID conroller is he widely used in he process indusry like perochemical, paper, pulp, oil & gas, as well as missile conrol sysems, because of is easy design and robus implemenaion in a broad range of operaional condiion. Unluckily, i was compleely complex une properly he gains of he PID conrollers because various indusrial plans are frequenly loaded down wih difficulies such as high order, ime delays, and nonlineariies. During he long ime various heurisic program procedures have been proposed during he uning of PID conrollers. These convenional procedures are very famous amid conrol engineers because one and only can use hem, especially as no or small observaion abou he plan under conrol is available. These procedures provide sable, healhy and compleely grea Achievers in spie of his he gains are no a all assured of being opimal. Even, hose convenional uning process frequenly breaks down o accomplish suiable Achievemen in he case of plans having nonlineariy, higher order or ime delay. Thus, inelligence echniques have been inroduced by he researchers according o esablished he uning an easier one. As for a laes scheme of PID uning is recommended based on he Fuzzy gain programming approach. A neural neworks uned PID conroller wih he help of fuzzy crieria is presened. As for his paper presens a PID uning approach founded wih respec o Muli-objecive Geneic Algorihm (MOGA) and his performance is mached by Copyrigh o IJIREEICE

2 ISSN (Online) Vol. 2, Issue 6, June 214 convenional echniques of uning. The MOGA uned PID (MOGA-PID) conroller is well-ried on several sophisicaed echniques. II. SYSTEM MODEL As reference we consider a DC shun moor as is shown in figure 1. DC shun moors have he field coil in parallel (shun) wih he armaure. The curren in he field coil and he armaure are independen of one anoher. As a resul, hese moors have excellen speed and posiion conrol. Hence DC shun moors are ypically used applicaions ha require five or more horse power. The equaions describing he dynamic behavior of he DC moor are given by he following equaions; K T : Torque consan in N.m/Ampere T m : Torque developed by he moor in N.m θ (): Angular displacemen of shaf in radians J: Momen of ineria of moor and load in Kg.m 2 /rad B: Fricional consan of moor and load in N.m/ [ rad ] sec A. Numerical values The DC moor under sudy has he following specificaions and parameers 1. Specificaions:- 2hp, 23 vols, 8.5 amperes, 15rpm 2. Parameers:- J = Kg m 2 /rad b = N m/( rad ) sec K =.274 vol/(rad/sec) R = 4 ohm L = H The overall ransfer funcion of he sysem is given by Figure (1):- Diagram of DC shun Moor. θ s =.274 V s s s s (6) V = Ri + L di d + e b 1 T m = K T i a (2) T m = J d 2 θ d 2 d θ + B d e b = e b = K b d θ d (3) (4) Afer simplificaion and aking he raio of θ (s) V(s) θ(s) V(s) = we will ge he ransfer funcion as below: K b S Js +b Ls+R +K 2 b rad V (5) The PID conroller has been brodly used since i invened in 191. The combinaion of proporional conrol acion, inegral conrol acion and Derivaive conrol Acion is Termed proporional plus Inegral plus derivaive conrol Acion. I improves boh he ransien and seady sae response characerisics. I is similar o lead lag compensaor or band rejec filer, i reduces he rise ime. The peak overshoo depends on properly uned values of T i and T d. I eliminaes he seady sae error beween inpu and oupu. I increases he TYPE and ORDER by he sysem is One. The hree main parameers involved are Proporional (P), Inegral (I) and Derivaive (D). The proporional par is responsible for following he desired se-poin, while he inegral and derivaive par accoun for he accumulaion of pas errors and he rae of change of error in he process respecively. Where, R: Armaure resisance in ohm L: Armaure inducance in henry i: Armaure curren in ampere V: Armaure volage in vols e b : Back emf volage in vols Figure (2):- Block diagram of a convenional PID conroller K b : Back emf consan in vol/ (rad/sec) Copyrigh o IJIREEICE

3 ISSN (Online) Vol. 2, Issue 6, June 214 e() = r() y() is called as error signal and u() is he conroller oupu for his specific error signal. Opimizaion Technique Daa u() = K p e + K i e d + K d d d e() (7) MOGA Where, Error, e() =Se poin- Plan oupu K P = Proporional gain K i = Inegral gain K d = Derivaive gain Also, he equaion (6) can be rewrien in Laplace form as: u(s) = e s (K p + K i /s + K d s (8) Finally, under he above sraegy he ransfer funcion of he PID conroller or he conrol law is esablished by u s C(s) = = K e s p + K i + K s ds (9) Tuning of PID by MOGA:- Commonly, he PID conroller scheme mehod using he inegraed absolue error (IAE), inegral of squared-error (ISE), inegraed of ime-weighed-squared-error (ITSE) is frequenly occupied wih conrol sysem design on accoun of i can be classified experimenally in he frequency domain. IAE = r y d = e ISE = e 2 ()d() ISTE = e 2 d() d (1) (11) (12) I is he preferred of he conrol engineer so ha which individual crierion of he conrol sysem requiremen addiional consideraion. So as per he demand a higher weigh can be allowed, alhough given he oher requiremen specificaion a he same ime. Ye, he oal sum of he weighs in an objecive funcion mus be equal o one, in order o he oal performance of he sysem may be confirmed. I shows he resilience in PID uning while applying MOGA. III. ABOUT GENETIC ALGORITHM John Holland was he faher of geneic algorihm who discovered in early 197. Geneic algorihms (Gas) are adapive heurisic search algorihm based on he evoluionary ideas of naural expansion. As such he denoe Conrol Inpu Conrol Oupu Figure (3):- MOGA based PID Tuning Scheme. and inellecual vicimizaion of a random search used o opimizaion problems. Alhough randomized, GAs are absoluely no in random, insead he deed of hisorical knowledge o direc he search ino he reason of excellen performance in he search space. The key echnique of he GAs is designed o fabricae processes in general sysem mandaory for evoluion, mainly hose follow on he ehics firs laid down by Charles Darwin of survival of he fies. GA has been sudied as a saisfacory and effecive mehod for finding ou difficul opimizaion problems. By exacly avoiding local minima, i converges o global minima. I originaes from an iniial populaion obaining a number of chromosomes where for each one correlae o a resul of he given problem. Then he achievemens of each original are calculaed by using a correc finess funcion. Essenially, GA consiss of five significan seps: iniial populaion, finess funcion, Selecion, Crossover and Muaion. These are also known as GA drivers. The applicaion of five basic operaors confesses he formaion of new children, which may be locaed excellen han heir parens. This algorihm is repeaed for several generaions and finally sops when meeing produc ha is denoed he opimum resul of he problem. Copyrigh o IJIREEICE (a) Iniial populaion:- PID Conroller Is sars wih Randomly Originaed saes, hese saes are saisfacory o he problem. The populaion size of is creae on he naure of he problem, even so ypically consis of various hundreds or housands of feasible soluions. Commonly, he populaion is originaed randomly; admi he perfec range of possible soluions. Infrequenly, he soluions can be "sown" in he range, where opimal soluions are possible o be esablished.

4 (b) ISSN (Online) Vol. 2, Issue 6, June 214 Finess funcion:- A finess funcion is a cerain ype of objecive funcion ha is familiar wih summarize, because a single figure of meri, however close o a given design soluion is o complee he se of goals. In he range of geneic programming and geneic algorihms, a single design soluion is denoed by a sring of numbers (specified as a chromosome). Afer every overall esing or simulaion, he concep is o remove he 'n' wors design soluions, and o creae 'n' new ones as from he bes design soluions. Each and every design soluion have o be rewarded a figure of meri, o illusrae how close i comes o mee he overall requiremen, and i is developed by pu ino use he finess funcion o he es or simulaion, soluions are obained from ha soluion. Two main pars of finess funcions survive: he one where he finess funcion does no change while opimizing a fixed funcion or esing wih a fixed se of es cases and anoher one where he finess funcion is changeable, while niche separaion or develop he se of es cases. (c) Selecion:- Two pairs are seleced a random o reproduce. They are seleced based on heir finess funcion score. One may be seleced more han one, whereas one may no be seleced a all. Make a copy he seleced programs o he new populaion. The regeneraion process may be subdivided ino wo pars, firs is Finess Evaluaion and second is Selecion. The finess funcion is how is operaed he evoluionary process and is view is o idenify how well a sring (paricular) solves he problem, admiing as an evaluaion of he respecive performance of each populaion member. Basically four mos common mehods of he selecion: 1. Tournamen Selecion 2. Normalized geomeric selecion 3. Roulee Wheel selecion 4. Sochasic Universal is sampling abou geneic algorihm chromosomes o he nex. I is relaed o biological muaion. Muaion change more han one gene values in a chromosome from is iniial sae. In muaion, he soluion may compleely change from he las soluion. Hence, GA may come o a beer soluion by using muaion. Muaion occurs during evoluion by a userdefinable probabiliy. This has probably been se low. If i is se oo high, he search will become an original random search. Geneic Algorihm performs he following seps: 1.Originae an Iniial Populaion randomly or heurisically. 2.Calculae and save he finess for each paricular in he curren populaion. 3. Specify he selecion probabiliy a single ha i is reciprocal o is finess 4. Originae he nex curren populaion by mos probabiliies selecing he individuals from he earlies curren populaion, in order o goods produc of geneic operaors. 5. Repea sep 2 unil a sufficien resul is obained. A flow char of he general scheme of he implemenaion of he GA is shown in Figure. (d) Crossover:- For each pair o be maed, a crossover poin is preferred a random from wihin he bi sring. The offspring is developed by inerchange beween he parens a he crossover poin. Populaion is differen early in he process, hese reasons he crossover o be large in he beginning. However, i will sele down in fuure generaions. Hence, There are several ypes of crossover operaors like single poin crossover, wo poin crossover, arihmeic crossover ec. Figure (4):- flow char of he general scheme of he implemenaion of he Geneic Algorihm. Eliminae he negaive error componens by he help of ISE. q ISE = k=1 e 2 (k) In his simulaion, he objecive is o decrease he cos funcion. During ha moive he objecive funcion is preferred for he Inegral Square Error (ISE). The ISE squares he error o eliminae negaive error componens. (e) Muaion:- Muaion is a geneic operaor familiar wih a cure for geneic difference from one generaion of a populaion Copyrigh o IJIREEICE

5 Oupu y Oupu y ISSN (Online) Vol. 2, Issue 6, June Tuned PID Posiion Conrol Dc Moor START T Iniial Populaion K p,k i & K d Evaluae finess Selecion.5 Crossover Figure (6):- Tuned PID posiion Conrol of DC Moor wihou MOGA Muaion Eliis Model Tuned PID DC-Moor Responce of he Sysem wihou GA Tuned PID DC- Moor Responce of he Sysem wihou GA.8 Terminaion Condiion.6 Sop NO YES Figure (7):- Tuned PID DC Moor Response wihou MOGA Figure (5) :- Flow char of MOGA-PID Conroller. IV. SIMULATION & RESULTS A. Analysis of convenionally uned PID Conroller wihou Geneic Algorihm Here we are using DC moor Posiion Conrol wih PID Conroller wihou G.A. By he use of MATLAB programming PID conroller is uned & he resul is given below. B. Analysis of convenionally uned PID Conroller wih Geneic Algorihm Muli Objecive Geneic Algorihm (MOGA) PID Conroller performance depends on he convergence rae. The crieria like populaion ype, populaion size, creaion, funcion, selecion and much more are also affecing he convergence rae. Hence, is order o decline precocious convergence of Geneic Algorihm, so his exremely sraegies o selec he suiable operaors and crieria for i. Table I display he crieria and operaors of GA ha are accomplish by accurae experimenal research of his work. Copyrigh o IJIREEICE

6 Oupu y Oupu y ISSN (Online) Vol. 2, Issue 6, June 214 Table I:-Display he Crieria & Parameers of GA GA Parameer Value/Mehod Populaion ype Double Vecor Populaion size 2 Creaion funcion Feasible populaion Selecion Tournamen Table II: - COMPARISON OF PARAMETER WITH PID & MOGA-PID Parameer K p K i K d r s %OS PID MOGA-PID Muaion Adapive feasible Crossover Arihmeic crossover Generaion 65 From he above able all he parameer values are apply o G.A he PID conroller wih DC moor Posiion Conrol is opimized. The sysem response is given below. 1.4 Tuned PID DC-Moor Conrol wih MOGA Tuned PID DC-Moor Conrol wih MOGA Figure (1):- Comparaive Response beween MOGA-PID and PID Figure (8):- Tuned PID DC-Moor Conrol wih MOGA.4.35 Tuned PID DC Moor Posiion Conrol wih MOGA Tuned PID DC-Moor Posiion Cnrol wih MOGA Figure (11):- Comparaive Response beween MOGA-PID and Tuned PID DC-Moor Posiion Conrol Figure (9):- Tuned PID DC Moor Posiion Conrol wih MOGA. Copyrigh o IJIREEICE

7 ISSN (Online) Vol. 2, Issue 6, June 214 V. CONCLUSION The designed PID wih GA has much faser response han response of he classical mehod. The classical mehod is good for giving us as he saring poin of wha are he PID values. However he GA designed PID is much beer in erms of he rise ime and he seling ime han he convenional mehod. Finally he geneic algorihm provides much beer resuls compared o he convenional mehods. And also he error associaed wih he geneic based PID is much lesser han he error calculaed in he convenional scheme. In his paper, implemenaion of he geneic algorihm based PID conroller for he DC moor posiion conrol sysem is covered. In fuure GA based PID conroller will be implemened in DC moor posiion conrol sysem using Ma lab 7.1. G.A is applied o find opimal soluion for he parameer of DC moor wih PID conroller & indicaes ha G.A is powerful global searching mehod. This review aricle is also presening he curren saus of uning of PID conroller for speed conrol of DC moor using sof compuing echniques. REFERENCES [1] Neenu Thomas, Dr.P.Poongodi, 29. Posiion Conrol of DC Moor Using Geneic Algorihm Based PID Conroller,Proceedings of he World Congress on Engineering 29 Vol II WCE 29, London, U.K. [2] T. O..Mahony, C J Downing and K Fala, Geneic Algorihm for PID Parameer Opimizaion: Minimizing Error Crieria, Process Conrol and Insrumenaion July 2, Universiy of Srachclyde, pg [3] K Ogaa, Modern Conrol Sysems, Universiy of Minnesoa, Prenice Hall, 1987 [4] B.Nagaraj,Dr.N.Murugananh A Comparaive Sudy of PID Conroller Thning Using GA, EP, PSO and ACO ICCCCT-1 IEEE Trans [5] Phillip David Power, Non Linear Muli Layer Percepron Channel Equalisaion,Chaper 4 Geneic Algorihm Opimisaion, in IEEE Transacions,The Queen Universiy of Belfas,April 21. [6] Kalyanmoy Deb, Opimizaion for Engineering Design Algorihm & Examples,Indian Insiue Of Technology Kanpur, Prenice Hall, 25. [7] Liu Fan, Er Meng Joo Design for Auo-uning PID Conroller Based on Geneic Algorihms Nanyang Technological Universiy Singapore IEEE Trans on ICIEA 29 [8] Grefensee, Opimizaion of conrol parameers for geneicalgorihms. IEEE Trans on SMC, 1986, 16(1): [9] ASTROM K.J., HAGGLUND T.: The fuure of PID conrol, Conrol Eng. Prac., 21, 9, (11), pp [1] B. C. Kuo, Auomaic Conrol Sysems, 5h ed. Englewood Cliffs Prenics-Hall, [11] J. G. Ziegler and N. B. Nichols, Opimum seings for auomaic conrollers, Trans. ASME, vol. 64, pp , [12] M. Ge, M. S. Chiu and Q. G. Wang, Robus PID conroller design via LMI approach, Journal of Process Conrol, vol. 12, no.1, pp. 3-13, 22 [13] David E. Goldberg, Geneic Algorihms in Search, Opimizaion and Machine Learning. The Universiy of Alabama, Addison-Wesley Publishing Company Inc, 1989 [14] Chipperfield, A. J., Fleming, P. J., Pohlheim, H. and Fonseca, C. M., A Geneic Algorihm Toolbox for MATLAB, Proc. Inernaional Conference on Sysems Engineering, Covenry, UK, 6-8 Sepember,1994. [15] Q.Wang, P Spronck and R Trach, An Overview Of Geneic Algorihms Applied To Conrol Engineering Problems, Proceedings of he Second Inernaional Conference on Machine Learning And Cyberneics, 23. [16] K. Krishnakumar and D. E. Goldberg, Conrol Sysem Opimizaion Using Geneic Algorihms, Journal of Guidance, Conrol and Dynamics, Vol. 15, No. 3, pp , [17] A.Varsek, T. Urbacic and B. Filipic, Geneic Algorihms in Conroller Design and Tuning, IEEE Trans. Sys. Man and Cyber, Vol. 23, No. 5, pp , Copyrigh o IJIREEICE 165