Position control of DC Servomotor with Nonlinearity Using ICA Based on FLC

Transcription

1 oition control of DC Srvomotor with onlinarity Uing ICA Bad on FLC Ali Soltani Elctrical Enginring Dpartmnt Thran Urban& Suburban Railway Opration Company Thran, Iran Abtract DC Srvomotor ar ud in wid varity fild uch a robotic, indutry, and mchatronic ytm that prci poitioning i conidrabl. onlinariti uch a Backlah, Dad Zon and load chang limit th prformanc of prci poition control of DC rvomotor. Uing multi-loop control ytm bad on principl of cacad control, thi papr dal with poition control of DC rvomotor with non-linar paramtr uch a backlah, dad zon and load chang. To liminat th ffct of onlinariti Fuzzy Logic Controllr (FLC) ar propod in poition and pd control loop. In ordr to achiv bttr control prformanc, th Imprialit Comptitiv Algorithm (ICA) i applid to optimiz th paramtr of th FLC coniting of fuzzy control rul and normalization factor. Simulation rult how th bttr prformanc of propod ICAoptimizd FLC bad driv in comparion with FLC and ICAoptimizd I. Kyword- DC Srvomotor; onlinariti; Fuzzy Logic Controllr (FLC); Imprialit Comptitiv Algorithm (ICA) I. ITRODUCTIO Th DC rvomotor ar utilizd in application uch a robotic arm, indutrial machin tool, and mdical application. For uch application poition control of DC rvomotor ar mor important but nonlinariti uch a backlah, dad zon, and load chang cau undirabl ffct on th ytm fficincy [1]. Gnrally, convntional controllr lik I, ID ar applid to control th poition of a DC rvomotor. But, th prformanc of convntional controllr i dpndnt on th xact machin modl and accurat gain [2]. Morovr, nonlinar factor uch a backlah, dad zon, load diturbanc, and thrmal chang machin paramtr and accordingly dirupt th prformanc of th convntional controllr. So, th control chm ar not abl to liminat th ffct of th nonlinariti appropriatly [1]. To ovrcom th ffct of th nonlinariti, advantag can b mad of artificial intllignc tchniqu uch nural ntwork, gntic algorithm, and Fuzzy Logic Controllr (FLC)[1, 3-5]. FLC i an intllignt but computationally impl controllr [6, 7]. Th advantag of FLC ovr convntional controllr ar that it i abl to handl nonlinariti and that it dign i indpndnt of ytm paramtr [8]. Howvr, thr i no ytmatic procdur for digning and tuning th FLC. It i tak tim and rquir th dignr to Mohammad Rza Ghadiri Elctrical Enginring Dpartmnt Ilamic Azad Univrity, Qazvin Branch Qazvin, Iran m.r.ghadiri@qiau.ac.ir b particularly xprincd and killful for th tdiou tak of fuzzy tuning [8-10]. In thi papr, at firt cacad I controllr uing cacad control tructur, optimizd by Imprialit Comptitiv Algorithm (ICA) ar dvlopd to control th poition of DC rvomotor with and without nonlinariti. Aftr that, in ordr to liminat th nonlinariti ffct, two FLC ar propod a poition and pd controllr. To avoid th lngthy computation and to achiv a bttr control prformanc, th ICA i mployd to tun th paramtr of th FLC coniting of fuzzy control rul and normalization factor. Alo prntd i amnt of imulation rult obtaind uing th propod tchniqu in comparion with FLC and ICA-optimizd I. II. MODEL OF DC SERVOMOTOR Fig. 1 giv th block diagram of DC rvomotor. A modl of a DC rvomotor bai of thi block diagram can b rprntd by blow quation a follow: [ F F ] () () () ω () F1 () F2 = = = 1 () () 2 ( J. + B)( L a. + R a ) + K ( R a + L a ) 2 ( )( ) J. + B 2 K V a TL L a. + R a + K whr V a () i armatur voltag a quation 2. T L () i load torqu and K i rvomotor contant tho can b xprd a quation 3 and quation 4, rpctivly. Alo, Equation 5 how th rlationhip btwn th angular poition and th angular pd [11]. V Figur 1. Block diagram of DC rvomotor () = L I + R I E() a a a a a + (1) (2)

2 T M T L = J. ω ( ). + B. ω( ) K = k ϕ.φ (4) θ 1 = ω (5) () () whr J B, rvomotor angular vlocity rvomotor angular poition armatur currnt armatur ritanc armatur inductanc lctromagntic torqu momnt of inrtia cofficint of friction rvomotor contant. III. THE ROOSED COTROL SCHEME Th chmatic rprntation of th propod controllr i hown in Fig. 2. Thi controllr i bad on principl of cacad control and conit of thr control loop namd poition control loop, pd control loop, and currnt control loop[12]. In thi papr, th controllr of th poition and th pd control loop ar I or fuzzy logic typ. Alo, th controllr of currnt control loop i I-typ. A it i illutratd in th figur th ICA i utilizd to optimiz th paramtr of controllr in ordr to atify th dign critria. (3) B. Fuzzy Logic Controllr (FLC) Fig. 4 dpict propod configuration of th FLC that i applid a poition and pd controllr. Th input of FLC ar th rror ignal and th drivativ of th rror ignal. Thn th hav to b fuzzifid. Th fuzzy control algorithm includ a t of fuzzy control rul that ar rlatd through th concpt of MF and th compoition rul of infrnc. Fuzzy control t hav to b dfuzzifid bcau th plant cannot rpond dirctly to th control t. On th othr hand, th controllr output ΔU i ummd or intgratd in ordr to gnrat th actual control ignal U a pd in poition control loop or currnt i in pd control loop. Morovr,,, and ar normalization factor. Input variabl of FLC hav to b normalizd ovr a rang pcifid for MF and alo, output variabl of FLC ha to b normalizd ovr a rang pcifid for plant. An appropriat normalization ha a dirct impact on fficincy of th controllr. Alo, th prformanc of a FLC dpnd on th lction of th control rul, MF, and normalization factor. In lin with thi, th ICA i ud to optimiz th fuzzy control rul and th normalization factor [13]. Figur 4. Block diagram of FLC C. Imprilit Comptitiv Algorithm (ICA) Figur 2. Cacad controllr optimizd by ICA A. onlinar Dc Srvomotor Th block diagram of th DC rvomotor modl with nonlinariti i hown in Figur 3. Th nonlinarity uch a backlah, dad zon, and load chang wr addd to th DC rvomotor modl to mak th modl rlativly act th am way a th ral DC rvomotor. Figur 3. Block diagram of nonlinar DC rvomotor Figur 5. Flowchart of Imprialit Comptitiv Algorithm

3 ICA i a rcntly introducd optimization algorithm. Optimization through thi algorithm ha bai on th concpt of imprialitic comptition. Fig. 5 portray th flowchart of ICA. ICA tak advantag of th aimilation policy adoptd by imprialitic countri inc th 19th cntury. According to thi policy, th imprialit k to improv th conomical, cultural, and political ituation of thir rpctiv coloni o a to win thir loyalty. Thi thory u th trm mpir to rfr an imprialit and it coloni. Th powr of an mpir dpnd on th powr of it imprialit and it coloni. In imprialitic comptition, wakr imprialit lo thir coloni to mor powrful mpir. Aftr dividing all coloni among imprialit and crating th initial mpir, th coloni tart moving toward thir rlvant imprialit tat. Thi movmnt i a impl modl of aimilation policy that wa purud by om imprialit tat. Fig. 6 how th movmnt of a colony toward th imprialit. In thi movmnt, x and θ ar random numbr with uniform ditribution a hown in quation (4) and (5) rpctivly and d i th ditanc btwn colony and th imprialit. x ~ U 0, β d (6) θ ~ U γ, γ (7) whr β and γ ar arbitrary numbr that modify th ara whr coloni randomly arch around th imprialit. Th wak mpir, onc thy lo all thir coloni, will b th coloni of othr mpir. Evntually, all th wak mpir will collap, laving only on powrful mpir [14]. Th proportional and intgral gain of th poition I controllr ar pcifid by 1 and 2, rpctivly. 3 i proportional gain and 4 i intgral gain of th pd I controllr. Alo, 5 and 6 ar proportional and intgral gain of th currnt I controllr, rpctivly. Th ix point (i, 1 i 6) ar t togthr to form th array country. Country = [1, 2, 3, 4, 5, 6] (8) Th prformanc of th dignd I controllr ar valuatd on th bai of a cot function. Th cot function i th Intgral of Abolut Error (IAE). In ordr to minimiz thi cot function, th ICA look for th bt array country (i.., th array of i'). Cot Function (9) In ICA, th initial numbr of coloni i t at 100, vn of which ar chon a th initial imprialit. Alo β and γ ar t at 2 and 0.6 (Rad) rpctivly. Th maximum itration of th ICA t at 80. B. Optimizing FLC Uing ICA Dpnding on th opration of th ytm, twnty fiv control rul and nin control rul can b writtn in fuzzy logic for poition and pd controllr, rpctivly. To dign uch controllr, in th poition control loop th input variabl of poition rror and drivativ of poition rror Δ and alo, output variabl ar conidrd to hav fiv MF: (gativ Big), (gativ), (Zro), (oitiv), and B (oitiv Big) a hown in Fig. 7. Tabl І how th twnty fiv fuzzy if-thn rul of poition FLC. Figur 6. Motion of coloni toward thir rlvant imprialit Figur 7. MF of th input and output of poition FLC IV. OTIMIZIG I COTROLLERS AD FLCS USIG ICA A. Optimizing I Controllr Uing ICA To mploy th ICA in optimizing th proportional and intgral gain of I controllr in poition, pd, and currnt control loop, th gain in th ICA ar codd in th form of th array country. In addition, Intgral Abolut Error (IAE) i dfind a cot function with th purpo of minimizing it to atify th dign critria. To optimiz th I controllr uing ICA, th proportional and intgral gain of ach I controllr ar pcifid by man of two point. Sinc, thr ar thr I controllr in th control loop, ix point hav to b optimizd through ICA. Hnc, to optimiz th paramtr of I controllr uing ICA th paramtr ar codd a follow: TABLE I. Δ B DECISIO TABLE OF OSITIO FLC Additionally, in th pd control loop th input variabl of pd rror and drivativ of pd rror Δ ar conidrd to hav thr MF:,, and a hown in Fig. 8. Th MF of th output ( ) ar,,,, and B i hown in Fig. 9. Tabl ІI how th nin fuzzy if-thn rul of pd FLC. B B B B B

4 TABLE II. DECISIO TABLE OF SEED FLC TABLE IV. DECISIO TABLE F SEED FLC FOR OTIMIZATIO Δ Δ B Figur 8. MF of input of pd FLC Alo, th normalization factor of poition FLC,, and can b pcifid by 35, 36, 37. Evntually, thr point 38, 39, 40 ar ud for th normalization factor of pd FLC,, and. Hnc, th problm of finding th paramtr of FLC ar rducd to th problm of dtrmining 40 point (i, 1 i 40).Th 40 point ar put togthr to form th array Country. Country = [1, 2, 3,, 39, 40] (10) Alo, th prformanc of th dignd FLC ar valuatd on th bai of th cot function IAE. In ICA, th initial numbr of coloni i t at 150, ightn of which ar chon a th initial imprialit. Alo β and γ ar t at 2 and 0.6 (Rad) rpctivly. Th maximum itration of th ICA t at 100. V. SIMULATIO RESULTS Th fuzzy control rul optimizd by ICA ar hown in Tabl V and VI. TABLE V. DECISIO TABLE OF OSITIO FLC OTIMID BY ICA Figur 9. MF of output of pd FLC To utiliz th ICA in optimizing th poition and pd FLC, th paramtr of th FLC conit of fuzzy control rul and normalization factor, in th ICA ar codd in th form of th array country. Alo, a cot function i dfind o that it i minimizd in ordr to atify th dign critria. To optimiz th paramtr of FLC uing ICA th paramtr ar codd a follow: Th fuzzy control rul of poition FLC can b pcifid by man of twnty fiv individual point 1 to 25 a hown in Tabl III. Similarly, th fuzzy control rul of pd FLC can b rprntd by man of nin individual point 26 to 34 a hown in Tabl IV. TABLE III. Δ B DECISIO TABLE OF OSITI FLC FOR OTIMIZATIO B Δ B TABLE VI. B B B B B B B B DECISIO TABLE OF SEED FLC OTIMID BY ICA Δ For valuation purpo, firt a comparion i drawn in MATLAB toolbox for th DC rvomotor which u I controllr and ar optimizd through ICA. Thi comparion i btwn th two tat of with nonlinariti and without nonlinariti in ordr to tudy th poition rpon of th rvomotor in ach ca. Th prformanc of th DC rvomotor wa valuatd for a priod of 1 againt a rfrnc poition of 0.5 Rad. Alo, th validity of th ytm ha bn xamind with load torqu B B

5 Figur 10. oition rpon of DC rvomotor uing ICA-I controllr chang TL=0.38.m at t=0.4. Th imulation rult of th both optimizd controllr with and without nonlinariti ar plottd a hown in Fig. 10. A i hown in thi figur, nonlinariti cau ocillation in th poition tracking control ytm. At th nxt tag, th poition rpon of th DC rvomotor with ICA-optimizd I (ICA-I) controllr i compard with FLC at th prnt of nonlinariti a hown in Fig. 11. Alo, th comparion of output currnt of DC rvomotor with ICA-I controllr and FLC i hown in Fig. 12. A ar hown in Fig. 11 and Fig. 12 DC rvomotor with FLC can ovrcom th nonlinariti and liminat th ocillation. Figur 11. oition rpon of DC rvomotor with nonlinariti Figur 12. Currnt of DC rvomotor with nonlinariti Evntually, th poition rpon of th DC rvomotor with th FLC and with th propod ICA-optimizd FLC Figur 13. oition rpon of DC rvomotor with nonlinariti (ICA-FLC) i plottd a hown in Fig. 13. Thi figur dpict that th rpon of th DC rvomotor with ICA-FLC i rlativly bttr than FLC in trm of th accuracy of poition tracking. Th cot function IAE ar compard in Tabl VІІ. It i obviou from thi tabl that ICA-FLC bad driv ha a bttr prformanc in comparion with FLC and ICA-optimizd I controllr. TABLE VII. COMARISO OF COST FUCTIOS Cot function Mthod ICA-I controllr FLC ICA-FLC VI. IAE COCLUSIO In thi papr, a mthod of optimizing FLC uing ICA wa propod for th poition control of a DC rvomotor with nonlinar paramtr uch a backlah, dad don, and load chang uing multi-loop control ytm bad on principl of cacad control. In ordr to prov th upriority of th propod controllr chm, it wa compard with FLC and ICA-optimizd I controllr in trm of prformanc. Comparativ imulation rult indicat that th ICA-optimizd FLC bad driv i mor fficint than FLC and ICAoptimizd I. AEDIX Following ar th pcification of th DC motor chon for th imulation. Armatur ritanc: 2 Armatur inductanc: Srvomotor contant: 0.1. / Srvomotor contant: 0.1. / Momnt of inrtia: 1. Cofficint of friction: Width of dad zon: 2V=4V Dad-band width of backlah: 2D=1 REFERECES

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