Brushlss DC motor spd control stratgy of simulation rsarch Xiang WEN 1,*,Zhn-qiang LI 2 1,2 Collg of Elctrical and Information Enginring, Guangxi Univrsity of Scinc and Tchnology, Liuzhou Guangxi 55006, China Abstract. In viw of th brushlss DC motor spd rgulation problm, an idal control stratgy is dsignd. Through th modl and analysis of Brushlss DC motor, th mathmatical modl of th brushlss DC motor is obtaind. By comparing thr control stratgis of PID control stratgy, fuzzy control stratgy and fuzzy PID control stratgy, PID, fuzzy and fuzzy PID ar dsignd rspctivly for simulation tst. Th simulation rsults show that th fuzzy PID has good control ffct. Kywords. Brushlss DC motor; Fuzzy ; Control stratgy 0. Introduction Th DC brushlss motor is dividd into two typs bcaus of th diffrnt typs of its winding driv currnt wavforms [1]: On is th squar wav prmannt magnt synchronous Motor, bcaus th armatur drivr currnt is th squar wav (trapzoidal wav), which is calld Brushlss DC Motor. Th othr is th prmannt magnt synchronous motor, which is calld th prmannt magnt synchronous motor bcaus th armatur drivr currnt is a sin wav. Compard with th sinusoidal prmannt magnt synchronous motor, brushlss DC motor has obvious supriority, fdback dvic is simplr, th powr dnsity is highr [2], th output torqu is biggr, th control structur is simplr, mak th motor and invrtr fully play thir own potntial. Thrfor, th application and rsarch of brushlss DC motor hav bn paid mor and mor attntion. In many cass, othr kinds of motors hav bn rplacd by thir tchnological advantags. Compard with othr typ motor, brushlss DC motor in th form of squar wav xcitation brushlss DC motor, improv th utilization rat of th prmannt magntic matrial and rducd th volum of motor, incrasing th motor output, with high fficincy, high rliability charactristics. This papr adopts 22 conduction mthod [3], rotor ach cornr 60 lctrical dgrs, Invrtr bridg is a convrtr, th stator magntic stat is a corrsponding chang. Howvr, th principl and procss of anti-lctromotiv forc and lctromagntic torqu gnration ar similar to thos of traditional brushlss dc motors, so th analysis procss is similar. In ordr to nsur th stability of th motor spd, th motor spd closd loop control [,5,6] is ralizd by masuring th motor spd. In this papr, thr control stratgis, PID control stratgy, fuzzy control stratgy and fuzzy PID control stratgy, ar usd to simulat th brushlss DC motor. PID control algorithm has bttr control ffct on linar tim invariant systm [7]. Fuzzy control [8,9] can solv th systm difficult to modl th control problm, bcaus it dos not nd th xact modl of th controlld objct, and oftn adjust th tim is short. Howvr, th fuzzy is difficult to liminat th stady-stat rror bcaus it dos not hav intgral links. Fuzzy control PID control algorithm for nonlinar tim-varying systms can achiv good control ffct. * Corrsponding author: 920592971@qq.com Th Authors, publishd by EDP Scincs. This is an opn accss articl distributd undr th trms of th Crativ Commons Attribution Licns.0 (http://crativcommons.org/licnss/by/.0/).
Fuzzy PID control is a combination of fuzzy control and PID control, which taks full advantag of th advantags of both [9,10]. At th sam tim, it provs that it has bttr control ffct. xprssd as [ ] 1. Working principl and modl analysis of Brushlss DC motor [ ] [ ] 1.1 Working principl In ordr to raliz th commutation without mchanical contact, th brushlss DC motor cancls th brush, and th armatur winding and prmannt magnt stl ar placd on th stator and rotor sid rspctivly, thus bcoming th "DC -DC motor" mchanism. In ordr to control th spd and th rotation dirction of th motor, th brushlss DC motor must b ralizd by th rotor position snsor, th control circuit and th powr invrtr bridg. Th powr driv mod is dividd into [3]: half bridg typ, full bridg typ (1. 22 conduction mod, 2. 33 conduction mod), C-Dump typ, H bridg typ, Four switch typ. 1.2 Brushlss DC motor, mathmatical modl Th transfr function is drivd from th thr-phas full bridg driv and th 22 winding mod of stator winding. At this point, ach phas of th stator winding lads to a 60 dgr lctrical angl, and ach lctrical cycl of th motor undrgos a 6 commutation. In th commutation procss, th thr-phas winding has currnt flow bcaus of th diod frwhling. Whn th shutdown phas currnt is rducd to 0, th frwhling diod stops, th commutation procss is compltd, th nw motor in two-phas conduction stat. Commutation torqu rippl causd by commutation is an important dynamic procss of Brushlss DC motor. Howvr, du to its short duration, it has littl ffct on th ffctiv valu of th lctrical quantity. Thrfor, in th stady stat analysis and th transfr function dduction, it is nglctd to simplify th calculation. It is assumd that only two phas windings ar connctd and thir currnts ar qual and opposit. Tak A and B phas winding conduction as an xampl. (1.1) Th linar voltag quation of Brushlss DC motor is [ ] [ ] [ ] (1.2) By (1.2) availabl (1.3) Irrspctiv of th transint procss of commutation, that is, whn th A and B phass ar stady conduction, th siz of and ar qual and th sign is opposit, and th formula (1.3) can b rwrittn as (1.) Typ: -DC bus voltag; - winding wir rsistanc, ; - winding quivalnt lin inductanc, ; - Lin back EMF cofficint, Similar to othr motors, th powr and torqu of Brushlss DC motor can b analysd from th point of viw of nrgy transfr. Th lctric powr from th powr supply whn th motor is running, th powr of small part into th coppr loss and iron loss, most of th air gap magntic fild to transfr torqu to th rotor of th prmannt magnt rotor, this powr is part of th lctromagntic powr, instad it is qual to th lctromotiv forc of th thr-phas winding and th phas currnt and th product of that. (1.5) Rgardlss of mchanical losss and stray losss of th rotor, th lctromagntic powr is convrtd into rotor kintic nrgy, so (1.6) Typ: - Elctromagntic torqu; - Mchanical angular spd of motor. By formula (1.5) and (1.6) 2
(1.7) Typ: (1.8) - th maximum valu of th air gap flux dnsity distribution of th rotor prmannt magnt; - Th maximum valu is _m pr phas winding chain, ; - A contrary to th wavform function of lctromotiv forc; - A contrary lctromotiv forc. By substituting (1.8) for (1.7), anothr form of th torqu quation can b obtaind [ ] (1.9) Typ: - motor pol count. Whn th brushlss DC motor running in 120 conduction mod, without considring th phas chang of transint procss, so th typ (1.9) can b simplifid to Typ: Motor quation - motor torqu cofficint; - winding phas currnt in stady stat. Typ: LL - load torqu; (1.10) LL (1.11) J - Rotor momnt of inrtia; - Cofficint of viscous friction. In formula (1.), th rlation btwn th bus voltag and th angular spd can b obtaind by rprsnting th currnt with angular vlocity, and thn th motor transfr function is introducd. It will b (1.10) in substitution (1.11) LL (1.12) Th transfr function of th load will b discussd latr, considring th no-load condition at which th armatur currnt is i JJ Rplac (1.13) with (1.) Thrfor ( JJ (1.13) ) ( JJ ) (1.1) (1.15) Th transfr function of th brushlss DC motor is obtaind by Laplac transformation and sorting (1.15) LL JJ ( JJ LL ) ( ) (1.16) Th transfr function shown in quation (1.16) is a two ordr systm and is sortd into th canonical form of th two ordr systm (1.17) Typ: Natural frquncis of two LL JJ ordr systms; ξ 1 JJ LL LL JJ - two ordr systm. Whn th load is not zro, it can b rgardd as th input of th systm, and th systm structur is shown as shown. T L (s ) U d 1 I (s ) T (s ) (s ) 1 ra L as K T Js B V E a According to th suprposition principl, at this tim th output quals th sum of th rsponss of and LL. Whn =0 is shown in Fig. * That is 1 LL LL+ K 1 JJJ (1.18) LL * ( LL )(JJJ ) + ( LL ) LL (1.19) At this point, th transfr function btwn th load torqu and th spd is LL LL LL LL JJ ( JJ LL ) ( ) (1.20) Thrfor, th spd rspons of Brushlss DC motor undr th combind action of voltag and load torqu is 3
LL LL ( LL ) LL JJ ( JJ LL ) ( ) 2. Control stratgy dsign Th transfr function (1.21) btwn th known input voltag and th output spd is considrd. On this basis, th block diagram of th PID, fuzzy and fuzzy PID ar concivd rspctivly, as shown in figur. r1 U rout G dv Error opration r1 Error opration r1 Error opration d c d t d c d t fuzzy PID (a).pid fuzzy U (b).fuzzy T i T p T d PID U G dv G dv rout (c).fuzzy PID Figur thr structural block diagrams Tak th main circuit paramtrs, rspctivly U 120V, r a 1m, L a 0. 0001H T T 0.0275 2 J 0.0002kgm B V 0. 00586wb K 0.0275, T L 10Nm. 2.1 PID dsign A block diagram of th systm consisting of th PID rout is shown in Figur (a). Th main circuit paramtr is substitutd into.19 10-1.22s s) 5 2 2. 10 s 5.58 10 s 1 G ( dv Aftr th addition of PI control, th transfr function of th PI action is st to, and th opn-loop transfr function of th systm bcoms: (.19 10-1.22s G s) Gdv( s) T( s) 5 3 2. 10 s 5.58 10 s 2 1 2.2 fuzzy dsign A block diagram of th systm consisting of a fuzzy is shown in Figur (b). Th spcific dsign procss of fuzzy is as follows: 1) Dtrmin th input languag variabls for rror and rror chang c, th output variabl is r. ( k) r rf ro( k) c( k) ( k) ( k 1), 2) Slct fuzzy substs,c, u={nb (ngativ larg), NM (ngativ middl), NS (ngativ small), ZE (zro), PS (positiv small), PM (positiv middl), PB (positiv larg)}. 3) Dtrmin fuzzy control ruls. ) By rsolving th ambiguity, th output control R, and thn aftr procssing, th output voltag. 2.3 fuzzy PID dsign A block diagram of th systm consisting of a fuzzy PID is shown in figur (c). Th fuzzy PID is combind with fuzzy and PID, rror and rror chang c as input, using th fuzzy control ruls to modify th PID paramtrs to mt th diffrnt momnts of and c on PID paramtrs. Th dsign procss is similar to th fuzzy. Th input linguistic variabls ar rror and rror variation c, but th output variabls bcom proportional, intgral and diffrntial paramtrs, namly, kp ki and kd. At run tim, th control systm complts th on-lin adjustmnt of PID paramtrs by procssing th fuzzy logic ruls, look-up tabl and opration. 3. simulation rsults and analysis
simulatd ffct PID Fuzzy Fuzzy PID ovrshoot big small small dbug tim long short middl stady-stat rror middl big small To vrify th ffctivnss of th abov thr control stratgis. In th MATLAB/Simulink softwar, th simulation modls of th thr schms ar built, in which th initial PID tuning paramtrs ar consistnt. Th stting spd is as follows. Th simulation modl is shown in Figur 5, and th simulation rsults ar shown in Figur 6 Figur 5 Simulink simulation modl Figur. 6 Comparison of th simulation rsults of th thr control schms Through th simulation, th PID ovrshoot is rlativly larg, th adjustmnt tim is rlativly long; fuzzy PID, th ovrshoot is small, th adjustmnt tim is slightly shortr than th PID, th stady-stat rror is almost zro; fuzzy ovrshoot, and adjust th shortst tim, but thr is a larg stady-stat rror. Dtails ar shown in tabl 1. Tabl 1 Th simulation rsults of th thr kinds of control schm. Conclusion In this papr, thr diffrnt control stratgis simulation of Brushlss DC motor, through th xprimntal rsults, th fuzzy PID combind with fuzzy control and PID small ovrshoot and small stady-stat rror, good simulation ffct. 5. Rfrnc 1. Zhang Yan. DSP brushlss DC motor spd control systm of high prformanc rsarch basd on [D]. Xi'an Elctronic and Scinc Univrsity, 2007. 2. Yin Yunhua. Dsign and Simulation of Brushlss DC motor control systm basd on DSP [D]. North Cntral Univrsity, 2007. 3. Xia Changliang. Brushlss DC motor control systm [M]. Scinc Prss, 2007... Du Juan, Guo Zhonghua, Ma Hua ji. Spd control systm of Brushlss DC motor basd on adaptiv fuzzy PID control [J]. lctronic tchnology and softwar nginring, 2016, (03): 139-11. 5. Lian QinJian. Dsign and Simulation of Brushlss DC motor driv systm of lctric vhicl basd on DSP [D]. Xi'an Univrsity Of Architctur And Tchnology, 201. 6. Wang Ling, Liu Wiguo. Simulation of Brushlss DC motor spd control systm basd on fuzzy PI control [J]. computr simulation, 2009, (10): 186-189. 7. Wi Hua, Li Qun, Chn Dbao. A nw nonlinar paramtr fuzzy PID control mthod of [J]. computr tchnology and dvlopmnt, 2008,18 (2): 237-239. 8. Chng Lirong, Sun Changzhi. Simulation of thr phas brushlss DC motor spd rgulation systm [J]. microcomputr information, 2007, (0): 251-252. 9. Zhang Jinhuan. PID control systm and fuzzy adaptiv PID control systm rsarch and comparison [J]. Journal of Wuhan Univrsity of Tchnology, 2005,27 (5): 286-290. 5
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