Using DTC Method to Reduce Torque Ripple in BLDC Sensorless Motors

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Deborah Bond
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1 J. asic. ppl. Sci. Rs., 3s)7, 13 13, TxtRoad Publication SSN 93 Journal of asic and pplid Scintific Rsarch Using DT Mthod to Rduc Tou Rippl in LD Snsorlss Motors mir Movahdi 1, Gholam Rza Lalzar 1 Dpartmnt of Elctrical Enginring, Najafabad ranch, slamic zad Univrsity, sfahan, ran Malk shtar Univrsity of Tchnology-Faculty of Marin Scinc and Tchnology sfahan, ran Rcivd: Jun 1 13 ccptd: July 1 13 STRT n this papr to stimat th rotor position in snsorlss LD motor driv, th mthod of th ratio functions lin by lin flux is u. This mthod, compa to othr mthods which ar valuatd to stimat th rotor position, has low softwar and hawar volum and thrfor, its implmntation is asy and also manufacturing cost is lss. lso this mthod has an appropriat fficincy in a wid rang of spd and stimat th rotor position is indpndnt of spd and rotor funcy. lso in this papr, Dirct Tou ontrol DT) mthod is u to dsign snsorlss LD motor driv. DT is on of th most innovativ and fficint mthods in control of th lctrical machin. High spd in rspons to changs in tou, simplicity of implmntation, indpndnc to machin paramtrs and nds of lss computation ar th advantags of this mthod. t th nd of this papr, simulation rsults by using softwar MTL shows good function of snsorlss LD motors with DT mthod. KEYWORDS: Snsorlss, LD motor, DT mthod, tou NTRODUTON Using of D motors has high propagation in industry bcaus of th salint faturs such as, xtnsiv control of spd, high fficincy and so on. Th only disadvantag of this motor is its nd of th commutator and th brushs, bcaus ths componnts ar constantly bing rodd and thrfor thy incras th nds of motor to srvic and maintnanc. n or to scap from th problms with th hlp of th magntic fild proprty, control of D motors is lctrical. Ths typs of motors ar calld rushlss D Motor LD) [1]. For LD motors, gnrally hall snsors ar u to dtrmin th angular position of th rotor []. Using lctro mchanical snsors not only incrass th cost and complxity of hawar driv, it will also dcras th stability and rliability. Dirty working conditions, tmpratur and xistnc of high mchanical vibrations du to th snsitivity of th position snsors, can caus many problms. So it is not rcommndd to us th mchanical position snsors in applications of spac, limitd and inaccssibility, and finishd pric ar important and or th high capability of th systm rliability is consid. So a lot rsarch has bn don for snsorlss drivs to b abl to position, spd and tou without using position snsors mountd on th rotor shaft [3, ]. onvntional mthods of snsorlss control ar classifid into fiv catgoris. Th first mthod, is ba on back-mf []. Rducing th rang of back-mf at low spds and th problms associatd with its masurmnt, th xistnc of voltag nois and masurmnt rrors and poor prformanc of this mthod at low spds is among th disadvantags of this mthod. Th scond mthod, is a mthod of stimating stator lakag flux []. rating rrors of intgration at low spds, high computational volum and bing snsitiv to changs of motors paramtrs is among th disadvantags of this mthod. Th thi mthod is to us a variation of th stator inductanc [7]. This poor prformanc at low spds and high volum of hawar and softwar that incras th pric of motors, is disadvantag of this mthod. Th fourth mthod, is mthods which ar ba on control thory [8]. This mthod is not fficint in noisy fdback signals and also at low spds will hav many rrors. To solv problms of ths mthods, in this papr to stimat th rotor position of snsorlss LD motor driv, th mthod of using functions of th lin by lin flux which is th sam mthod of using suitabl functions of back-mf, is u. This mthod compa to othr mthods, has low hawar and softwar volum and thrfor, its implmntation is asy and cost lss. t also has an appropriat fficincy in a wid rang of spds and stimat of th rotor position is indpndnt of th rotor spd and funcy, thrfor, has not th xisting problms in back-mf masurmnt mthods such as funcy dpndnc and motors spd and masurmnt problms and filtring [9, 1]. Modling * orrsponding uthor: mir Movahdi, Dpartmnt of Elctrical Enginring, Najafabad ranch, slamic zad Univrsity, sfahan, ran. _movahdi8@yahoo.com

2 Movahdi and Lalzar, 13 Motor and driv ba on DT, is th most ffctiv modling of LD motor driv which can b u for various rasons. DT mthod du to its simplicity and high-spd in rspons to changs in th tou rfrnc, is consid on of th most fficint control tchniqus of lctrical machin, which can b u for control typs lctric machins. n this papr, w hav trid to valuat th prformanc and also simulatd DT control mthod. High spd in rspons to changs in tou, implmntation simplicity, lack of dpndnc on machin paramtrs and nd of low computation is anothr advantag of this mthod [11-1]. For LD motor trapzoidal wav form of back-mf is u in or to minimiz th tou rippl and to maximiz productivity and tou capability. Th rsults of LD motor simulation by MTL softwar shows th simplicity and good prformanc of this mthod in control of th motor. -snsorlss control mthod to stimat th rotor position n this papr to stimat th rotor position of snsorlss LD motor driv th mthod of functions of lin by lin flux is u. Phas-to-nutral voltags quation is achivd as in quation 1). dia dar dia d k f ar )) dia d d f ar )) Va Ria L Ria L Ria L k.. d dib dbr dib d k fbr )) dib d d f br )) Vb Rib L Rib L Rib L k.. 1) d dic dcr dic d k f cr )) dic d d f cr )) Vc Ric L Ric L Ric L k.. d n th abov quation, k is calld cofficint back-mf. n quation 1), ar is consists of a fixd amount plus a priodic function of rotor position θ). f ar θ) function is th flux lakag of phas-a which ar changd with rotor position. Most manufacturrs of LD motors, don t put th star connction rotor in disposal of th usr, Thrfor, th quation of lin by lin voltag V ab by using quation 1), is obtaind as follows. d ia ib ) df abr ) Vab R ia ib ) L k.. ) dt d n rlation ), ω and f abr θ), ar rspctivly, rotor spd and function of lin by lin flux. W dfin a nw function as quation 3). df abr ) 1 dia dib H ) V V ) R i i ) L 3) ab a b a b d.k n quation 3), H ab θ) has changd with rotor position and it is u for th stimation of th rotor position. To dlt spd ω in quation 3), w can us two function of lin by lin H xy θ) and achiv nw quation ). dib dic Vb Vc ) R ib ic ) L H ) bc G ) G ) bc / ab ) H ) ab dia dib Va Vb ) R ia ib ) L Function Hθ) bc and Hθ) ca ar obtaind just lik quation ). Figur 1 displays th changs of th functions G 1 θ), G θ) and G 3 θ) accoing to rotor angular position. ccoing to this figur, th tim of commutation ar ba on th points which ths functions includ th maximum of rang. To stimat th rotor position and dtrmination of commutation points can us G 1 θ), G θ) and G 3 θ) functions altrnativly.

3 J. asic. ppl. Sci. Rs., 3s)7, 13 Figur 1. hangs of G i θ) functions accoing to th rotor angular position lso tabl 1 listd th rspctiv of Gθ) u functions in th diffrnt oprating rang of dgrs. With combin of rspctiv of ths functions w can obtain a continuous and unit Gθ) and it can b u to stimat th commutation points. Tabl 1. U Gθ) functions in ach oprating mod LD Motor Functions G 1θ) G θ) G 3θ) Oprating rang <θ< π/ and 11π/1<θ<π π/<θ<7π/ π/<θ<π/ 7π/<θ<9π/ π/<θ<π/ 9π/1<θ<11π/ Mod 1 and and 3 and 3- Dirct Tou ontrol DT) mthod Th lctromagntic tou of a prmannt-magnt brushlss machin in th synchronously rotating rfrnc fram can b xprs as follows [11]. 3 P d d T [ ) ) Ld Lq ) ] ) d d d L, L ) q Tou pulsations ar associatd mainly with th flux harmonics, th influnc of highr or harmonics in th stator winding inductanc usually bing ngligibl. Thrfor th lctromagntic tou can b xprs as follows. 3 P d d T [ ) ) Ld Lq ) 7) d d Th lctromagntic tou quation, for LD motor, with ithr a nonsalint-or salint-pol rotor, can thn b simplifid as follows. 3 P T ) 8) or, in th stationary rfrnc fram, as: 3 P T s s s s ) 9) Whr s, s, s, and s ar th α and β axs stator currnts and flux linkags, rspctivly, viz. s os Sin, Sin os 1) s

4 Movahdi and Lalzar, 13 s os Sin, Sin os 11) s For nonsalint-pol brushlss machins with a nonsinusoidal stator flux linkag, th lctromagntic tou, for LD motor, can b simplifid as: 3 P d d T [ ) ) ] 1) d d n th rotating-axs rfrnc fram, or as in th stationary rfrnc fram. 3 P d d r r T [ s s ] 13) d d r os Sin, Sin os 1) r Th stator flux-linkag vctor can b obtaind from th masu stator voltags currnts s and s. V s and V s and s Vs Rs s )dt, s Vs Rs s ) dt 1) Th magnitud and angular position of th stator flux-linkag vctor is obtaind as: 1 s s s, tan ) 1) r s r s s L, L 17) s s s s Six nonzro-voltag spac vctors ar dfind for a LD driv as shown in figur. Figur 3 show th idalizd phas currnt wavforms for LD opration, and thir rlationship with th voltag spacvctor sctors and switching stats [11]. S 1 S 3 S 3 11) V 11) 11),, ),, ),, ) S S S V 11) 11) V 11),, ),, ) a, b,c ) S S S S 1 S Figur. Six nonzro-voltag spac vctors ar dfind for a LD driv n a LD driv, howvr, only two phass ar conducting in th 1 conduction mod, xcpt during commutation priods whn all thr phass conduct, th unxcitd phas conducting via a frwhling diod. Sinc th uppr and lowr switchs in th sam phas lg may both b simultanously off in LD driv, irrspctiv of th stat of th associatd frwhl diods [Figur. ] six digits ar ui to rprsnt th stats of th invrtr switchs, on digit for ach switch. Thus, th voltag spac vctors, V,, V, and V ar rprsntd as switching signals 1 1), 1 1), 11 ), 1 1), 11), 1 1), rspctivly, whr, from lft to right, th logical valus xprss th stats of th uppr and lowr switching signals for phass, and, rspctivly. Th zrovoltag spac vctor is dfind as ). S 7

5 J. asic. ppl. Sci. Rs., 3s)7, 13 t t t V V1 V V3 V V Figur 3. Show th idalizd phas currnt wavforms for LD opration Figur shows a schmatic of a DT LD driv [11]. s can b sn from tabl, th switching pattrn of th invrtr can b dtrmind accoing to th stator flux-linkag and tou status from th outputs of two rgulators shown in figur, and th sctor in which th stator flux linkag is locatd at that instant of tim. n ach sctor, if th actual stator flux linkag is th sam as th commandd stator flux linkag ), only on nonzro-voltag spac vctor and a zro-voltag vctor ar u to control th incras T=1) or dcras T=) of th tou, sinc during any dgr lctrical priod only two phass ar xcitd and controlld in a LD driv, as indicatd in Tabl. n addition, whn th actual flux linkag is smallr than th commandd valu 1), th nonzro-voltag spac vctor is u to incras th flux linkag, whil whn th actual flux linkag is gratr than th commandd valu 1 ), th nonzro-voltag spac vctor is u to dcras th stator flux linkag. Tabl. Switching tabl for DT of LD driv Tou 1 Flux V V V V V V V Sctor 3 V V V V V V V V V V V V V V 3 P dr T [ d d r d s s ] V, V s s s s Vs Rs Vs Rs ) dt ) dt s s 3 s s r r L s s s s L s s Figur.. Schmatic of DT LD driv 8

6 Movahdi and Lalzar, 13 - Simulation rsults n th this sction, simulation rsults for snsorlss LD motor corrsponding spd of 3 rpm and 1 rpm ar shown. n this papr th initial spd consid 1 rpm. n figur, th curv of tou is shown accoing to motor spd. s obsrvd in this figur, th motor tou is swing around th rfrnc valu Nm) and aftr a fw switchs rachs its rfrnc valu Tou [N.m] Tou [N.m] Rotor spd [rpm] Rotor spd [rpm] 1rpm 3rpm Figur. urv of changing tou accoing to motor spd Gnratd tou is shown in figur, phas-c currnt rachs to its final lvl bfor th phas-b currnt rachs to zro. Th rsults of phas-a currnt dcra and as th rsult is shown in figur, th tou dcras in rang of tim in commutation. ccoing to ths figurs, th avrag valu of th tou is Nm and tou follows rfrnc valu wll. lso it can b sn that th tou accoing to th figur, has a littl rippl, which is th main advantags of DT mthod. Th spds of th motor is shown in th figur 7. Tou Tou [N.m] [N.m] Tim [s] Tim [s] 1rpm 3rpm Figur. Motor tou 9

7 J. asic. ppl. Sci. Rs., 3s)7, 13 1 Rotor spd Rotor spd [rpm] 8 [rpm] Tim [s] Tim [s] 1rpm 3rpm Figur 7. Motor spd n figur 8, wavform of th currnt phas a, b and c ar magnifid to study bttr. Th wavform of phas-a, xisting puls in currnt, is sn in th middl of th guidanc rang 1 dgr. Th pulss cratd by commutation btwn th two phass b and c. LD motor trapzoidal wavform voltag back-mf u in or to minimiz th tou rippl and maximiz productivity and tou capability. Phas-a currnt Tim [s] Phas-b currnt Tim [s] Phas-c currnt Tim [s] Figur 8-a. Figur of magnifid wavform phass currnt for 3rpm 7

8 Movahdi and Lalzar, 13 8 Phas-a currnt Tim [s] Phas-b currnt Tim [s] Phas-c currnt Tim [s] Figur 8-b. Figur of magnifid wavform phass currnt for 1rpm Magnifications of wavform back-mf for phas-a ar shown in figur 9. ccoing to this figur, backmf rang of voltag in Stady stat at spd of 3 rpm quals to. volts and in spd of 1 rpm quals to 19. volts. 1 Phas-a back-mf Phas-a back-mf [V] [V] Tim [s] Tim [s] 1rpm 3rpm Figur 9. Figur magnification of wavform of back-mf phas-a s sn in th simulation rsults, DT mthod for low and high spds, in snsorlss LD motors, has good rsults. -onclusion n this papr to stimating rotor position of snsorlss LD driv motor w hav bn u th mthod that using functions of th ratio of lin by lin flux. This mthod compa with othr mthods, has littl hawar and softwar volum and thrfor, its implmntation is asy and construction costs lss. lso this mthod has suitabl fficincy in wid rang of spds and stimat th rotor position is indpndnt of funcy and spd of th rotor, so it has not th xisting problms in th mthod of masuring th back-mf, such as funcy dpndnc and motor spd. 71

9 J. asic. ppl. Sci. Rs., 3s)7, 13 n continuanc is u dirct tou control mthod DT) for th dsign of snsorlss LD motor driv. DT mthod du to its simplicity and high spd in rspons to changs in th tou rfrnc is consid on of th most fficint mthods for control of lctrical machins, which can b u for control of many typs of lctric machins. n this papr w try to valuat th opration styl and simulation of DT control. High spd in rspons to changs in tou, as of implmntation, indpndnc on machin paramtrs and a low computation, ar th advantags of this mthod. REFERENES [1] J. S. Mayr, O. Wasynczuk, "nalysis and modling of a singl-phas brushlss D motor driv systm", EEE Trans. on Powr Systms, Vol. 9, pp. 7379, Sp [] M. Gougani, M. hapariha, J. Jatskvich,. Davoudi, "Hall snsor-ba locking lctric diffrntial systm for LD motor drivn lctric vhicls", EEE/EV, pp. 1-7, March 1. [3] N. Matsui, "Snsorlss PM brushlss D motor drivs, "EEE Trans. on ndustrial Elctronics, vol. 3, no., pp. 3-38, 199. [] Y. Jin Yong, L. i Qiang, "Study of position dtction mthod for snsorlss brushlss D lctromotor", EEE/EMS, Vol., pp , ug. 1. [] S. Gui-Jia, J. W. Mckvr; "Low cost snsorlss control of brushlss D motors with improvd spd rang", EEE Trans. on Powr Systms,Vol. 19, pp. 9-3, March. [] N. Ertugrul, P. carnly, " nw algorithm for snsorlss opration of prmannt magnt motors", EEE Trans. on Powr Systms, Vol. 3, pp , Fb [7] Y. S. Lai, F. S. Shyu, S. S. Tsng, "Nw initial position dtction tchniqu for thr-phas brushlss D motor without position and currnt snsors", EEE Trans. on Powr Systms, Vol. 39, No., Pp. 891, pril 3. [8]. Trzic, M. Jadric; "Dsign and implmntation of th xtndd kalman filtr for th spd and rotor position stimation of brushlss D motor", EEE Trans. on Powr Systms, Vol. 8, pp , Dc. 1. [9] K. Ta-Hyung, L. yung-kuk, M. Ehsani, "Snsorlss control of th LD motors from nar zro to high spd", EEE Trans. on Powr Systms, Vol. 19, pp. 13-1, Nov.. [1] T. H. Kim, M. Ehsani, "Snsorlss control of th LD motors from nar-zro to high spds", EEE Trans. on Powr Systms, Vol. 19, No., pp.13-1, Nov.. [11] Y. Liu, Z. Q. Zhu, D. How, "Dirct tou control of brushlss D drivs with ucd tou rippl", EEE Trans. on Powr Systms, Vol. 1, pp. 99, pril. [1] Y. Liu, Z. Q. Zhu, D. How, "ommutation tou rippl minimization in dirct tou controlld- PM brushlss D drivs", EEE Trans. on Powr Systms, Vol. 3, pp , aug. 7. [13] S.. Ozturk, W.. lxandr, H.. Toliyat, "Dirct tou control of four-switch brushlss D motor with non-sinusoidal back mf", EEE Trans. on Powr Systms, Vol., pp. 3-71, Fb. 1. [1] S.. Ozturk, Oh Yang, H.. Toliyat, "Powr Factor orrction of dirct tou controlld brushlss D motor driv", EEE/, pp. 97-3, Sp. 7. 7

Preliminary Fundamentals

Preliminary Fundamentals 1.0 Introduction Prliminary Fundamntals In all of our prvious work, w assumd a vry simpl modl of th lctromagntic torqu T (or powr) that is rquird in th swing quation to obtain th acclrating torqu. This