On Position Sensorless Control for Permanent Magnet Synchronous Motor Based on a New Sliding Mode Observer

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1 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp Snsors & Trnsducrs 24 by IFSA Publishing, S. L. On Position Snsorlss Control for Prmnnt Mgnt Synchronous Motor Bsd on Nw Sliding Mod Obsrvr, 2 Qixin Zhu, 2 Zhng Zhng, Hongli Liu, 3 Guoping Zhng School of Mchnicl Enginring, Suzhou Univrsity of Scinc nd Tchnology, Suzhou, 259, Chin 2 School of Elctricl nd Elctronic Enginring, Est Chin Jiotong Univrsity, Nnchng, 333, Chin 3 Shnzhn Hn s Motor Tchnology Compny Limitd, Shnzhn, 5858, Chin Tl.: , fx: E-mil: bob2cn@63.com Rcivd: 5 July 24 /Accptd: 3 Sptmbr 24 /Publishd: 3 Octobr 24 Abstrct: For th problms of buffting nd phs dly in trditionl rotor dtction in snsorlss vctor control of prmnnt mgnt synchronous motor (PMSM), th Sigmoid function is proposd to rplc sign function nd th pproch of picwis linriztion is proposd to compnst phs dly. To th problm tht th output of trditionl low pss filtr contins high-ordr hrmonic, two-stg filtr including trditionl lowpss filtr nd Klmn filtr is proposd in this ppr. Bsd on th output of trditionl first-ordr low-pss filtr, th Klmn filtr is usd to gt modifid bck-emf. Th phs-lockd loop control of rotor position is doptd to stimt motor position nd spd. A Mtlb/Simulink simultion modl of PMSM position srvo control systm is stblishd. Th simultion nlysis of th nw sliding mod obsrvr s bck-emf dtction, position nd spd stimtion, lod disturbnc nd dynmic procss r crrid out rspctivly. Simultion rsults vrify fsibility of th nw sliding mod obsrvr lgorithm. Copyright 24 IFSA Publishing, S. L. Kywords: Prmnnt mgnt synchronous motor, Sliding mod obsrvr, Phs compnstion, Two-stg filtr, Phs-lockd loop control.. Introduction To obtin th xct rotor position nd spd informtion in th PMSM vctor control systm, position nd spd snsor should b instlld on th motor shft, but th using of position nd spd snsor not only incrs th systm cost, but lso rduc th systm robustnss. Thrfor, in rcnt yrs, th ppliction of snsorlss control tchnology in PMSM spd control systm bcoms spcilly importnt [, 2]. Currntly, position nd spd snsorlss control tchniqus usully hv sttor flux stimtion mthod [3], modl rfrnc dptiv mthod [4], stt obsrvr stimtion mthod [5, 6] nd rtificil intllignc stimtion mthod [7], tc. Obsrvr mthods bcom th most populr nd sliding mod obsrvr [8, 9] mthod is on of thm. Howvr, convntionl sliding mod obsrvr xists mny problms, so it nd to b studid nd improvd, sinc th convntionl sliding mod obsrvr just us simpl first-ordr low-pss filtr to obtin motor bck-emf stimtd vlu. According to th rltionship btwn bck-emf nd th motor rotor 7

2 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp position, th rotor position nd spd informtion cn b obtind. As th sliding mod mk systm srious buffting, bck-emf ftr filtring hs lrg phs lg. Currntly, in th position nd spd snsorlss PMSM vctor control systm, mny wys hv bn proposd to stimt th motor rotor position nd vlocity. Litrtur [] uss th lctromgntic corrltivity of PMSM to stimt th rotor position nd spd. This mthod hs simpl clcultion nd fst dynmic rspons, but it is vry snsitiv to th motor prmtrs, nd whn motor spd is low, stimt will not vry ccurt. Litrtur [] hs proposd mthod of trickling high frquncy voltg to th motor, nd dtctd th currnt to obtin rotor spd nd position informtion simultnously. Although this mthod cn b pplid to rltivly wid spd rng, thr r still dficint tht nois problms would b brought bout ftr high frquncy signl hs bn injctd, nd thr r mny strict rquirmnts to th hrdwr circuit. Switching function in litrtur is rplcd by sturtion function [2, 3], buffting cn b wknd by choosing rsonbl boundry lyr thicknss. But only its rotor position stimtion mthod hs bn vrifid ccording to thory, th motor spd stimtion nd closd-loop control hv not bn rsrchd in dpth [4]. Ths points limit th furthr pplictions of sliding mod obsrvr in snsorlss PMSM control systm to som xtnt. Bsd on sliding mod control thory, nw typ of sliding mod obsrvr is proposd in this ppr. Instd of th trditionl sign function, sigmoid function [5, 6] hs ffctivly limintd chttring [7]. In som high prformnc pplictions, bck-emf is obtind mrly by convntionl first-ordr low-pss filtr, which cn not b dirctly usd to clcult th rotor position, bcus it contins mor disturbncs. Thrfor, two stg filtr is proposd in this ppr. This two stg filtr contins first-ordr low-pss filtr nd convntionl Klmn filtr. Firstly, th bck-emf is obtind through first-ordr low-pss filtr. Thn, th convntionl Klmn filtr cn b usd to limint th high frquncy rippl in bck-emf. Spcific to first-ordr low-pss filtring, th motor rotor position stimtion hs lg, so picwis linr phs compnstion mthod is proposd. In ddition, s th ccurcy of rotor position stimtd from th trditionl pproch is not stisfid, th phs-lockd loop tchniqu is doptd to stimt th rotor position, which grtly improvs th ccurcy of th rotor position. Bsd on nw snsorlss PMSM vctor control systm with thr-ring structur, nmly th position loop, vlocity loop nd currnt loop, PMSM position snsorlss srvo control systm simultion modl is stblishd on Mtlb / Simulink pltform. Th bck-emf, stimtion of position nd vlocity, lod disturbnc nd dynmic procss of th nw sliding mod obsrvr is nlyzd rspctivly. Th simultion rsults show tht th nw sliding mod obsrvr lgorithm is fsibl nd ffctiv. 2. Mthmticl Modl of PMSM In th two-phs sttionry α rfrnc frm, th mthmticl modl of PMSM is s shown in qution (-) to qution (-4). di R = i + ( u ), (-) dt L L di R = i + ( u ) (-2) dt L L ψ f = ω sin θ (-3) L ψ = f ω cos θ (-4) L whr i α, i r th currnts of α xis nd xis rspctivly, u, u r th sttor voltgs of α xis nd xis rspctivly, α, r th motor ψ f bck-emf of α xis nd xis rspctivly, is th rotor flux, ω is th rotor spd, θ is th rotor ngl, L is th sttor inductnc, R is th sttor rsistnc. 3. Th Dsign of Improvd Sliding Mod Obsrvr 3.. Th Dsign of Nw Obsrvr Th structur of improvd sliding mod obsrvr is shown in Fig.. Improvd sliding mod obsrvr minly includs fiv prts tht r currnt obsrvr, Sigmoid function, Klmn filtr, rotor position phs-lockd loop nd picwis linr compnstion. Th currnt obsrvtion modl is s shown in qution (2-) nd qution (2-2). di R k i u H ( i = + i ), (2-) dt L L L di R k i u H ( i = + i ), (2-2) dt L L L whr i, i r th nw sliding mod obsrvr s obsrving currnts of α xis, k is th gin of sliding mod obsrvr, H is Sigmoid function. Eqution (3) is th dfinition of H function. 8

3 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp i α i i α u u i ( ) kh i i ( ) kh i i E α E θ r Δθ θ ω Fig.. Th structur of nw sliding mod obsrvr. 2 H( i i ) ( i) i + =, (3) H( i i ) 2 i ( i ) + whr constnt is th slop of th Sigmoid function. Eqution (2-), (2-2) rspctivly substrcts qution (-), (-2), th currnt rror qution (4-), (4-2) cn b obtind. ( ) d i i R ( i i ) k H ( i = + i ) dt L L, (4-) ( ) d i i R ( i i ) k H ( i = + i ) dt L L, (4-2) Dfin th sliding surfc, T i i S =, (5-) i = i i, (5-2) i = i i, (5-3) Thrfor, systm stt qution (6-), (6-2) cn b obtind. di R i k H ( i ), (6-) dt = L + L di R = i + k H ( i ) dt L L, (6-2) Whn th trjctory of stimtion rror rchs th switching surfc, S =. In othr words, th obsrvd vlu of th currnt vntully convrgs to th ctul currnt vlu, tht is to sy, i = i, (7-) i = i, (7-2) So qution (8-), (8-2) cn b drivd by qution (6-), (7-) nd qution (6-2), (7-2) rcptivly. ( ) = k H i, (8-) ( ) = k H i, (8-2) 3.2. Th Dsign of Klmn Filtr[8] In qution (8-) nd (8-2) th nd contins bck-emf informtion. A rltivly smooth bck-emf cn b obtind ftr th trditionl firstordr low-pss filtr, ssuming tht nd r th rltivly smooth bck-emf signl. And qution (9-), (9-2) cn b drivd. 9

4 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp ωc ωc = = * k H i s+ ω s+ ω ( ) c c ( ) ωc ωc = = * k H i s+ ω s+ ω c c, (9-), (9-2) In som high prformnc pplictions, th bck- EMF, which r stimtd by qution (9-), (9-2) contin mor disturbnc, thus cn not b dirctly usd to stimt rotor position nd spd. So it is ncssry to crry out th scond filtring. Whn th Klmn filtr is introducd, stt qutions of bck-emf r shown in qution (-), (-2), (-3). d dt de dt de dt =ω E k E, (-) =ω E k E, (-2) α ω = E E E E whr ( ), (-3) E, E r th bck-emf stimtd vlus of th improvd sliding mod obsrvr; ω is th rotor ngl stimtd vlu; k is th sliding cofficint of th improvd sliding mod obsrvr. By rctngnt convntionl mthod nd bck- EMF stimtd vlu in qution (-), (-2), (-3), stimtd vlu of rotor ngl nd rotor spd cn b obtind, s shown in qution () nd qution (2). E θ = rctn E, () dθ ω =, (2) dt 3.3. Estimting th Rotor Position nd Spd by Phs-lockd Loop Rotor position s clcultion lwys dopts rctngnt trditionl mthod which is shown in qution (). Actully, rotor position nd spd ccurcy is not stisfid whn qution () nd (2) r usd. In ordr to furthr improv th prcision of rotor position nd spd stimtd vlu, phslockd loop tchniqu is introducd nd its structur is shown in Fig. 2. E nd E r th improvd stimtd vlu of sliding mod obsrvr s bck-emf, thy cn b obtind by th Klmn filtr. E E Δθ k p + Fig. 2. Th structur of rotor position phs-lockd loop. ki s From qution (), qution (3) cn gt, E E sinθ tnθ = = cosθ, (3) Thn ngl cn lso b clcultd s follows. sinθ θ = tn, (4) cos θ From th structur of rotor phs-lockd loop, th stimtd vlu of rotor position θ is obtind, from Fig. cn gt qution (5). θ E cos ˆ Δ = θ sin ˆ θ, (5) E r r Rgultd by th PI controllr continully, th complt trcking of ˆr θ to θ b chivd whn θ quls to ˆr θ Phs Compnstion of Estimtd Rotor Angl Th stimtd vlu of bck-emf ftr through th convntionl first-ordr low-pss filtr hs phs lg, nd phs lg will incrs s th motor s oprting frquncy incrss. So th stimtd vlu of rotor position comprd to ctul vlu will hv lrg phs lg, which will rsult in instbility of motor oprtion, nd thrfor th stimtd vlu of rotor position should hv phs compnstion ccordingly. Th trditionl compnstion pproch of phs ngl is tht using lg phs ngl compnsts for th stimtd vlu of rotor position. Δ θ is th lg phs ngl, s ω θˆr 2

5 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp ( ω ω ) Δ θ =, (6) tn / c θ is th finl rotor position: θ =Δ θ + θ, (7) Furthrmor, this trditionl mthod rlts to th dividr nd th rctngnt clcultion, so tht ctul progrmming will still fc mny difficultis. Thrfor, this rticl dopt picwis linr compnstion mthod to compnst th position stimtd vlu corrspondingly. Tht is to sy, th motor rotor ngl compnstion is dividd into diffrnt sgmnts which r ll doptd lin pproximtion mthod, nd diffrnt sgmnts r limitd by motor ngulr frquncy vlu. Thn ch sgmnt motor ngulr frquncy hs its own slop nd constnt phs compnstion vlu. Simultion rsults show tht rotor position stimtion rror cusd by first-ordr low-pss filtr cn b clcultd by first-ordr trnsfr function whos cut-off frquncy is 5 HZ. In this ppr, th phs ngl compnstion vlu undr typicl spd cn b obtind by th Bod digrm of first-ordr filtr. Th compnstion vlu of phs ngl undr typicl spd is shown in Tbl. According to th compnstion vlu of phs ngl in Tbl, four sgmntd stimtd vlu of position compnstion cn b obtind, which is shown in Tbl 2. ω is th motor spd. Tbl. Th compnstion vlu of phs ngl undr typicl spd. Motor spd/(rd/s) Compnstion ngl Δ θ Tbl 2. Th stimtd vlu of compnstion ngl. Motor spd/(rd/s) Compnstion ngl Δ θ ~2.26ω+9.9 2~4.837ω ~6.434ω ~8.6ω Simultions nd Anlysis Th simultion modl of PMSM snsorlss control systm is stblishd bsd on th sliding mod obsrvr. Simultion systm dopts i d = currnt control strtgy, th control systm is consistd of n xtrnl position loop, vlocity loop nd n innr currnt loop. PMSM snsorlss lgorithm simultion modl bsd on th nw sliding mod obsrvr is shown in Fig. 3. Th prmtrs in simultion r slctd s follows: R=.62 Ω, L =2.75 mh, d L =2.75 mh, 2 ψ f =.8627 Wb, J=.367 kg m, motor pol logrithmic P=4, DC bus voltg of th invrtr U =3 V, crrir frquncy is 5 khz. For th dc position givn vlu rng from *pi(rd) to 85*pi(rd), th simultion modl hs bttr trcking prformnc. 4.. Simultion Anlysis of th Bck-EMF Th stimtd vlu of rotor position cn b obtind ftr bck-emf pss through phs-lockd loop, so th qulity of th bck-emf will dirctly ffct th stimtd vlu of rotor position nd vlocity. Th two stg filtring is usd to gt th improvd bck-emf signl. In simultions, th position givn vlu is 2*pi(rd), slip cofficint of th improvd sliding mod obsrvr is 5, firstordr low-pss filtr s cutoff frquncy is 5 HZ. Th wvform of th bck-emf is shown in Fig. 4, th bck-emf pss through th first low-pss filtr is not smooth which contins mor hrmonic componnts, so th bck-emf is not suitbl for clcultion of th rotor position. Whil Figur 5 shows th wvform of th bck-emf which hs pss through th scond filtr, th bck-emf is rltivly smooth nd hs lss hrmonic componnts which is suitbl for clcultion of th rotor position Simultion Anlysis of th Position nd Vlocity Estimtion Th stimtd vlus of position nd vlocity r obtind by bck-emf pss through phs-lockd loop. Comprd to th convntionl rctngnt mthod, rotor position nd vlocity stimtd vlus ccurcy will b highr. In ddition, first-ordr lowpss filtr will rsult in th stimtd vlu of rotor position hv lrg rror. So th stimtd vlu of rotor position should b compnstd. As shown in Fig. 6, Fig. 7, Fig. 8 nd Fig. 9, th ccurcy of th spd nd position stimtd vlus which pss through th phs-lockd loop r highr. According to th compnstion vlu of phs ngl in Tbl, four sgmntd stimtd vlu of position compnstion cn b obtind, which is shown in Tbl 2. ω is th motor spd. q 2

6 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp Spd ctul vlu 2 *pi PID Position ctul vlu Position controllr Continuous powrgui Currnt controllr iq PI PI Spd controllr PI Uq Ud fcn tht Ulf Ubt Prk invrs trnsformtion id Prk trnsformtion Id Iq Ilf fcn Ibt tht tht Position ctul vlu Position stimtd vlu Position rror vlu Ulf puls Ubt svpwm Univrsl Bridg g + DC - A B C SMO Th scond fitring PLL clcultion Phs ngl compnstion tht bt w lf Stp PMSM Tm A B m C Clrk trnsformtion Ilf Ibt I fcn Ib Ic SMO Th first filtring ulf lf ilf ubt bt ibt <Sttor currnt is _ (A)> <Sttor currnt is _b (A)> <Sttor currnt is _c (A)> Isbc <Rotor spd wm (rd/s)> 4 Gin <Elctromgntic torqu T T (N*m)> <Rotor ngl thtm (rd)> 4 Gin.5*pi W Spd ctul vlu Spd stimtd vlu Spd rror vlu Fig. 3. Th simultion modl of PMSM control systm bsd on th nw sliding mod obsrvr. 22

7 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp Bck-EMF ftr th first filtring V Simultion tim(s) Fig. 4. Th wvform of bck-emf ftr th first filtring. Bck-EMF ftr th scond filtring V Simultion tim(s) Fig. 5. Th wvform of bck-emf ftr th scond filtring. 4 Without phs-lockd loop 2 with phs-lockd loop Rotor spd rd/s ctul spd stimtd spd position spd Rotor spd rd/s 5 5 Actul spd Estimtd spd Spd rror Simultion tim(s) Fig. 6. Th wvform of th stimtd spd using th nw sliding mod obsrvr without phs-lockd loop Simultion tim(s) Fig. 7. Th wvform of stimtd spd using nw sliding mod obsrvr with phs-lockd loop. 8 Without phs-lockd loop 7 With phs-lockd loop nd without phs ngl compnstion Rotor position rd ctul position stimtd position position rror Rotor position rd ctul position stimtd position position rror Simultion tim(s) Fig. 8. Th wvform of th stimtd position using th nw sliding mod obsrvr without phs-lockd loop Simultion tim(s) Fig. 9. Th wvform of th stimtd position using nw sliding mod obsrvr with phs-lockd loop nd without phs ngl compnstion. 23

8 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp With phs-lockd loop nd phs ngl compnstion 2 5 With phs-lockd loop nd th position givn vlu suddnly chngs ctul spd stimtd spd 5 Rotor position rd ctul position stimtd position position rror Rotor spd rd/s Simultion tim(s) Fig.. Th wvform of stimtd position using nw sliding mod obsrvr with phs-lockd loop nd phs ngl compnstion Simultion tim(s) Fig. (b). Th wvform of th stimtd spd using sliding mod obsrvr with phs-lockd loop Simultion Anlysis of Systm Dynmic In ordr to study th dynmic prformnc, th simultion rsults of th stimtd vlus of position nd spd r prsntd whn th position givn vlu hs suddn chng. Fig. () nd Fig. (b) r rspctivly th simultion rsults of th wvform of th stimtd spd without phslockd loop nd with phs-lockd loop. Fig. (c) is th simultion rsult of th wvform of th stimtd position with phs-lockd loop nd without phs ngl compnstion, howvr, Fig. (d) is th simultion rsult of th wvform of th stimtd position with phs-lockd loop nd phs ngl compnstion. At th bginning, th givn objctiv position is 2*pi(rd), whil t.7 s, th givn objctiv position chngs to 4*pi(rd) suddnly. From th simultion rsults, w know tht whn th givn position vlu chngs suddnly, th sliding mod obsrvr cn still b quickly nd ccurtly trck th ctul rotor spd nd position with vry short priod of djustmnt tim. Rotor position rd With phs-lockd loop nd without phs ngl compnstion ctul position stimtd position position rror Simultion tim(s) Fig. (c). Th wvform of th stimtd position using nw sliding mod obsrvr without phs-lockd loop nd without phs ngl compnstion. 4 With phs-lockd loop nd phs ngl compnstion 4 With phs-lockd loop nd th position givn vlu suddnly chngs 2 3 Rotor spd rd/s ctul position stimtd position Simultion tim(s) Fig. (). Th wvform of th stimtd spd using sliding mod obsrvr without phs-lockd loop. Rotor position rd ctul position stimtd position position rror Simultion tim(s) Fig. (d). Th wvform of th stimtd position using nw sliding mod obsrvr without phs-lockd loop nd phs ngl compnstion. 24

9 Snsors & Trnsducrs, Vol. 8, Issu, Octobr 24, pp Simultion Anlysis of Lod Disturbnc 25 With phs-lockd loop nd lod suddnly chngs In ordr to study th spd nd position trcking prformnc of nw sliding mod obsrvr nd rspons vlocity of th systm whn th lod chng suddnly, th corrsponding simultions r givn. Motor s givn position vlu is 2*pi (rd), lod rting is (N m) strting from s, th lod is muttd to 2.5 (N m) t.3 s. Th motor s sttor currnt, th lctromgntic torqu nd spd stimtion wvforms in th whol dynmic procss r givn in th Fig. 2, Fig. 3 nd Fig. 4. As cn b sn from th simultion rsults, whn th lod chngs suddnly, th motor sttor currnt, th lctromgntic torqu nd spd will b djustd to norml only ftr smll fluctution. Th rsults show tht th nw sliding mod obsrvr cn work proprly whn th lod chngs suddnly. Th systm hs good robustnss to suddn lod chng, nd n bility to rspond quickly. Sttor currnt A Sttor currnt whn lod suddnly chngs Simultion tim(s) 5 Fig. 2. Th rspons of sttor currnt whn lod chngs suddnly. Rotor spd rd/s ctul spd stimtd spd Simultion tim(s) Fig. 4. Th wvforms of ctul spd nd stimtd spd whn lod chngs suddnly. 5. Conclusions Bsd on sliding mod vribl structur control thory, nw typ of sliding mod obsrvr which is usd to stimt rotor position nd spd of PMSM is proposd in this ppr. Sigmoid function is introducd to th nw sliding mod obsrvr which cn rduc frquncy chttring problm. Improvd bck-emf is obtind by two filtring, phslockd loop structur is introducd to stimt th rotor position nd spd, nd picwis linr compnstion mthod is doptd to compnst for th rotor position stimtion. Th simultion modl of PMSM position snsorlss srvo control systm is st up by Mtlb/Simulink. Th simultion rsults show tht bck-emf hrmonics r much lss nd mor smooth ftr two filtring, th bck-emf is suitbl to stimt position nd spd. Th ccurcy of PMSM s rotor position nd spd stimtd vlu will b highr ftr through position phs-lockd loop structur. And vi phs compnstion, th stimtd vlu of rotor position cn trck th ctul vlu wll. Whn th lod chngs suddnly, th nw sliding mod obsrvr is bl to trck th rotor position nd vlocity ccurtly nd quickly. Elctromgntic torqu N*M Simultion tim(s) Fig. 3. Th wvforms of lctromgntic torqu. Acknowldgmnts This work ws prtly supportd by Ntionl Ntur Scinc Foundtion of Chin ( nd 6644) nd Qing Ln Projct of Jingsu Provinc, Chin. Rfrncs []. N. Imi, S. Morimoto, M. Snd, t l, Influnc of rotor configurtion on snsorlss control for prmnnt mgnt synchronous motors, IEEE Trnsction on Industry Applictions, Vol. 44, Issu, 28, pp

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54, Issu 5, 27, pp. 2398-246. [4]. Q. L. Wng, C. W. Zhng, X. Zhng, Vriblstructur MRAS spd idntifiction for prmnnt mgnt synchronous motor, Procdings of th CSEE, Vol. 29, Issu 9, 28, pp. 7-75. [5]. W. Q. Lu, Y.

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Three Phase Flat Motors Three Phase Saw Arbor Motors. for sawing, milling, routing of wood, plastics and metal. type of protection IP 54

Three Phase Flat Motors Three Phase Saw Arbor Motors. for sawing, milling, routing of wood, plastics and metal. type of protection IP 54 Thr Phs Flt Motors Thr Phs Sw Arbor Motors for swing, milling, routing of wood, plstics nd mtl of protction IP 54 Thr phs flt motors with br of protction IP 54 Thr phs flt motors of protction IP 55 (possibl