MODELING AND SIMULATION OF SENSORLESS CONTROL OF PMSM WITH LUENBERGER ROTOR POSITION OBSERVER AND SUI PID CONTROLLER

Size: px

Start display at page:

Download "MODELING AND SIMULATION OF SENSORLESS CONTROL OF PMSM WITH LUENBERGER ROTOR POSITION OBSERVER AND SUI PID CONTROLLER"

Agnes Nichols
6 years ago
Views:

1 Jounal of Elctcal Engnng MODEING AND SIMUAION OF SENSORESS CONRO OF PMSM WIH UENBERGER ROOR POSIION OBSERVER AND SUI PID CONROER GHADA A. ABDE AZIZ, MOHAMED. I. ABU E- SEBAH, Elctonc Rsach Insttut, Dokk, Cao, Collag of ngnng an tchnology, Aab acamy fo scnc tchnology & matm tanspot, A. SHAOU an F. ISMAI 4,4 Faculty of Engnng, Cao Abstact: hs pap psnts an nvstgaton an valuaton of th pfomanc of th sufac Pmannt Magnt Synchonous Moto v un th Smplf Unvsal Intllgnt PID contoll (SUI PID). h stmaton of th oto poston an th angula sp n ynamc at w v by th us of th unbg stat obsv fo cunts an MRAS (Mol Rfnc Aaptv Systm) obsv. It also shows how to us a unbg stat obsv n a fl ont contol (FOC) schm to mplmnt a snsolss vcto contol statgy. h mathmatcal scptons of th systm an smulaton sults hav bn psnt n ths pap. y wos: Sufac Pmannt Magnt Synchonous Moto, unbg Stat Obsv, SUI PID contoll, MRAS obsv, Snsolss vcto contol. NOMECAURE I, Stato cunts I V, V Stato voltags ω Roto angula sp ( a s ) θ Roto poston angl ( a ) R Stato Rsstanc ( Ω ) Moto tou constant F Factonal Coffcnt oa tou ( N. m ) J Roto nta ( P λ p M g.m ) Numb of Pol Pas h matx coffcnt gan Rfs to th stmat valu EMF constant Popotonal gan constant Intgal gan constant h stat o n th -axs h stat o n th -axs h SUI PI contoll gan P. Intoucton MSM has w applcaton n AC svo systm, compa to oth machns bcaus of ts avantags lk uck spons, xcllnt contol pfomancs, small sz, lght wght, hgh pow/ wght ato, lag tou/ nta ato, smooth tou opaton, contoll tou at zo sp, hgh sp opaton, hgh tou poucton capablty, hgh ffcncy an compact stuctus []. h moto vs n th nfomaton of oto sp to achv sp contol loop. Roto sp can b masu by snsos attach to oto shaft whch tansmt th moto sp to th v contoll. Howv, usng mchancal snsos plac on th machn shaft hav many awbacks []-[]. Fst, th mchancal snso psnc ncass th volum an th global systm cost. hfo t us an avalabl shaft n whch can consttut a awback wth small sz machns. Moov, th nstallaton of ths snso us a chock latng to th stato, opaton whch povs to b lcat an cass th lablty of th systm. hs umnt las to th pap n th fl of snsolss contol schms that stmat th sp of th oto wthout any snsos attach to th otatng shaft [4]. In ths pap, to ovcom poblms lat to th mchancal sp snsos, th aaptv unbg obsv fo oto poston an angula sp stmatons s stu un th SUI PID contoll fo PMSM v systm.. h contol systm block agam Fg. shows th block agam of snsolss contol of PMSM. h systm has bn bult usng th matlab/ smulnk. h v systm conssts of: - PMSM, Cunt contoll, Aaptv unbg obsv fo stmatng both oto poston & angula sp an th SUI PID contoll. h stmat oto angula sp ω s compa wth th fnc angula sp whch t s st to 4 a/sc. h sultng angula ω f

Jounal of Elctcal Engnng www.j.o Fg.. Block Dagam of Snsolss contol of PMSM sp o s pocss n th SUI PID contoll to gulat th oto sp. h output of ths contoll s.

2 Jounal of Elctcal Engnng Fg.. Block Dagam of Snsolss contol of PMSM sp o s pocss n th SUI PID contoll to gulat th oto sp. h output of ths contoll s.h stat fam tansfomatons of Clak, Pak, f an nvs-pak a us to tansfom th cunts an voltags. PMSM mol h statos of th PMSM an woun oto synchonous moto a smla. In aton, th s no ffnc btwn th back EMF pouc by a pmannt magnt an that pouc by an xct col. Hnc, th mathmatcal mol of a PMSM s smla to that of th woun oto SM [5]. h lctcal ynamc uaton of th moto n th oto fnc fam can b wttn as:- V R = + P ω () t V R λ P ω = P ω () t h lcto-magntc tou:- Fo constant flux opaton whch pouc lctc tou [ I ] I = P λ = I mantan at zo, (4) hs tou uaton of th PMSM smla to th gula c machn an hnc povs as of contol wh, th tou pns only on th uaatu componnt of th stato cunt. h tou balanc uaton s:- ω t = J + Fω + [ I + ( I I ] = P λ ) () (5) Both stato cunts n th oto fnc fam I & I can b obtan by ntgatng uatons () & (). ω t = [ Fω ] J (6) h oto poston θ n stat spac vatv fom s:- θ t = ω (7)

3 Jounal of Elctcal Engnng h nvs Clak tansfomaton can also b foun as: a b c = α β (9) Fg.. Analytcal mol of PMSM. Coonat tansfomatons In o to stuy th pfomanc of PMSM mol un snsolss contol, two ffnt tansfomatons w ma: h fst on s Clak-tansfomaton whl th scon s Pak tansfomaton... Pak tansfomaton Pak-tansfomaton poucs th systm mol; th cunt an voltag vctos onto a otatng coonat tm nvaant systm as shown on Fg.4.. Clak tansfomaton Clak-tansfomaton tansfoms th -phas systm nto a - phas tm o vc vsa.. Fg. 4. Pak tansfomaton cosθ = snθ snθ cosθ α β () α β = Fg.. Clak tansfomaton a b c (8) An th nvs Pak tansfomaton s: α β cosθ = snθ snθ cosθ () 4. Cunt contoll h cunt contoll block us to gulat th stato cunt an t has fv nputs:,,, & ω an two outputs; V & f f V. h cunt contoll has bn mplmnt accong to th cunt contoll uatons;

4 Jounal of Elctcal Engnng V R = V Pω Wh; + Pω λ f Pω R f f + t s mantan at zo snc th s no flux waknng opaton n ths pap. () h popos SUI PI contoll s a classcal PI wth a unvsal PID constant, so no spcfc sgn s n an thfo no n fo a systm mol. h SUI PID contoll constants P an I a th absolut valus of os an ntgaton of os as shown n Fg.5. = f I () = f I (4) 5. h SUI PID sp contoll h sp contoll was mplmnt to gulat th oto sp by compang th fnc angula sp wth th stmat angula sp. h output of ths contoll s. f h PID contoll conssts of th tms [6]:- h fst contoll tm: P = o (5) P h scon contoll tm: I = I o. t (6) o h th contoll tm: D = (7) t h followng valus can thn b substtut nto th PID contoll uaton:- P = ABS o (8) ( ) o ( ) I = ABS. t (9) o = ABS () t Slctng th contoll constants fom th abov xplanaton las to a smpl sgn algothm an smplf aaptv wghtng fo th th tms. h popos ntllgnt PID contoll s constuct by usng th mult g of fom contoll (MDOF) concpt [7], [8]. Applyng th ntllgnt PID contoll lmnats th n to know th systm stay stat gan. C m = C * M * o + C * ( o) () M C C m = C * o * ( M ) + () M M Fo M ff C m = C * o * M () 6. unbg Aaptv Obsv h stat spac of PMSM mol of uatons & s constuct accong to th followng latons bas on th knowlg of nputs an outputs of th systm: X = t Y Wh; [ AX + BU = CX ] X = ; U [ V ] V λ Y = [ ] ; R A = Pω C = Fo SPMSM, Fg. 5. SUI PID contoll Pω R = ; ; B= ω P (4) =. o stmat th oto = poston an th angula sp; th stato cunt n & ; 4

5 Jounal of Elctcal Engnng ctons ( & ) n th otatng fam a us as th stmat vaabls an th oto sp ω as th gulat vaabl. h scon o unbg obsv s gvn by: X = A ( ω ) X + B ou + ( Y Y ) t Y = C X (5) Wh; ω s th stmat angula sp (a/sc) an s a constant coffcnt matx whch s chaactz by an uaton contanng a tm whch cocts th cunt stat stmatss by an amount popotonal to th pcton o. h pcton o s th ffnc btwn th stmat an actual cunt. hs cocton nsuss stablty an convgnc of th obsv vn whn th systm bng obsv s unstabl [9]. X = ; Y = R Pω A = (ω ) ; R Pω B = o Pω. ; ajustabl on. h oto angula sp s bult aoun th followng aaptv mchansm: t λ ) (6) Wh; = & =. λ ω = p( ) + ( Wh; & a th stat os. h tackng pfomanc of th sp stmaton an th snstvty to nos a pnng on popotonal an ntgal coffcnt gans. h ntgal gan s chosn to b hgh fo fast tackng of sp. Whl, a low popotonal p gan s n to attnuat hgh funcy sgnals not as noss []. By stmatng th oto angula sp, th stmat oto poston θ can b obtan by: θ = ω. t (7) MRAS stuctu fo stmatng th oto angula sp an th oto poston s llustat n Fg. 6. h schm conssts of mols; fnc mol an ajustabl mol wth aaptaton mchansm. h fnc mol block psnts th actual systm havng unknown paamts valus. h ajustabl mol block has th sam stuctu of th fnc on, but wth ajustabl paamts nsta of th unknown ons. h aaptaton mchansm block upats th ajustabl mol wth th stmat paamt untl satsfactoy pfomanc s achv. h PMSM mol was cons to b th fnc mol an th unbg obsv was cons as ajustabl mol to obtan th stmat stato cunts []. t 7. Roto angula sp obsvaton h oto angula sp s constuct usng th mol fnc aaptv systm (MRAS). h MRAS pncpl s bas on th compason of th outputs of th two stmatos. h fst on s npnnt of th obsv vaabl nam as mol fnc, whl th scon s th ajustabl on. h o btwn th two mols fs an aaptv mchansmm to tun out th obsv vaabl []. In ths pap, th actual systm s cons as th mol fnc an th obsv s us as th Fg. 6. MRAS Stuctu 5

6 Jounal of Elctcal Engnng 8. Smulaton sults Bas on th moto paamts ncat n th appnx, th smulaton of th snsolss contol of PMSM has bn ca out usng th Smulnk n Matlab. h stato cunt s coupl usng th fl ont contol nto both &. In ths pap th moto was tst at no loa an sun loang contons wth constant stato sstanc at Ω. h PWM swtchng funcy of th nvt s st to Hz. h DC lnk voltag of th nvt s mantan at V. h fnc angula sp of th moto s st to 4 a/sc. Usng only th th phas stato cunts th uaatu an ct axs cunts, oto angula sp an poston a stmat by th unbg stat obsv. h stmat angula sp was gulat va convntonal PI contoll wth low = an abov =5 an th constant coffcnt matx =. Fg. 7 shows th actual, stmat an th fnc angula sps. At statng, th moto has ap changng, both th actual an th stmat sps tack th tagt sp at t=.6 sc. h systm spons convgs to th mol fnc on. h stmat oto angula sp ω tacks th actual oto angula sp ω n a vy shot tm naly. sc by th vtu of th SUI PI contoll. Aft loang, both th stmat an actual oto angula sps opp but n a vy shot tm an by th vtu of th SUI PI contoll thy tun back agan to th fnc valu (tagt) n lss than. sc. At t=.4 sc an o occus wth angula sp o=65 a/sc an at t=.4 sc th o convgs to zo n.57 sc thanks to th aaptv contol algothm as shown on Fg. 8. At t= sc, wth a sun loang, th sp o cass an thn tun back agan to zo as both Actual an stmat sps a ual. h sp o btwn th stmat an th fnc s th nput to th SUI PI contoll to gulat t an th output of th contoll s. Fg. 9 shows th moto lctomagntc tou, whch stats smoothly an at t=.5 sc t bcoms.8 N. m thn fom t=.6 sc to t=.8 sc, th lctomagntc tou was oscllatng aoun N. m an thn t tun back agan to.8 N. m whn loa an thn t tun back agan to.8 N. m. p f Sp(a/sc) Sp o(a/sc) Aft loang th moto tou oscllats aoun.8 N. m Actual sp agt sp Estmat sp m(sc) = Fg. shows th -axs cunt, th actual an stmat stato cunt at axs I. h stmat cunt I tacks th actual axs cunt I of th moto at t=.5 sc an both bcom A at t=.6 sc an both oscllat aoun th zo axs. Aft loang at t= sc, both stmat an actual a ual to zo. Fg. shows th -axs cunt, th actual an stmat stato cunt at th axs, I : th stmat axs cunt I tacks th actual axs cunt I at t=.6 sc an both of thm hav th sam chaactstcs of th moto lctomagntc tou n both cass ung th statng up wth no loa an aft loang at t= sc an both oscllats aoun 4A. Fg. shows th otatonal paamts (Sn an Cos of th stmat oto poston). Fg. 7. h actual, tagt an stmat angula sps at statng an thn a sun loang m(sc) Fg. 8. h angula sp o 6

7 Jounal of Elctcal Engnng (N.m) 5-5 Sn & Cos ( thta stmat) Cos(thta stmat) Sn (thta stmat) I(A) m(sc) 5 Estmat I Actual I m(sc) 5 Fg. 9. h Elctomagntc tou Fg.. h actual an stmat -axs cunt m(sc) Conclusons hs pap psnts a snsolss contol of PMSM usng th SUI PID contoll an unbg aaptv obsv to stmat both oto angula sp an th oto poston. h ffcncy of usng lunbg aaptv obsv has bn stu an ncat on th smulaton sults n th smulnk/ matlab softwa packag. hs tchnu of stmaton fo both oto angula sp an oto poston nsta of usng mchancal snsos; ncass th systm lablty an ucs th systm cost. h aaptv wth contol algothm fo th oto angula sp assocat wth th SUI PI sp an cunt contolls show goo pfomancs at statng an at sun loang conton. APPENDIX Fg.. h Sn & Cos (stmat thta) Moto paamt us n th smulaton:- I(A) Estmat I Actual I m(sc) Fg.. h actual an stmat -axs cunt Pow.7 W Funcy 5 Hz n Voltag 8 V - Sta n Cunt.4 A - Sta No. of Pol Pas Rat angula Sp 4 a/sc Stato Rsstanc Ω / phas - axs Inuctanc ( ) 7.75mH - axs Inuctanc ( ) EMF Constant 7.75mH.98V/a/sc 7

8 Jounal of Elctcal Engnng Fcton Coffcnt Momnt of nta.7 g.m coffcnt oa ou.5 N.m REFERENCES: [] Wang Song, Sh Shuang - Shuang, Chn Chao, Yang Gang an QuZh-jan, Intfcaton of PMSM bas on EF an Elman Nual ntwok, Pocngs of th IEEE Intnatonal confnc on Automaton an ogstcs Shnyang, Chna August 9. [] S. Nakashma, Y. Inagak, I. Mk, "Snsolss Intal Roto Poston Estmaton of Sufac Pmannt Magnt Synchonous Moto ", IEEE ans. In. Appl.,Vol. 6, No. 6, Novmb, pp [] J. Jang, J. Ha, M. Ohto,. I, S. Sul, "Analyss of Pmannt-Magnt Machn fo Snsolss Contol Bas on Hgh-Funcy Sgnal Injcton", IEEE ans. In. Appl., vol.4, N.6, Novmb/Dcmb 4, pp [4]. Nabt,. Ab, an H. Bnalla, Snsolss ct tou contol of Bushlss AC machn usng lunbg obsv, Jounal of hotcal an Appl Infomaton chnology, 5-8 JAI. [5] P. PIAY an A. RISHNAN, Molng of Pmannt Magnt Moto Dvs, IEEE ansactons On Inustal Elctoncs, VO. 5, NO.4, Novmb 988 pp: [6] hat, F.M.H., Ahm, F.I., an Abu-Elsbah, M.I., "Snsolss PM Moto wth Mult Dg of Fom Fuzzy Contol, Wol Acamy of Scnc Engnng an chnology 6, 5. [7] Dhaoua, R., Mohan, N., an Noum, I., Dsgn an mplmntaton of an xtn alman flt fo stat stmaton of a Pmannt Magnt Synchonous Moto, IEEE ans. Pow Elct., July 99, pp [8] Schol, M., Snsolss Contol of Pmannt Magnt Synchonous Motos, Elctc Machns an Pow Systms, Vol., 994, pp [9] [] Gouz Fatn, Sbta assaâ, "Sp Snsolss IFOC of PMSM Bas On Aaptv unbg Obsv", Wol Acamy of Scnc, Engnng an chnology 44,. [] S. Suwankawn, an S. Sangwongwanch., Dsgn statgy of an aaptv full-o obsv fo sp snsolss nucton moto vs- tackng pfomanc an stablzaton, IEEE tans. on pow lcton. 5 (), pp: 96-9, 6. [] H. am, M. Bn Ham,. Sbta, an M. N. Ablkm, DC Snsolss Inucton Moto Dvs bas on MRAS Smultanous of Roto Sp an Stato Rsstanc, Intnatonal Jounal of Elctcal Pow Engnng: IJEPE, (5): 6-, 8. 8

Switching FOC Method for Vector Control of Single-Phase Induction Motor Drives

Switching FOC Method for Vector Control of Single-Phase Induction Motor Drives Intnatonal Jounal of Elctcal an Comput Engnng (IJECE) Vol. 6, No., Apl 16, pp. 474~483 ISSN: 88-878, DOI: 1.11591/jc.6.9146 474 Swtchng FOC tho fo Vcto Contol of Sngl-Phas Inucton oto Ds ohamma Jannat*,