Confn nc s, FRANC CE ctoncs 006 Pa ustal El b 6-0, EEE Indu Nomb 3 nd I Spd and Poston Estmaton fo PM Synchonous Moto usng Slf-Compnsatd t d Back-EMF k Obss Maco TURSINI, Robto PETRELLA, Alssa SCAFATI Unsty of L Aqula Dpt. of Elctcal and Infomaton Engnng (DEIE Unsty of Udn Dpt. of Elctcal, Managmt and Mchancal Eng. (DIEGM SS6- Adancd d contol and obsaton of AC ds Thusday, Nomb 9 th, 006, 8:00 AM
Am of th pap - pod full analytcal dscpton of pously-poposd spd and poston obss fo PM synchonous motos, basd on back-emf stmaton - calculat th (stady-stat oto poston stmaton os - popos a al-tm compnsaton statgy fo oto poston stmaton o n a tansduc-lss PMSM d - aldat analytcal sults by mans of smulaton analyss and compa y y y p thm wth xpmnts
Tansduc-lss d schm * ω * d Rl = 0 * q Rq Rd * q * d dq αβ * α * β SV PWM α β Lunbg/ Sldng Mod Obs α β ˆ q ˆ d dq α β αβ αβ 3 a b c θˆ * snθˆ ( ˆα ˆ β ωˆ snθˆ cosθˆθ Obs cosθˆ ωˆ ( ( Kalman Flt * * α β PMSM α β θˆ = accos ˆ β ˆ α ˆ β
Pmannt Magnt Synchonous Moto β s ω d Hypothss: q β β β N α θ - symmtcal-snusodal snusodal machn - non salnt oto - psntd by two-phas qualnt stato-fxd αβ wndngs α s S α α Dynamcal modl: & = [ A ] [ B ] [ B ] =, ] [ α β T = ] [ α, β =, ] [ α β T T Rs [ A] = [] I L s [ B] = [] I L s
Back-EMF and PMSM Extndd Modl Th back-emf componnts contan th nfomaton on th oto poston: α β ( θ ( θ = kω sn θ = k ω cosθ In od to aang back-emf obs, back-emf componnts a addd to th stat though a coupl of fcttous dynamc quatons: & & [ A] [ B] [ B] = = 0 T = [ α, β, α, β] Extndd stat x ]
Stat and dstubanc obss & ˆ = ˆ &ˆ = [ L]z [ A] [ B] ˆ [ B] z Lunbg obs (LO Sldng mod obs (SMO xˆ & = ~ z [ K ] ( = K ˆ z [ K ] sgn ( î ~ = ~ ~ [ ˆ [ A ] xˆ [ B ] [ K ]( xˆ = [ A ] xˆ [ B ] [ K ] sgn ( & [ ] T [ K ] = k [ I ] l k [ I ] Gan matx k, l Gan coffcnts
Why and how to dlop a compnsaton law? Roto poston stmaton o (dffnc btwn stmatd and actual poston dynamcs: & & = [ A] [ B] = & l k k If known, thy t can b on-ln compnsatd! Soluton of th poblm s dffcult n th tm-doman. Lt us consd th qualnt s-doman tansf functons: ( s = [ A ] E ( s [ B ] E ( s k E ( s se 0 se s = V& s l k E ( ( ( s 0 Aft som calculatons: E L ( s = s V ( s E ( s & ( s s ( s s ( s s ( s s = s h s V& ( s s = h ± Δ = h ± j Δ ; h = ( k R L ( k R L mk, s s Δ = s s 4 m = l L s
Back-EMF stmaton o Th asymptotc stablty s a suffcnt condton fo th xstnc of th snusodal stady-stat stat spons to snusodal xctaton: k k ω cos(ωt φf ( t = F ( jω ω = ω ω sn(ωt φf α ( t ( t = A cos (ω t φ F β = Asn(ωt φf F ( jω φ F ( h ( h Δ ω = ω = ω ] ( Δ ω 3h A [ h ( ω Δ( ω Δ ( hω = F ( jω kω ω = actang ω= ω ( Δ ω 3h h ( h Δ ω Actual oto spd
Calculaton of th oto poston stmaton o αβ componnts of th stmatd back-emf: ˆ ˆ α β = = α β α β (t = k (t = k ω ω sn ω t A cos ( ω t φ cosω t A sn ( ω t φ F F Roto poston stmaton os: θˆ ˆ θ = actg k ω A cosφφ A F snφ F Lunbg obs θˆ θ = actg ( ω L l s Sldng mod obs Fo a gn st of moto paamts, th (stady-stat stat t oto poston stmaton o dpnds on oto spd, but t s ndpndnt on fdng cunt (.. load toqu
Poston stm maton o [d dgs] Lunbg SMO 800 600 6000 k -7.4-6. -5.9-5.08 000 pm -6.97-3. -0.37-0.08 000 pm -3.63 -.99-5.5-4.93 3000 pm Poston o ( θˆ θ [dgs] 0-5 -0-5 -0-5.078-6. -0.079-4.98 Smulaton sults Stady-stat stmaton os Commnts: - LO oto poston stmaton os tnd to SMO ons fo hgh alus of gan k - fo th sam alu of gan l, SMO has small stmaton o wth spctd to LO - stmaton o achs non- nglgbl alus at hgh spd LO - compnsaton s possbl by l = 8.8; k = 600-3. consdng th analytcal o l = 8.8 as a fst attmpt SMO LO SMO l = 56.56; k = 600 l = 56.56 -.99-5 0 500 000 500 000 500 3000 Roto spd [RPM] - actual mplmntaton could lad to dffnt sults du to un-modlld ffcts
Poston stmato on o [dgs] o [dgs] ton stmaton Pos 0 - - -3-4 -5-6 -7-8 0 - - -3-4 -5-6 0.5-3 -6. Lunbg Obs Poston stmaton o Compnsatd poston stmaton o load nston l = 8.8 k = 600 0.05 0. 0.5 0. 0.5 0.3 0.35 0.4 0.45 0.5 Tm [s] -5.5-3 -5.08 Sldng Mod Obs Smulaton sults Tansnt stmaton os Condtons: - off-ln opaton of th obs - no-load spd tansnt fom 0 to 000 RPM -. Nm (60% atd load toqu nston at 0.35s - poston stmaton o s P oston stmaton o compnsatd by mans of Com pnsatd poston stm aton o analytcal alus load nston l = 8.8-7 0 0.05 0. 0.5 0. 0.5 0.3 0.35 0.4 0.45 0.5 Tm [s]
Expmntal sults Th d systm Bakng tst bnch IEE-488 contolld hystss bak (Magtol HD-70 70-8NA-0040 PMSM und tst atd pow /cunt 630 W -.5 A ms (* atd spd/toqu 3000 pm (* -.0 Nm (* pol pas 4 no-load back-emf @ atd spd 8.7 Vms (* stato sstanc.9 Ω stato nductanc 6 mh oto nta 0-5 kgm nt DC oltag 300 V Contol & pow lctoncs 6-bt fxd-pont DSP mcocontoll IGBT ntllgnt pow modul 50 μs s contol and modulaton cycls
uncompnsatd Expmntal sults 500 RPM SMO opaton 9 thotcal compnsaton ˆ ω ( θ, mon θ Condtons: - no-load - 500 to 000 RPM - 500 RPM slow ayng amp ncmnts Commnts: mpcal compnsaton - nos s latd to sdual chattng on th back-emf stmats - thotcal compnsaton s not th xact on, but pods good sults - mpcal compnsaton s obtand by ayng th slop of th compnsatng angl
uncompnsatd Expmntal sults 500 RPM LO opaton 9 ˆ ω ( θ, mon θ Condtons: - no-load - 500 to 000 RPM - 500 RPM slow ayng amp ncmnts - sam gans as SMO mpcal compnsaton Commnts: - poston o has dffnt slop - nos s low
Expmntal sults SMO toqu/spd analyss Commnts: - load toqu affcts poston stmaton o (dffntly fom thotcal sults - th ffct of th load toqu s qut small (lss than dgs n y condton - o-compnsaton s obtand f thotcal laws a adoptd (dottd lns - compnsaton wth thotcal alus lads to a maxmum o of 5 dgs
Conclusons - such laws yld satsfactoy compnsaton also dung fast tansnts Th possblty to compnsat th ntnsc oto poston stmaton o n a tansduc-lss contol schm fo PM synchonous motos basd on back- mf obss has bn analysd: - t s possbl to aluat a thotcal compnsaton law fo th stady- stat opaton, both wth Lunbg and Sldng Mod obss - t has bn pon that th psnc of akalman flt n cascad to th back-emf obs dos not ntoduc addtonal poston o at stady- stat, and nglgbl on dung tansnts f slow amp-ayng spd fnc s usd - th un-modlld ffcts n th actual d, moto and al-tm systm ntoduc som dscpancs fom thoy: xact compnsaton qus apop adjustmnt by xpmntal tsts