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NAOSITE: Naaak Uvty' A Ttl Autho() Ctato Stablty ompao of IPMSM o xt EMF Tuj, Mo; Mzuak, Hoh; Ha 4 Itatoal Pow Elto ECCE-ASIA), pp.393-398; 4 Iu Dat 4 URL Rht http://hl.

1 NAOSITE: Naaak Uvty' A Ttl Autho() Ctato Stablty ompao of IPMSM o xt EMF Tuj, Mo; Mzuak, Hoh; Ha 4 Itatoal Pow Elto ECCE-ASIA), pp ; 4 Iu Dat 4 URL Rht 4 IEEE. Poal u of th m IEEE mut b obta fo all oth lu pt/publh t pomotoal pupo, at w tbuto to v o lt, th wok oth wok. Th oumt owloa

2 Stablty Compao of IPMSM Sol Vto Cotol Sytm U Ext EMF Mo Tuj, Hoh Mzuak, S-h Hamaak Naaak Uvty, Gauat Shool of E 4 Bukyo-mah, Naaak, 85-85, Japa Abtat Sol vto otol of a to pmat mat yhoou moto (IPMSM) ha b tu may pap. Th xt ltomotv fo (EMF) ba mtho o of th ptatv ytm. W popo a mplf mtho whh tmat th oto poto u th otoll volta wthout u obv. I th pap w hav ompa th mtho thouh tajto of pol a xpmtal tat po fo tablty tuy. Kywo to pmat mat yhoou moto, ol vto otol, xt EMF, tablty aaly I. INTRODUCTION Bau of hh ffy a mall z, PMSM u may applato. Epally, IPMSM pobl to pou hh tou by u luta tou. To alz a vto otol of IPMSM, a o fo tt oto poto u bau t ay to otol ut aoa wth th poto of th oto. Howv, th a poblm; th ot of th poto o, z of th appaatu a w of th al l. Thfo, may ol otol mtho wthout u th poto o a popo []-[6]. Th mtho u th xt EMF o of th ptatv ol otol mtho. Th xt EMF tmat by a tuba obv, a th potoal fomato obta by u t [][]. O th oth ha, w hav popo a mpl ol mtho ba o th xt EMF [7]. Th oto p tmat by th output volta of th -ax PI ut otoll wth th o-tf otol wthout u th tuba obv. Althouh mla mplfato popo al pap [5][6] fo a o-alt pol PMSM, ou popo mtho a b appl to IPMSM by u th xt EMF. I th pap, w u th tablty by ompa th ult of th popo mtho wth tho of th ovtoal xt EMF ol o. Th oot lo of la mol, tat po obta by ola mol a xpmt a motat. A. Ext EMF Mol of IPMSM Volta uato of IPMSM o - otat f fam yhoz wth th mat pol poto xp a follow [] : v R pl L v = L R pl E () x wh, Ex = {( L L ) ψ} ( L L ) p () By ovt th f fam whh otat at a aula p a how F., th follow uato a b obta fom (): v R pl L = v L R pl (3) δ δ δ Th o tm of th ht all th xt EMF a xp a θ δ E ( x ) L = o δ θ (4) B. Covtoal Mtho Covtoal ol vto otol ytm how F. [][]. Th xt EMF tmat by u tuba ob follow; = { v L ( R L ) } (5) δ { ( ) } = v L R L δ δ δ b R δ b S ψ β N θ θ α N θ R a a (6) II. SENSORLESS SYSTEMS R v F.. Mol of IPMSM.

3 Fom (4), th mat pol poto o θ omput by th follow uato: θ = ta (7) δ U (7), th oto aula p tmat by K = K p θ (8) By u amp offt ζ a atual aula fuy, th PI p tmato a of F.3 a a follow [] : Kp = ζ, K = (9) To u th flu of o, th oto aula p tmat u a low-pa flt a follow: = () Th pol poto omput by th follow uato. θ = () By o th ff btw th -δ ax a - ax, th atual poto tmato oθ a b xp a follow fom F.: θ = θ θ () PI PI θ θ ta ê ê δ PI PI v v δ φ θ Dtuba Obv / v a v b v δ PWM INV. φ θ v a b F.. Covtoal Sol Vto Cotol Sytm. θ K p K θ θ θ Ex Ex δ oθ (3) Fom (3), th poto oθ appoxmat a θ (4) Ex Thfo, t pobl to tmat th poto o by u. I F.4, th -ax PI ut otol y th follow uato. K = Kp ( ) (5) Th - ax volta f v alulat by th follow uato o th fftal tm of (3). v = R L δ (6) Th oto aula p tmat by th follow uato u th output volta fom (4). K = Kp (7) Ex E x ha a a futo of p by lt fftal tm of (). E {( ) x = L L ψ } (8) By u amp offt ζ a atual aula fuy, th PI otol a of (7) a a am a (9). Fu 3 how alo a uvalt blok aam fo popo p tmato how F.4. R v L v δ φ v a b / θ F.4. Popo ol vto otol ytm. III. θ δ STABILITY ANALYSIS φ v F.3. Appoxmat blok aam fo p tmato. C. Popo Mtho Popo ol vto otol ytm how F.4 [7]. Fom (4), wh th o of th mat pol poto mall, th follow uato obta by appoxmat θ θ a oθ. A. Nola Mol I o to aalyz th ytm how F., w hoo th δ ax of F.. By aum al volta otol of PWM vt, w hav va = va, vb = vb, v = v (9) S -δ tafomato of otoll th am a th aaly, th follow lato obta fom (9). v = v, vδ = vδ () By u th atual o al θ, th - vaabl a xp by th follow o-oat tafomato.

4 v oθ θ v v = θ oθ () vδ oθ θ = θ oθ () δ Th - tat uato of IPMSM a obta by Pak uato a follow: p = ( v R L ) (3) L p = ( v R L ψ ) (4) L P P p = { ψ ( L L) } (5) 4J J wh, P umb of pol, J momt of ta, a T L loa tou. Th tuba obv b a follow: = z L (6) wh, z = ( v Lδ R L) (7) δ = z L δ (8) wh, z = ( vδ L Rδ Lδ) (9) Th PI otoll a low pa flt a xp by th follow uato. PI p otoll: pw = (3) = K ( ) K w (3) p D ax PI otoll: pw = (3) p v = K ( ) K w (33) Q ax PI otoll: 3 pw = δ (34) vδ = Kp( δ) Kw3 (35) PI p tmato: pz = θ (36) 3 = K pθ Kz3 (37) Low pa flt of p tmato: p = (38) By tak th vatv of (), w hav pθ = (39) A ola mol of th ol ytm how F. ha b obta. By u th mol, w a omput tat po. Th tay-tat valu a obta by tt p = o = th ola mol xpt fo (). Fom (36), w hav θ = (4) Th, obta fom (7) a = (4) Wh th moto ta a uta a ual to tho atual valu, th follow uato obta. θ = (4) I th a, th δ ax o wth th - ax. B. La Mol By o a mall vaato th vty of th ulbum pot of ola fftal uato, a la mol obta. A la mol of th IPMSM o - otat f fam a b xp a follow [7] : pδ x = AΔ x BΔ u B TΔT L (43) T T wh, Δ x = Δ Δ Δ, Δ u = Δv Δv By tak mall ptubato of () a (), w hav Δ v =Δv v Δ θ (44) δ θ Δ v = Δ v v Δ (45) Δ = Δ Δ θ (46) Δ δ =Δ Δ θ (47) Fom (7), th follow uato obta. δ Δ θ = Δ Δ δ δ δ (48) By u (4), w hav Δ θ = Δ δ (49) A la mol of th otoll of F. xp a follow(f to Appx): pδ w = AwΔ w AxΔ x BΔ (5) wh, Δ w = Δz Δz Δz T Δ Δw Δw Δw Δθ, [ ] 3 3 Δ = Δ Δ Th Δw tat vto. Δz a Δz fo tuba obv, Δz3 fo p tmato, Δw fo p PI otol, Δw a Δ w3 fo ut PI otol a ay. Th latohp btw th otoll a th moto put xp a follow ( Appx): Δ u = FwΔ w FxΔ x FΔ (5) Fom (43),(5) a (5), th la mol of ovall ytm follow: x p Δ x = Δ A BF BF w x Δw Ax Aw Δw BF BT Δ ΔT L (5) B A fo th popo mtho how F.4, a la mol v th am ma [7]. U th la mol b abov, th tablty aaly pfom by omput th valu of ytm matx. Th tt IPMSM ha th follow at a omal valu: at output 8W, at p T 3pm, P = 8, R =.4Ω, L = 3.4mH, L = 3.8mH, ψ =.845Wb a J =.48km. W u th fft of th vaabl paamt whh a th

5 amp offt ζ, th atual aula fuy of th PI p tmato a th o aula fuy of th PI p otoll. I th a, th p f N = 5pm, th ut off fuy of LPF = 3a/, th loa tou T L =.6Nm. Th ob of th ovtoal ytm t a = 6a /. Th ut-off fu of all PI ut otoll a a/. F.5 how th tajto of pol fo ha of a. Th oot lo of th ovtoal mtho a th popo mtho a how (a) a (b) ptvly. Fom F.5, t obv that th ytm bom ollat wh mall a la. By ompa th oot lo of th popo mtho a tho of th ovtoal mtho, t fou that th omat oot lo a vy lo. F.6 how th tajto of pol fo ha of a ζ. Fom F.6, th ytm bom utabl wh ζ mall a la. Th omat oot lo a alo vy lo fo th ovtoal mtho a th popo o. F.7 how th oot lo wh th pol poto tmat by th output of th LPF wthout u () th ovtoal mtho a θ = / (53) By ompa th oot lo of F.5(a) a tho of F.7, th ff ou wh la. I F.7, th ytm bom utabl wh la bau of LPF. I a al ytm, a lay ou θ fo p- fom PWM otol by a DSP. Coutly, t o 5 N = 5pm = 5 ~ 6a / =.6 Nm = ~ a / ζ =.5 = 3a/ = 6a/ = 6 = 5 N = 5pm =.6 Nm ζ =.5 = = 5 (a) Covtoal mtho = 5 ~ 6a / = ~ a / = 3a/ = 6 = 45 = 3 = 5 = = 5 = = (b) Popo mtho F.5. Tajto of pol fo ha of a N = 5pm = 5 ~ 6a / =.6 Nm = 5a / ζ =. ~. = 3a/ = 6a/ ζ =. = 6 45 ζ =.5 ζ =. = N = 5pm =.6 Nm ζ =. ~. (a) Covtoal mtho = = 5 ~ 6a / = 5a / = 3a/ = 45 ζ =.5 ζ =. = 5 = 3 (b) Popo mtho F.6. Tajto of pol fo ha of a ζ. N = 5pm = 5 ~ 6a / = ~ a / ζ =.5 = 3a/ =.6 Nm = 6a/ = 5 = 5 = 3 = = 6 = 45 = Covtoal mtho F.7. Tajto of pol fo ha of a wh θ omput by. that th a lmt of a how F.7 patal ytm v f w u (). IV. SIMULATION AND EXPERIMENTAL RESULTS Wth th otol paamt that w u th tablty aaly, w mulat th tat po fo th tp ha of p f fom 5pm to 55pm by th o-la mol. I ato, w pfom th xpmt at th am oto. Smulato ult a how F.8,,, 4 a 6. Copo xpmtal ult a how F.9,, 3, 5 a 7. Th paamt fx

6 a a ζ a ha. th atual p, N th tmat p, θ th mat pol poto o. I F.8, th ollato of low fuy obv both mtho a th poto oθ la. I F.9, th xpmtal ult a mla to th mulato ult. Wh =, th omat pol lo to th maay ax fom F.5. Thfo, t o that th ollato obv. If l tha, th ytm bom utabl xpmtally. Wh = 5, th oot tablz F.5, th ollato uh a F.6 appa F.. Th xpmtal ult of F. a oo amt wth th mulato ult xpt fo th hh fuy ppl. F. th a wh futh a. Sp tmato a a, th poto o bom oably mall. I th xpmtal ult of F.3, th ppl of hh fu a obv N a θ. Howv, th valu a po oly th DSP a hh fuy ppl of th atual p whh mpotat fo th applato mall. Fom F. (4) (7) how th ult fo th ha of ζ. It ofm that th ytm bom ollat o utabl wh ζ mall. (a)covtoal mtho (b)popo mtho F.. Expmtal ult ( = 5, ζ =.5, = 5 ). (a)covtoal mtho (b)popo mtho F.. Smulato ult ( =, ζ =.5, = 5 ). [m ] (a)covtoal mtho (b)popo mtho F.8. Smulato Rult ( =, ζ =.5, = 5 ). (a)covtoal mtho (b)popo mtho F.3. Expmtal ult ( =, ζ =.5, = 5 ) (a)covtoal mtho (b)popo mtho F.9. Expmtal ult ( =, ζ =.5, = 5 ) [m ] [m ] (a)covtoal mtho (b)popo mtho F.4. Smulato ult ( = 5, ζ =.5, = 5 ). [m ] [m ] (a)covtoal mtho (b)popo mtho F.. Smulato ult ( = 5, ζ =.5, = 5 ). (a)covtoal mtho (b)popo mtho F.5. Expmtal ult ( = 5, ζ =.5, = 5 ).

7 [m ] [m ] [6] J. K. Sok, J. K. L, a D.C. L, Sol Sp Cotol of Noalt Pmat-Mat Syhoou Moto U Roto- Poto-Ttak PI Cotoll, IEEE Ta. I. Elto, vol.53, o, pp , 6. [7] M. Tuj, K. Kojma, G. Maaa, D. Akafuj, S. Hamaak, Stablty Stuy of a Pmat Mat Syhoou Moto Sol Vto Cotol Sytm Ba o Ext EMF Mol, IEEJ Joual of Iuty Applato, vol. o.3 pp.4854,. (a)covtoal mtho (b)popo mtho F.6. Smulato ult ( = 5, ζ = 3., = 5 ). [m ] [m ] (a)covtoal mtho (b)popo mtho F.7. Expmtal ult ( = 5, ζ = 3., = 5 ). Covtoal mtho mpov hh fuy ppl of tmat p by th hlp of tuba obv. Howv, th ppl of atual p whh mpotat fo th applato a almot am. Th ut-off fu of all PI ut otoll a a/. Th flu of th fuy fo popo mtho ot tv. V. CONCLUSIONS Fo IPMSM ol vto otol u th xt EMF, w hav ompa th popo mtho wth th ovtoal mtho by th oot lo, o-la mulato a xpmt. Co th pot, th ult of th popo mtho almot th am a tho of th ovtoal mtho. Thfo, t olu that th popo mtho uful bau of t mpl tutu. REFERENCES [] Z. Ch, M. Tomta, S. Dok, a S. Okuma, A Ext Eltomotv Fo Mol fo Sol Cotol of Ito Pmat-Mat Syhoou Moto, IEEE Ta. I. Elto, vol.5, o., pp.88-95, 3. [] S. Momoto, K. Kawamoto, M. Saaa, a Y. Taka, Sol Cotol Staty fo Salt-Pol PMSM Ba o Ext EMF Rotat Rf Fam, IEEE Ta. I. Applat, vol.38, o4, pp.546,. [3] K. Sakamoto, Y. Iwaj, T. Eo, T. Tauh, T. Nk, M. Kawamata, a A. Kawamua, Poto Sol Vto Cotol of Pmat Mat Syhoou Moto fo Eltal Houhol Appla, Po. of PCC-Naoya 7, LS4-3-3, pp.95, 7. [4] K. Yamaaka, T. Ohh, a M. Hojo, A Novl Poto Sol Vto Cotol of Pmat-Mat Syhoou Moto, Po. of PCC-Naoya 7, DS8-3, pp.9-95, 7. [5] B. H. Ba, S. K. Sul, J. H. Kwo a J.S. Byo, Implmtato of Sol Vto Cotol fo Sup-Hh-Sp PMSM of Tubo-Compo, IEEE Ta. I. Appl., vol.39, o3, pp.8-88, 3. APPENDIX k δ LδK k L K KpKp KpK δ Kp K Aw = δ K p K Kp K δ K k3δ L k4 K k 3 L k 5 L δ k k LKp LKp LLK p wh, k =, k =, k3 = δ δ δ k4 = L R Kp, k5 = L R Kp K p k 3 δ k4 L KpK k 3 L k5 p L / δ k, B = Ax = K p k K v Kp F w = K pkp Kp K K v Kpo K p F x = K p K p F = KpK p

Noise in electronic components.

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