Proposal of Torque Feedforward Control with Voltage Phase Operation for SPMSM

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1 VT-- SPMSM Proposal of Torque Feedforward Control with Voltage Phase Operation for SPMSM Takayuki Miyajima (Yokohama National University) Hiroshi Fujimoto (The University of Tokyo) Masami Fujitsuna (DENSO CORPORATION) Abstract SPMSMs (Surface Permanent Magnet Synchronous Motors) are employed for electric power steering systems and machine tools. Theore, SPMSM drive systems should achieve fast torque response, wind operating range, and low torque ripple. For fast torque response and wind operating range, fast flux weakening control is necessary. However, current feedback control cannot achieve fast flux weakening control because it cannot operate voltage phase directly. In this paper, a torque feedforward controller with voltage phase operation is proposed. In transient state, voltage limit should be considered with derivative terms. By use of PWM hold model for FF controller, derivative terms can be considered. Finally, simulations and experiments are performed to show the advantages of the proposed method. PWM (SPMSM, voltage amplitude saturation, PWM hold model, torque feedforward control ). (SPMSM) SPMSM d, q () PWM () (FF) (3) (4) FF () (6) (7) (8) (9) FB () () FF SPMSM FF PWM. SPMSM dq SPMSM dq y = x = [ ] T, u = [v d v q] T (), (), (3) ẋ(t)=a c (ω e )x(t)b c u(t) [ ω e K e ] T } () y(t)=c c x(t) () [ ] R ω L e L A c(ω e) B c = ω e R L L (3) C c I v d, q : d, q R: L: ω e :, q : d, q K e : T (4) T = K mt (4) K mt = P K e, P : /6

2 E V [k] T[k] t T [k] Current Reference Generator i d[k] i q[k] Decoupling Control C d[z] C q[z] Td[k] Tq[k] SVM θe[k] θe[k] i u[k] SPMSM i w[k] uw θ INV e[k] dq [k] [k] kt u (k )T u PWM Fig.. PWM hold Fig.. Block diagram of conventional method qaxis PWM V [k], ±E(E: ) () PWM (3) (4), () ON T [k] ẋ(t) = A c x(t) B c u(t), y(t) = C c x(t) () x[k ] = A sx[k] B s T [k], y[k] = C sx[k] (6) A s = e A ct u, B s = e A ct u / B c E, C s = C c (7) PWM (6), (7), E E T [k] 3 SPMSM PWM () PWM ω e K e T u E = V dc (V dc : PWM (8), (9), () T = [ T d ) x[k ]=A s (ω e )x[k] B s (ω e ) T q ] T ( T d, q : d, q ON T [k] [ ] } T ω e K e T u V dc (8) y[k] = C sx[k] = C cx[k] (9) A s (ω e ) = e A c(ω e )T u, B s (ω e ) = e A c(ω e ) T u Bc V dc () SPMSM () 3. 3 (), () FB (3) PI C d, q (s) T u stin C d, q [z] vd v 3 V q > V max (V max := 3 dc : Fig max min T K mt daxis Point at the intersection of voltage limit circle with constant torque line ) C d, q [z] v d [k]=v d [k] ω e[k]l q[k] () vq [k]=v q [k] ω e[k](l d [k] K e) () C d, q (s)= L d, qs R, τ = T u (3) τs 3 (T : ) d, q i d, i q (4), (), (6), (7) i d[k]= ω ek el R ωel (i q max)(i q min) (4) max if T [k] > K mt max i q[k]= min elseif T [k] < K mt min () otherwise T [k] K mt max = ωeker Va R ω el R ω el (6) min = ωeker Va R ω el R ω el (7) V a i d[k] > i d[k] = (Space Vector Modulation: SVM) θ e(=.ω et u) (3) (8) T [k] T [k] = T [k] Tmax if T [k] > Tmax (8) T [k] otherwise T [k] = [ T d [k] T q[k]] T (9) T u T max (:= 3 3 ): dq ON T a T [k]: /6

3 C[z] Current i [k] T ff[k] T B s (ωe)as(ωe))ˆx[k]b s (ωe)i [k] T [k] [k] Reference [ ωeke/] Generator T T ff[k] ˆx[k] 4 Pn[z] I C[z] e[k] i[k] HPWM (SVM) θe[k] θe[k] θe[k] dq uw Fig. 4. Block diagram of conventional method SPMSM INV S () i [k] 6 Fig. 6. Eq. (3) Eq. () δff[k] δff[k] Tmax sinδff[k] Tmax cos δff[k] Tmax sinδff[k] Tmax cos δff[k] Eq. () B s (ωe)as(ωe))ˆx[k] B s (ωe)i [k] [ ωeke/] T C[z] C [z] T ff[k] Feedforward controller C [z] of proposed method T [k] Current Reference Generator Fig.. i [k] 3 C[z] T ff[k] T ff[k] T [k] ˆx[k] Pn[z] I C[z] e[k] i[k] HPWM (SVM) θe[k] θe[k] θe[k] dq uw SPMSM INV Block diagram of proposed method S () 4 FF C [z] FB C [z] (8) () T ff [k]=b (ω e )A(ω e )ˆx[k]B (ω e )x d [k ] [ ] T ω ek et u V () dc FF C [z] FF FB C [z] ˆx[k] := [î d [k] î q [k]] T i [k ] (8) C [z] FB C d [z], C q[z] 3 3 FF FF 6 () FB FF FB 3 3 FF C[z] () FF T ff [k] > T max d, q ON T ff = T max () i q T [k] i q[k] =A s î d [k] A s î q[k] B s T dff [k] ( ) B s T qff [k] ωeke () V dc A sij, B sij (8) A s (ω e ), B s (ω e ) i j T dff, qff : T ff d, q T dff [k] = T max sin δ ff [k], T qff [k] = T max cos δ ff [k] F [k] () () (3) F [k] := i ω q[k]a s î d [k]a s î q[k]b e K e T u s V dc () B s Bs ( )} F [k] = T max sin δ ff [k] tan Bs (3) B s δ ff : T ff () (3) (4) F [k] > T max (4) (4) T ff [k] d, q (3) δ ff () sin F [k] T δ ff [k]= max tan B s B s π sin F [k] () T max tan B s B s () δ ff q δ ff d i d î d [k ] 3 3 (4) FF ω e >, d /dt < ω e <, d /dt > q () δ ω e = q () δ ω e >, d /dt > ω e <, 3/6

4 d /dt < q q ω e >, i q î q [k] ω e <, i q î q[k] δ ff SPMSM q d/dt () d/dt δ v q = V a cos δ (6) δ = V a L sin δ =,... δ =, π [rad] (6) R SPMSM T (7) T = K mt ω e L V a sin δ (7) d/dt δ T δ(= ±π/ [rad]) q q (8) g δ ff g = [k ] k d [k ] = (A s k d A s) [k] (A sk d A s)[k] (B s k d B s ) T d [k] (B s k d B s ) T q [k] B s ω e K e T u V dc (8) k d : (k d > ) ω e > g d q δ (8) T d [k]= T max sin δ ff [k], T q[k]= T max cos δ ff [k] g/ δ ff = (9) g δ ff = (B s k d B s) T max cos δ ff [k] (B s k d B s ) T max sin δ ff [k] = (9) (9) (3) δ ff δ ff [k] = tan B sk d B s B s k d B s if ω e > & i q î q [k] tan B sk d B s B s k d B s elseif ω e < & i q î q[k] T ff [k] otherwise (3) k d k d δ q (3) k d k d = K I s ( F [k] T max) (3) Table. Inductance L Resistance R SPMSM Parameters of SPMSM.8 [mh].7 [mω] Pairs of poles P 4 Back EMF constant K e 73.8 [mv/(rad/s)] K I = 6 T u stin i d î d [k ] > i d î d [k] F [k ] T max F [k] > T max F [k ] = T max δ ff [k ] (3) 4. SPMSM T u =. [ms], V dc =36 [V] [rpm]. [Nm] 7 V a V a =.9V max dq ON T a, dq ON ()δ (3), (33) T a = T d T q (3) δ = tan T d T q (33) 7(c), 7(g), 7(k) T max FB FF FF q d q. [rpm] [Nm] V dc = 7 [V] V dcn 36 [V] V dcn /V dc 4/6

5 (a) (Conventional) (e) (Conventional) (i) (Proposed) (b) (Conventional) (f) (Conventional) (j) (Proposed) 7 Fig (c) T a (Conventional) (g) T a (Conventional) Simulation results (k) T a (Proposed) Angle of Input [rad] Angle of Input [rad] Angle of Input [rad] (d) δ (Conventional) (h) δ (Conventional) (l) δ (Proposed) θ =.9ω et u 8 d q FF d d q 6. FF SPMSM FB FB d, q FB FB H. Fujimoto, Y. Hori, and A. Kawamura: Perfect Tracking Control based on Multirate Feedforward Control with Generalized Sampling Periods, IEEE Trans. Ind. Eletron., Vol. 48, No. 3, pp ,. K. P. Gokhale, A. Kawamura, and R. G. Hoft: Deat beat microprocessor control of PWM inverter for sinusoidal output waveform synthesis, IEEE Trans. Ind. Appl., Vol. 3, No. 3, pp. 9 9, T. Miyajima, H. Fujimoto, and M. Fujitsuna: Control Method for IPMSM Based on Perfect Tracking Control and PWM Hold Model in Overmodulation Range, IPEC-Sapporo, pp ,. 4 T. Miyajima, H. Fujimoto, and M. Fujitsuna: Control Method for IPMSM Based on PWM Hold Model in Overmodulation Range -Study on Robustness and Comparison with Anti-Windup Control-, IEE of Japan Technical Meeting Record, SPC--9, pp. 3 8, (in Japanese). J.-K. Seok, J.-S. Kim, and S.-K. Sul: Overmodulation Strategy for High-Performance Torque Control, IEEE Trans. Power Electronics, Vol. 3, No. 4, pp , /6

6 (a) (Conventional) (e) (Conventional) (i) (Proposed) (b) (Conventional) (f) (Conventional) (j) (Proposed) Fig (c) T a (Conventional) (g) T a (Conventional) Experimental results (k) T a (Proposed) Phase of input [rad] Phase of input [rad] Phase of input [rad] (d) δ (Conventional) (h) δ (Conventional) (l) δ (Proposed) B.-H. Bae and S.-K. Sul: A Novel Dynamic Overmodulation Strategy for Fast Torque Control of High- Saliency-Ratio AC Motor, IEEE Trans. Ind. Appl., Vol. 4, No. 4, pp. 3 9,. 7 S. Lerdudomsak, S. Doki, and S. Okuma: Novel Voltage Limiter for Fast Torque Response of IPMSM in Voltage Saturation Region, T.IEEJapan, Vol. 8-D, No., pp , 8 (in Japanese). 8 K. Kondo, K. Matsuoka, Y. Nakazawa, and H. Shimizu: Torque feed-back control for salient pole permanent magnet synchronous motor at weakening flux control range, T.IEEJapan, Vol. 9-D, No., pp. 64, 999 (in Japanese). 9 T.-S. Kwon, G.-Y. Choi, M.-S. Kwak, and S.-K Sul : Novel Flux-Weakening Control of an IPMSM for Quasi-Six-Step Operation, IEEE Trans. Ind. Appl., Vol. 44, NO. 6, pp. 7 73, 8. H. Nakai, H. Ohtani, E. Satoh, and Y. Inaguma: Development and Testing of the Torque Control for the Permanent-Magnet Synchronous Motor, IEEE Trans. Ind. Electron., Vol., No. 3, pp. 8 86, K. Ohi, K. Tobari, and Y. Iwaji: High Response Feild Weakening Control by Voltage Phase Operation, T.IEEJapan, Vol. 9-D, No. 9, pp , 9 (in Japanese). K. Sakata and H. Fujimoto: Perfect Tracking Control of Servo Motor Based on Precise Model Considering Current Loop and PWM Hold, T.IEEJapan, Vol. 7-D, No. 6, pp , 7 (in Japanese) 3 J. Kudo, T. Noguchi, M. Kawakami, and K. Sano: Mathematical Model Errors and Their Compensations of IPM Motor Control System, IEE of Japan Technical Meeting Record, IEE Japan, SPC-8-, pp. -3, 8 (in Japanese). 6/6

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