Online Compensation of Parameter Variation Effects for Robust Interior PM Synchronous Motor Drives

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1 Online Compensation of Paamete Vaiation Effects fo Robust Inteio PM Synchonous Moto Dives 713 JPE Online Compensation of Paamete Vaiation Effects fo Robust Inteio PM Synchonous Moto Dives Rajenda L. Shestha and Jul-Ki Seok Chilime HydoPowe Company, Rasuwa, Nepal Powe Convesion Lab., Dept. of Electical Eng., Yeungnam Univesity, Gyeongsan, Koea Abstact This pape pesents an online voltage distubance estimato to achieve pecise toque contol of IPMSMs ove a high speed opeating egion. The poposed design has a type of state-filte based on a Luenbuge-style closed loop stato cuent vecto obseve. Utilizing the fequency esponse plot (FRF) appoach, the estimation accuacy and the paamete sensitivities ae analyzed. Accuate toque contol and impoved efficiency ae povided with the decoupling of the effect of the paamete vaiations. The feasibility of the pesented idea is veified by laboatoy expeiments. Key Wo: Accuate toque contol, Inteio pemanent magnet synchonous moto, Paamete vaiations, Voltage distubance estimato I. INTRODUCTION Inteio pemanent-magnet synchonous motos (IPMSMs) have eceived a geat deal of attention in the field of automotive taction applications due to thei unique featues, such as high efficiency, high powe density, and a wide constant powe speed ange 1. The dive systems in these applications equie stict toque egulation specifications that ae less than ±5% of the ated value in the oveall opeating ange 2. The Maximum Toque Pe Ampee (MTPA) opeation, which computes the theoetical cuent command vecto to minimize the coppe losses, is the most widely used appoach to achieve the desied ai gap toque of IPMSMs 3, 4. Cuent contol is the most widely used appoach to manipulate the ai gap toque of IPMSMs. It should be noted, that when using cuent contol, both the ai gap toque and the flux linkage ae open loop vaiables. Thus, accuate toque contol is often pecluded because of model eos due to paamete vaiations. In the constant powe egion, the magnetic satuation effect as well as tempeatue vaiations significantly influence the accuacy of the toque contol because the flux vaies as the oto speed inceases. One common emedy fo cuing this poblem involves lookup tables based on steady-state measuements of the moto voltages, cuents, and toque 5 7. Multi-dimensional o numeous look-up tables ae equied to cove the whole MTPA space, including the high satuation and PM flux/stato esistance vaiations. This is computationally intensive due to Manuscipt eceived Jan. 19, 2011; evised Jun. 17, 2011 Recommended fo publication by Associate Edito Kyeong-Hwa Kim. Coesponding Autho: doljk@ynu.ac.k Tel: , Fax: , Yeungnam Univesity Chilime HydoPowe Company, Nepal the non-lineaity caused by magnetic satuation and tempeatue vaiations. Futhemoe, a coss satuation effect is both intensive and vey difficult to estimate in offline metho. This pape pesents an online voltage distubance estimato design to achieve the pecise toque contol of IPMSMs ove a flux weakening opeating egion. The poposed design has a type of state-filte based on a Luenbuge-style closed loop stato cuent obseve. Utilizing the fequency esponse function (FRF) appoach, the estimation accuacy and the paamete sensitivities ae analyzed. With the poposed design, accuate toque contol and impoved efficiency ae povided with the decoupling of the effect of the paamete vaiations. II. IPMSM MODEL IN THE ROTOR REFERENCE FRAME A model of the IPMSM in the oto efeence fame is applied to design the voltage distubance estimato. The d-q axis voltage equation of the IPM machine in the synchonous efeence fame is given by: v v qs = Rs + pl d ω L q ω L d R s + pl q i i qs + 0 ω λ pm (1) whee: R s : stato esistance Ω v,v qs : d and q axes stato voltage in oto efeence fame V i,i qs : d and q axes stato cuent in oto efeence fame A L d,l q : d and q axes total stato inductances H λ pm : pemanent magnet flux linkage Wb p : diffeential opeato ω : oto speed. The well-known electo-magnetic toque equation of an IPMSM in the oto efeence fame is: T e = 3 2 P 2 ( λ i qs λ qsi ) (2)

2 714 Jounal of Powe Electonics, Vol. 11, No. 5, Septembe 2011 Fig. 1. Block diagam of the poposed d-axis voltage distubance estimation and compensation appoach. whee: λ = L di + λ pm: the d-axis stato flux. λqs = L q i qs : the q-axis stato flux. P : the numbe of poles. This equation can be ewitten in tems of the machine paametes of the IPMSM as: T e = 3 P λpm i qs + (L d L q )i 2 2 i qs. (3) The fist tem of (3) coespon to the PM alignment toque component poduced by the inteaction between the oto PM flux linage and the q-axis stato cuent. The second tem defines the eluctance toque due to the magnetic saliency. Since L d <L q and the cuent vecto lies in the thid quadant of the d-q cuent plane, the eluctance toque component of the above equation is additive. Because of the eluctance toque component, the cuent vecto command fo the cuent contol is geneally not linealy elated to the toque o the flux. The cuent vecto components ae computed to theoetically yield the minimum losses while still achieving the desied total toque. Such optimal cuent vecto computations can be implemented with vaying degees of complexity, whee the satuation and paamete adaptation can be included to impove the optimization. In the flux weakening egion, such an optimal phase displacement is heavily load-dependent due to the satuation and coss magnetization effect 7. Theefoe, inductance vaiations ae taken into account to achieve pecise toque contol at high spee. III. DESIGN AND ANALYSIS OF THE PROPOSED VOLTAGE DISTURBANCE ESTIMATOR A. Design and Analysis of the Distubance Estimato Fig. 1 and 2 show a block diagam of a d-q axis voltage distubance estimation stategy employing a closed-loop Luenbege-style stato cuent obseve 10. A familia popotional-integal-integal (PII) type obseve contolle has been adopted to estimate the voltage distubance esulting fom paamete vaiations. Because the command voltage vecto Vdqs is fed-fowad to the obseve, the voltage distubance eo ˆV dq D is estimated at the output of the obseve contolle. This can estimate and compensate fo voltage deviations esulting fom distubances and uncetainties. The Fig. 2. Block diagam of the poposed q-axis voltage distubance estimation and compensation appoach. estimated voltage distubance is compensated by the cuent contolle output in a feed-fowad manne. Fom the stato voltage equation, the d-axis stato cuent can be expessed as: I V (s) = + ω L q Iqs. (4) sl d + R s Fom the d-axis distubance obseve, the estimated d-axis cuent is given by: Î V (s) = + ˆV d D + ω ˆL q Iqs (5) sˆl d + ˆR s whee ˆ epesents the estimated vaiables. Then, the estimated distubance voltage is obtained as: ( ˆV d D (s) = b od + K od + K ) oid (I s s 2 ) Î whee b od, K od, and K oid epesent the d-axis state-filte gains. Substituting (4) and (5) into (6), the tansfe function of the d-axis distubance output can be obtained as: ˆV d D (s) = (V +ω L q Iqs) sl d +R s (s ˆL d + ˆR s ) + ω ˆL q Iqs (7) whee ˆL dq and ˆR s denote the inductance and the esistance eo, espectively. Using (4), (7) can be ewitten as: ˆV d D (s) = s 2 b od +sk od +K oid s 3 ˆL d +s 2 (b od + ˆR s )+sk od +K oid (6) s 2 b od +sk od +K oid s 3 ˆL d +s 2 (b od + ˆR s )+sk od +K oid (s ˆL d I + ˆR s I ) + ω ˆL q Iqs. (8) = G d (s)v d dist (s) As can be seen in (8), the state-filte fo the estimation of ˆV d D has an inheent phase lagging popety and a speed-dependent voltage, including the effect of ˆL q, which dominates at high fequencies in the estimation model. Thus, the deivative tem s ˆL d I and the esistance dop can be neglected at high fequencies.

3 Online Compensation of Paamete Vaiation Effects fo Robust Inteio PM Synchonous Moto Dives 715 Similaly, fo the q-axis distubance obseve, the tansfe function is as follows: s ˆV q D (s) = 2 b oq +sk oq +K oiq s 3 ˆL q +s 2 (b oq + ˆR s )+sk oq +K oiq (s ˆL q Iqs + ˆR s Iqs) + ω ( ˆL q Iqs + ˆλ pm ) = G q (s)v q dist (s) (9) whee b oq, K oq, and K oiq epesent the q-axis state-filte gains and ˆλ pm indicates the PM flux linkage eo. Equation (8) and (9) clealy state that ˆV dq D can be a diect indicato of model eos due to magnetic satuation and themal conditions. Fom G d (s)and G q (s), the estimation accuacy is diectly influenced by the eos in ˆL dq and ˆR s. To investigate the paamete sensitivity of the poposed estimato, the fequency esponse function (FRF), calculated fom (8) and (9), is plotted fo diffeent paamete eos. Fo automotive applications, as mentioned ealie, the common emedies fo avoiding paamete vaiation effects ae based on look-up tables. Howeve, these tables cannot pefectly cove the whole opeating egion without using a temendous numbe of tables. In this egad, it is assumed that a paamete deviation in the amount of ±20% inductance and ±50% stato esistance is inevitable in pactice. Thus, the esitmation accuacy of the designed state-filte should be examined unde these conditions. Fig. 3 and 4 show an FRF plot of the d-axis estimato with the detuned d-axis inductance (±20%) and the stato esistance (±50%), espectively. The state-filte bandwidth was set as 2000 ad/s. Despite the inductance eo condition, as shown in Fig. 3, the zeo-phase lag is achieved at up to appoximately 1000 ad/s. This implies that the poposed voltage distubance state-filte can achieve estimation without lagging within half of the obseve bandwidth. The magnitude is slightly inceased afte 500 ad/s, which means that it gives an estimation eo in magnitude in the tansient state. The esistance eo has nealy no impact on the estimation. The same esult is obtained fo the case of the q-axis estimato which is shown in Fig. 5 and 6. Fom the analysis, the poposed estimato is insensitive to electical paamete eos at high fequencies. B. Compensation Stategy fo Paamete Vaiations Based on (3), the toque eo T e esulting fom moto paamete vaiations can be obtained as: T e = 3 P 2 2 ( λ pm + ( L d L q )i ) i qs. (10) Fom (8) and (9), it can be seen that the outputs of the distubance estimato at high spee ae: Fig. 3. FRF plot of d-axis distubance estimato fo detuned L d by ±20%. Fig. 4. FRF plot of d-axis distubance estimato fo detuned R s by ±50%. Fig. 5. FRF plot of q-axis distubance estimato fo detuned L q by ±20%. ˆv d D = ω ˆL q i qs ˆv q D = ω ( ˆL d i + ˆλ pm ). (11) Then, combining (10) and (11), the estimated toque eo ˆT e can be descibed as: ˆT e = 3 ( P i ) ˆv d D + i qs ˆv q D. (12) 2 2 ω ω Fig. 6. FRF plot of q-axis distubance estimato fo detuned R s by ±50%.

4 716 Jounal of Powe Electonics, Vol. 11, No. 5, Septembe 2011 Fig. 7. Oveall block diagam of the system. Fig. 8. Expeimental setup. Fig. 7 shows an oveall contol block diagam of the poposed scheme to compensate the paamete vaiation effects. Hee, the estimated toque eo in (12) is subtacted fom the toque command in a feedfowad manne, which automatically adjusts the effective toque command. Thus, this design can be effective fo accuately estimating and compensating fo distubances ove high speed opeation anges while educing the computational complexity. A fixed MTPA cuve was implemented to utilize both the electomagnetic and the eluctance toque available in the IPMSM. The voltage feedback flux weakening contol scheme is applied above the base speed 11. IV. EXPERIMENTAL RESULTS The poposed algoithm was implemented on a 900W IPMSM, as descibed in Table I, and coupled to a 1.0 kw sevo moto as shown Fig. 8. An encode of 2500 pulsespe-evolution was mounted at one end of the test moto to measue the actual position. A pecise toque senso with ±0.25 % accuacy was installed between the IPMSM and the sevo moto to measue the actual geneated toque. The toque senso specifications ae listed in Table II. The PWM invete consists of IGBT modules and two phase cuents ae sampled with a ate of 50 µs. The dc-link voltage was set to 100 V and the coupled sevo dive was opeated with a 1300 /min speed command while a toque command Fig. 9. Toque contol pefomance without distubance voltage compensation. (a) d and q axis cuent (b) Refeence toque and measued toque. (c) Toque eo. (d) Estimated distubance voltage (e) Moto speed.

5 Online Compensation of Paamete Vaiation Effects fo Robust Inteio PM Synchonous Moto Dives 717 TABLE I RATINGS AND KNOWN PARAMETERS OF 900W IPMSM Ratings and Paametes Value Unit Rated toque 2.9 Nm Numbe of poles 8 R s 1.82 Ω L d 8.5 mh L q 20.2 mh λ pm Wb TABLE II SPECIFICATIONS OF TORQUE SENSOR Paametes Value Unit Supply Voltage V DC Output Range 2.0 Nm Output Voltage ±5 V Toleances ±0.1 % was applied to the IPMSM. At this speed, the IPMSM opeates in the flux weakening egion. Fo the opeation of the test moto, the MTPA contol scheme was used below the base speed and the voltage feedback flux weakening contol method was applied above the base speed. The online distubance obseve is pefomed evey 50 µs and the state-filte bandwidth is set as 500 ad/s. Fig. 9 shows the toque contol pefomance of the IPMSM without distubance voltage compensation. In ode to test the effect of paamete vaiations on the toque contol without distubance compensation, all the paametes wee intentionally changed to +20% of thei nominal value. The tests wee pefomed fo a 2Nm toque command in the test moto. In this test, the steady-state toque eo eaches to almost 0.25Nm, i.e. 12.5% of the ated toque as shown in Fig. 9(b) and (c). Fig. 9(d) is shown to monito the estimated voltage distubance unde the given conditions. The same expeiment was epeated using the distubance compensation in the testing system. Hee, the estimated distubance voltage was deliveed fom the contolle to compensate the paamete vaiation effects. The toque eo was nealy educed to zeo (less than ±2%) as shown in Fig. 10(b). This contol pefomance satisfies the ±5% toque egulation limit in automotive applications. By employing the poposed algoithm, toque accuacy can be achieved within the egulation limit of automotive applications in the flux weakening opeation anges. To examine the dynamic estimation pefomance of the poposed state-filte, L d was intentionally vaied stepwise +20% fom its nominal value unde a 1300 /min speed command as shown in Fig. 11. In Fig. 11(b), it can be seen that the magnitude and the phase eo in the contolled toque is aely found. Using the poposed algoithm, toque accuacy can be achieved within the ±5% egulation limit of automotive applications in pactical opeating conditions. The poposed state-filte has a simple stuctue and shows a fast estimation pefomance, without adding exta multidimensional look-up tables, when compaed to existing stategies 2-5, 8-9. It also identifies the vaiations of the IPMSM paametes due to magnetic satuation and tempeatue with minimal tuning effots. Fig. 10. Toque contol pefomance with distubance voltage compensation. (a) d and q axis cuent. (b) Refeence toque and measued toque. (c) Toque eo. (d) Estimated distubance voltage. (e) Moto speed. V. CONCLUSIONS Online voltage distubance obseves have been designed to compensate fo the paamete dependency of pecise toquecontolled IPMSMs ove a high speed ange. By utilizing the FRF appoach, the estimation accuacy and the distubance ejection popeties ae analyzed. Fom the expeimental esults, it is concluded that the adoption of the poposed state-filte makes it possible to achieve accuate toque contol in the pesence of high satuation and tempeatue vaiations. Although the analysis pesented in this pape is based on IPMSMs, the design concepts and conclusions can also be applied to nonsalient electic machines such as suface-mounted pemanent magnet synchonous machines and induction machines. ACKNOWLEDGMENT This wok was suppoted by a National Reseach Foundation of Koea (NRF) gant funded by the Koea govenment (MEST) ( ).

6 718 Jounal of Powe Electonics, Vol. 11, No. 5, Septembe B. Cheng and T. R. Tesch, Toque feedfowad contol technique fo pemanent-magnet synchonous motos, IEEE Tans. Ind. Electon., Vol. 57, No. 3, pp , Ma Y. Jeong, S.K. Sul, S. Hiti, and K. M. Rahman, Online minimumcoppe-loss contol of an inteio pemanent-magnet synchonous machine fo automotive applications, IEEE Tans. Ind. Appl., Vol. 42, No. 5, pp , Sep./Oct A. Consoli, G. Scacella, G. Scelba, and A. Testa, Steady-state and tansient opeation of IPMSMs unde maximum-toque-pe-ampee contol, IEEE Tans. Ind. Appl., Vol. 46, No. 1, pp , Jan./Feb H. Kim and R. D. Loenz, Impoved cuent egulatos fo IPM machine dives using on-line paamete estimation, in Conf. Rec. IEEE-IAS, pp , Oct Y. Jeong and S. K. Sul, Adaptive flux obseve with on-line inductance estimation of an IPMSM consideing magnetic satuation, in Conf. Rec. IEEE-PESC, pp , Jun H. B. Kim, M. C. Hak and R. D. Loenz, Sensoless contol of inteio pemanent magnet machine dives with zeo-phase lag position estimation, IEEE Tans. Ind. Appl., Vol. 39, No. 6, pp , Nov./Dec T. S. Kwon and S. K. Sul, Novel antiwindup of a cuent egulato of a suface-mounted pemanent-magnet moto fo flux-weakening contol, IEEE Tans. Ind. Appl., Vol. 42, No. 5, pp , Sep./Oct Fig. 11. Dynamic estimation pefomance of estimato changing L d by 20%. (a) Refeence toque and measued toque. (b) Toque eo. (c) Estimated q-axis distubance voltage. REFERENCES 1 S. R. Macminn and T. M. Jahns, Contol techniques fo impoved highspeed pefomance of inteio PM synchonous moto dives, IEEE Tans. Ind. Appl., Vol. 27, No. 5, pp , Sep./Oct Y. S. Kim and S. K. Sul, Toque contol stategy of an IPMSM consideing the flux vaiation of the pemanent magnet, in Poc. IEEE IAS Annu. Meeting, pp , S. Moimoto, M. Sanada, and Y. Takeda, Effects and compensation of magnetic satuation in flux-weakening contolled pemanent magnet synchonous moto dives, IEEE Tans. Ind. Appl., Vol. 30, No. 6, pp , Nov./Dec L. Zhong, M. F. Rahman, W. Y. Hu, and K. W. Lim, A diect toque contolled inteio pemanent magnet synchonous moto dive incopoating field weakening, IEEE Tans. Ind. Appl., Vol. 34, No. 6, pp , Nov./Dec Rajenda L. Shestha eceived his B.S. in Electical Engineeing fom Tibhuvan Univesity, Nepal, in 1999 and his M.S. in Electical Engineeing fom Yeungnam Univesity, Koea, in He is cuently a Plant Manage fo the Chilime HydoPowe Company, Rasuwa, Nepal. His eseach inteests include high-pefomance ac moto dives and contol systems. Jul-Ki Seok eceived his B.S., M.S., and Ph.D. fom Seoul National Univesity, Seoul, Koea, in 1992, 1994, and 1998, espectively, all in Electical Engineeing. Fom 1998 to 2001, he was a Senio Enginee with the Poduction Engineeing Cente, Samsung Electonics, Suwon, Koea. Since 2001, he has been a membe of the faculty of the School of Electical Engineeing, Yeungnam Univesity, Kyungsan, Koea, whee he is cuently an Associate Pofesso. His specific eseach inteests include high pefomance electical machine dives, sensoless contol of ac machines, and nonlinea system identification elated to the powe electonics field. D. Seok is cuently a membe of the Editoial Boad of the IET Tansactions on Electic Powe Applications. He is also seving as the cuent Vice Chai of the IEEE IAS-Industial Dive Committee (IDC) Pape Awad Depatment.