A PRACTICAL APPROACH TO COMPENSATION OF TORQUE RIPPLE IN HIGH-PRECISION PERMANENT MAGNET MOTOR DRIVES

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1 Preprnt of the paper presented on Internatonal Conference on Electrcal Drves and Power Electroncs September 2005, Dubrovnk, CROATIA ISBN DOI: full paper: A PRACTICAL APPROAC TO COMPENSATION OF TORQUE RIPPLE IN IG-PRECISION PERMANENT MAGNET MOTOR DRIVES Stefan Brock, Jan Deskur Insttute of Control and Computer Engneerng Poznan Unversty of Technology ul. Potrowo 3A Poznan POLAND {Stefan.Brock, Jan.Deskur}@put.poznan.pl Abstract. Torque pulsaton n permanent magnet synchronous motor mpars ther performance n crtcal applcatons, partcularly for drect-drve. A practcal approach to compensaton of selected torque harmoncs s presented. The approach consst of two steps: dentfcaton of domnant torque harmoncs (the coggng harmoncs and the flux lnkage harmoncs) and usng smple teratve search algorthm to tune the compensaton algorthm. The angular spectral analyss s used as a optmum crtera. The desgn of a rpple compensaton scheme s based on the fast, robust 2DFC current. The overall control scheme and expermental results are also presented. Proposed approach can be used as an automated self-commssonng scheme. Keywords. brushless drves, servo drves, moton control. 1. INTRODUCTION Permanent magnet synchronous motors (PMSM) are used wth preference for applcatons n hgh performance postonng systems and machne tool spndle drves. They enjoy the unque advantage that he absence of separate exctaton wndngs or magnetzng currents reduces the cooper losses. The problem of torque rpple n PMSM requres addtonal attenton [1 5]. The consequences are speed oscllatons, whch, although small n magntude, deterorate the performance of the drve n demandng applcatons. The effects of torque rpple are partcularly undesrables n some demandng moton control and machne tool applcatons. In addton, the torque rpple may excte resonances n the mechancal porton of the drve system, produce acoustc nose, and, n machne tool applcatons, leave vsble patterns n hgh-precson machned surfaces. Drect-drve motors are deal canddates for robotc and automaton applcatons such as arc weldng, laser cuttng or antenna trackng. They can, n prncple, mprove the postonng precson snce they lack the gearbox requred n conventonal electrc drve systems. owever, drect drve systems are more adversely affected by the motor s torque rpple. Therefore, drect drve motors requre accurate torque control. For the PMSM at least two addtonal torque components should be consdered besdes the nomnal torque. The frst component s due to the nteracton of the rotor s permanent magnets wth changng stator reluctance T cogg (coggng torque), whle the second s a consequence of the nonsnusodal flux-densty dstrbuton T elmag (electromagnetc rpple torque).

2 T T cogg elmag = f ( ) = f (, ) Coggng torque s ndependent from the motor current and can reach up to 4 % of the nomnal torque. The number of coggng torque perods per one rotaton depends on the number of stator slots and pole pars. Electromagnetc rpple torque s produced by the nteracton of the stator current MMF and the rotor fluxdensty. The predomnant rpple perods per revoluton are sx tmes the number of stator pole pars. The electromagnetc rpple torque can reach typcally 2 5 % of the nomnal torque. Prevous efforts to produce smooth torque profles can be put nto two categores. The frst category s focused on the desgn of the motor. The torque rpple content can be reduced usng specfc layouts of the stator wndng, adequate choce of the wdth of the magnet poles and the skewng technque. The man drawbacks of the quoted methods are the reduced nomnal torque and the ncreased complexty of motor constructon, resultng n hgher overall costs. The second category s focused on the control of the phase currents to suppress torque pulsaton from coggng and rpple torques. Control based methods wthout nfluencng the drve hardware can be easly and cheaply mplemented, however the obtaned torque s never entrely smooth. Paper [1] presents reducng the torque rpple for brushless DC drve. Fnte element analyss s used to calculate a back EMF profle. Later the phase currents durng the commutatonal ntervals are shapng. In paper [2] the adaptve estmaton technque s used n the determnaton of Fourer s coeffcents, whle the frequences of torque oscllatons are assumed to be known. Lyapunov s drect method s used to assure convergence between actual and estmated parameters. The proposed nonlnear torque control s estmatorbased, so a good knowledge of the machne parameters s needed. The survey paper [3] presents the complex state-varable approach. gh-bandwdth rpple compensaton s enabled usng a fast deadbeat current. An automated self-commssonng scheme extracts the pertnent fundamental and harmonc parameters from the drve system. In [4] the motor torque control problem was vewed as the optmzaton of a nonlnear mappng from commanded torque and motor poston to commanded phase current wth smultaneous mnmze copper losses. Smlar soluton was appled n work [5] for drect-drve. The organzaton of the paper s as follows. Frst, the dentfcaton of torque rpple s presented. In the thrd secton, compensaton technque of sgnfcant torque components s ntroduced. The effcency of the proposed technques n reducng the pulsaton torque was verfed wth experments. Some llustratve results presentng the possbltes and lmtatons of the proposed control methods are ncluded n the Secton 4. Nomnal PMSM parameters are gven n Appendx. (1) 2. IDENTIFICATION OF TE TORQUE RIPPLE The torque rpple functon s ndrectly acqured by operatng the machne at very low speed n complete closed loop system. The block dagram of whole system s presented on fg. 1 For low speed the torque harmonc frequency s then also very low and well wthn the bandwdth of the speed control loop. ence the speed compensates the torque rpple, ts output sgnal RegW q_comp can be use to dentfcaton. We proposed the angular spectral analyses (2), smlar to Fourer transformaton, but wth poston of rotor nstead of tme as ndependent varable:

3 poston ω ref ω ref Torque rpple compensator speed q-comp RegW_q-ref q-ref d-ref I d I q d q dq/ abc abc/ dq PWM modulator a,b,c PWM Inverter PMSM ω measurement of poston and speed Fg. 1 The block dagram of whole control system A A Re Im = = ( *cos( N * )* ) RegW q_ref revoluton/n ( RegWq_ref *sn( N * )* ) revoluton/n (2) The magntude of A varable can be nterpreted as a torque harmoncs number N. After analyss we found two predomnant harmonc: N =72 and N =216. The appled machne has 12 pole pars and 9 slots per pole. Therefore the harmonc N =72 s dentfed as electromagnetc rpple (6 tmes per pole pars) and the harmoncs N =216 s dentfed as coggng torque. It was checked, that coggng torque s ndependent from current and ampltude of electromagnetc rpple ncrease lnear wth torque current q. 3. TE COMPENSATOR SYSTEM A hgh bandwdth current control system was desgned for hgh-frequency torque rpple compensaton. A 2DFC (2 Degrees of Freedom Controller) was proposed. It comprses a dynamc feedforward structure wth predefne FIR response, PI feedback, and a ant-wndup lmter. A 2DFC has followng advantages: separate settng the parameters of responses for reference change and for dstrbuton (SEM) robustness for drve parameters very short executng tme constant delay for reference sgnal The constant delay for reference sgnal s mportant for correct work of torque rpple compensaton system. In our case the model of closed control loop can be replaced by delay block wth tme constant T d-cont =0.2 ms. The dentfed numbers of harmonc torque rpple are used for compensatng the mperfectons of the drve motor. The q-axs reference RegW q-ref controls the torque and hence s derved from the speed. The

4 addtonal sgnal q-comp compensates the coggng harmoncs (N =216) q-cogg and the flux lnkage harmoncs (N=72) q-elmag, respectvely. The compensaton sgnals are calculatng from equatons (3). q comp q cogg q elmag = = I = q cogg cogg max RegW + q_ref q elmag *sn * k ( 216*( + ωref * Td cont ϕcogg )) *sn( 72*( + ω * T ϕ )) elmag ref d cont elmag (3) The ampltude I cogg-max of q-cogg s constant, and t depends from parameters of machne only. The phase offset ϕ cogg s related to poston measurement system. Thanks to constant tme delay between commands current and real value of current, the speed correctons was proposed. The ampltude of q-elmag changes wth value of q current of machne together. Correctve coeffcent k elmag was ntroduced, to elmnate the nfluence of flux lnkage harmoncs. Value I cogg-max, k elmag,, ϕ cogg and ϕ elmag were tuned usng search method. Frst the coggng torque was compensated for no-load operatng of drve. For every step the sum of magntude A rev for one revoluton was calculated usng formula (2) and (4). Value I cogg-max and ϕ cogg were change accordng to (5) 2 2 ( A A ) A rev = + Re Im (4) revoluton mn mn ( Arev ) Icogg max, N = 216 ( Arev ) kelmag, ϕelmag N = 72 ϕ cogg (5) In the same way the parameters for compensatng electromagnetc rpple, k elmag,, ϕ elmag were selected. Of course n ths case the maxmal load of the drve was used, to maxmze the torque current q. 4. EXPERIMENTAL RESULTS In fgure 2 the torque rpple compensaton durng speed trackng s presented. The command value for the speed was selected to 0.1 rev/s (the maxmum speed of ths drect-drve s 2.35 rev/s). The test speed was Fg 2. Speed of system wthout and wth torque rpple compensaton

5 Fg 3. Output sgnal of speed wthout and wth torque rpple compensaton Fg 4. Speed harmoncs magntude wthout and wth torque rpple compensaton selected accordng to followng rules: for very low speed the torque harmoncs frequency s wthn the speed control loop bandwdth and speed rpple are compensated by ths ; for hgh speed the speed rpple are damper by drve nerta. For speed 0.1 rev/s the both speed harmoncs (72 and 216) are clearly vsble. On the fg. 2 (left) the speed s dsturbed by both harmonc. Of the fg. 3 (left) speed compensates only partly torque rpple. As a results hgh value of both speed harmoncs s presented on the fg. 4 (left). The speed n case on compensaton (fg. 2 rght) s smoother. Speed s used only for compensaton of load torque (fg. 3 rght). The values of both speed harmoncs (fg. 4 - rght) are consderably smaller 5. SUMMARY Torque pulsaton n PMSM mpars ther performance n crtcal applcatons. A practcal approach to compensaton of selected torque harmoncs s presented. The approach consst of two steps: dentfcaton of domnant torque harmoncs (the coggng harmoncs and the flux lnkage harmoncs) and usng smple teratve search algorthm to tune the compensaton algorthm. The angular spectral analyss s used as a optmum crtera. The desgn of a rpple compensaton scheme s based on the fast, robust 2DFC current. Proposed approach can be used as an automated self-commssonng scheme.

6 6. REFERENCES 1. Sozer Ylmaz, Torrey Davd A. : Adaptve Torque Rpple Control of Permanent Magnet Brushless DC Motors, Appled Power Electroncs Conference and Exposton, APEC '98. Conference Proceedngs 1998., Thrteenth Annual, Volume 1, Feb. 1998, pp:86-92 vol.1 2. Grcar Bojan, Cafuta Peter, Stumberger Gorazd, Stankovc Aleksandar M.: Control-Based Reducton of Pulsatng Torque for PMAC Machnes, IEEE Transactons on Energy Converson, Vol. 17, No. 2, June 2002, pp: oltz Joachm, Identfcaton and Compensaton of Torque Rpple n gh-precson Permanent Magnet Motor Drves. IEEE Transactons on Industral Electroncs, Vol. 43, No. 2, 1996, pp Aghl F., Buehler M., ollerbach J. M.: Torque Rpple Mnmzaton n Drect-Drve System. IEEE/RSJ Int. Conf. Intellgent Robots and Systems, IROS`98, p , Vctora, Canada, Oct Chapman, P.L.; Sudhoff, S.D.; Whtcomb, C.A.: Optmal current control strateges for surfacemounted permanent-magnet synchronous machne drves. IEEE Transactons on. Energy Converson, Volume 14, Issue 4, Dec. 1999, pp APPENDIX Nomnal motor data Maxmal electrc torque 150 Nm Nomnal electrcal torque for speed =0 50 Nm Maxmal voltage 310 V DC Maxmal current 5.8 A RM Torque coeffcent 25.8 Nm/A RMS Maxmal speed 141 mn -1 Stator resstance 19.6 Ω Drve nerta kgm 2