Torque Control of Switched Reluctance Motors

Transcription

1 7-P594 1 Torque Control of withe elutne Motors C. Moron 1, A. Gr 1, E. Tremps 1 n J. A. omolinos 2 1 E.U. Arquitetur Tén (U.P.M. ensors n Atutors Group, Mri, pin 2 ET Ingenieros Nvles (U.P.M. Mri, pin This pper presents the performne of n instntneous torque ontrol metho. The simultion n experimentl results illustrte the pility of withe elutne Motors (M eing use in the motor rive inustry. Bse on experimentl, the vntges of this ontrol metho n its isvntges in prtl implementtion were stuie. The moel use in the simultion is the liner mgnet moel whh hs the 12/8 struture, the sme struture s the experimentl swithe relutne motor. Inex Terms elutne Motors, Torque Control. T I. INTODUCTION HE WITCHED elutne Motor (M is n ol memer of the eletr mhine fmily. The first M n e tre k to the erly 19th entury [1]. The min vntges of M re their simple struture, ruggeness, n tht they re reltively inexpensive to mnufture. However, the primry isvntges, suh s the torque ripple, oust noise, n the iffulty in ontrolling, prevent it from eing epte y the inustry extensively. During the pst two ees, reserhes hve een one to reue the torque ripple n oust noise. everl rther omplte ontrol methos, motor esigns, n power eletrons inverter topologies hve een propose whh now mke the M possle nie for mny rive ppltions, suh s servo rives n trtion rives of Hyri Eletr Vehles (HEVs [2] [] [4] [5] [6] [7]. II. WITCHED ELUCTANCE MOTO DIVE 1 Bs truture Figure 1 illustrtes 6/4 motor with rotor tooth pir ligne with sttor phse A A. In Figure 1, the rotor is ligne with sttor phse A A n this is si to e t the ligne position for sttor phse A A. The ligne position is stle equilrium point in tht the phse urrent n not proue ny torque t this position, ut smll evtion of the rotor wy from this point will proue torque to push the rotor k. In ontrst, the unligne position is n unstle equilrium point euse ny smll isplement of the rotor wy from tht point results in the rotor moving wy. Figure 2 illustrtes the perio hnge of inutne versus rotor position ssuming tht no sturtion exists (A liner mgnets moel. β s enotes the sttor pole-r n β r enotes the rotor pole-r. The siss of Figure 2 is the mehnl rotor position. r enotes the solute torque zone within whh phse n proue non-zero torque. The ngles β s, β r re lso ine in Figure 1, whh gives more geometr view of these efinitions. FIG. 1 HEE In Figure 2, 2 is the ngle where the overlpping of the sttor n rotor poles ours. Before this position, the phse inutne keeps its minimum vlue L min. is the position where the sttor pole-r β s eomes fully overlppe with the rotor pole-r β r. Between the position 2 n, the phse inutne inreses linerly s the rotor moves. From 4, the full overlpping of the sttor n rotor poles ens n the phse inutne ereses linerly until the rotor rehes the position 5 where no overlpping exists n the phse inutne eomes L min gin. The intervl etween n 4 is terme e zone. During this intervl, the phse inutne keeps its mximum vlue L mx. If β r is equl to β s, there is no e zone. The 6/4 motor illustrte in Figure 1 is of this kin, tht is, oes not hve e zone. FIG. 2 HEE 2 The M Moel The expressions for the flux linkges of the ifferent phses re ust shifte y s = 2π/qn. For the three-phse M, the eletrl equtions re given y: φ( n, = + υ (1 φ( n, = + υ φ( n 2, = + υ The mehnl eqution of the M is ω J + Bω = ( n,,, (2 L where J is the motor inert, B is the visous oeffient n L is the lo torque n the torque is given y n, i, i, i = n, i + n, i + n, i ( ( ( ( ( Mnusript reeive Jnury 1, 28 (e on whh pper ws sumitte for review. Corresponing uthor: F. A. Author (e-mil: f.uthor@nist.gov. Digitl Oet Ientifier inserte y IEEE

2 7-P594 2, ( n, = f ( n, = φ( n,,,, ( n, = f ( n = φ( n,, ( n, = f ( n = φ( n (4 Expning equtions (1 gives φ( n, nω + υ φ( n, φ( n nω + υ φ( n φ( n nω + υ φ( n (5 Eqution (5 shows tht if the flux linkge φ(, i is known (for π/n, symmetry of the motor struture is gurntee the eletrl equtions of M is then etermine. For estlishing liner mgnets moel we efine L( with their Fourier series n then gives the instntneous torque simply s ( n 1 2 L 1 2 ( n i i i n, = = kk sin( kn (6 2 2 k= 1 In this form, Fourier eries of L( up to thir hrmons is given s L ( n = k os[ kn ( ( 1 ] (7 k = 1 φ ( n = k os[ kn ( ( 1 ] i (8 k = ( n, i = i n kk sin[ kn ( ( 1 ] (9 2 k= 1 where = 1, 2, stns for phse A,B,C, respetively, n the oeffients re given s =., 1 =.222, 2 =.4 n =.11. FIG. HEE Figure shows the trnsient torque wveform of M. The moel use in the simultion is the liner mgnet moel whh hs the 12/8 struture, the sme struture s the experimentl swithe relutne motor. For the simultion esre, the numer of rotor poles is set s n = 4 in the two step response to mke it oinient with the 6/4 M illustrte in Figure 1 n Figure 2. FIG. 4 HEE Figure 4 plots the inutne n phse torques of this speif moel with n = 8 etween -9, where the torque is lulte with onstnt phse urrent I = 2.5 A. III. TOQUE CONTOL METHOD For the M ppltion in servo systems, one of the ontrol purposes is to reue the torque ripple tht inherently exists in the verge torque ontrol. In verge torque ontrol, the urrent referenes of two susequent phses re esigne inepenently, i.e., the urrent profile etween two susequent phse exittions is not ontrolle. Therefore, high torque ripple will our uring ommuttion. Also, the flt top of the urrent shpe is expete to proue torque ripple. To reue or even eliminte the torque ripple, the ontrol of the torque t eh instnt in time is onsiere. Wlle n Tylor [8] presente n instntneous torque ontrol metho whh is the ontrol metho implemente in this work. This ontrol metho, like ll the other vne torque ontrol methos, ssumes tht perfet urrent trking is relize y urrent trking loop. Therefore, the tsk of ontrol is to efine the referene urrent suh tht the esire torque is trke instntneously. FIG. 5 HEE Figure 5 shows simultion result of this ontrol metho trking onstnt torque referene, where the moel is the -phse 12/8 M efine in setion 2. As shown in the figure, the ommuttion ngle is efine s the position where the two ent phses n proue the sme torque with the sme urrent in their winings. In the intervl [, + s ], phse is the strong phse tht n proue the lrgest torque of esire polrity for given urrent. The urrent referene of phse 1 is esigne to erese to zero linerly in the intervl [, 1 z ] so tht it is rought to zero efore it n proue negtive torque. The urrent referene of phse efore is esigne to inrese linerly from zero to i ( = g(½ (. The funtion i = g(, is otine y inverting experimentlly etermine funtion (, i. As the rotor position inreses, phse +1 will tke the ple of phse to e the strong phse t position + s. Then the referene urrent of phse is ommutte t + s n goes to zero linerly n phse +1 eomes the phse tht proues the esire torque. During the strong perio, e.g., the intervl + s for phse, the urrent referene is efine y i ( = g( ( with ( = ( 1 ( +1 ( to trk the esire torque instntneously. The referene urrent esign of this ontrol metho is to hve the strong phse proue the ommne torque. Thus the torque per mpere rtio of this ontrol metho is high. However, it oes not reh the mximum torque per mpere rtio euse the urrent hnges linerly with respet to uring the ommuttion. An lterntive instntneous torque ontrol metho is to efine t the position where two ent phses proue the sme torque with the sme flux linkge in their winings. Inste of efining the urrent referene, flux linkge referene is efine in similr wy to the mximum torque per mpere ontrol. uh ontrol metho is lle mximum torque per flux ontrol, whh implies tht it will reue the require phse input voltge for the sme esire torque, ompre to the mximum torque per mpere ontrol.

3 7-P594 IV. EXPEIMENTAL EULT The torque-ngle hrterist (, i is otine y n utomt ientiftion proeure in whh the position of the shft of the system is ontrolle preisely y the PM synhronous motor to inrement in steps of.9 o for n entire mehnl revolution (6 o. With onstnt urrent kept in one phse of the M, the torque is mesure y the torque trnsuer. The phse urrent is the inrese in steps of.24a n the proeure repete until the urrent rehes the limit urrent. A qurture enoer is use for mesuring inrementl ngulr position. Beuse the position is mesure in enoer ounts ( 4 for one revolution the inherent error of is 6 o /4 =.9 o. It turns out tht if the step size of the position referene tretory is not n integer times.9 o, the tul shft tretory woul osillte etween ±.9 o. Therefore, the step size of the position referene here is hosen to e.9 o (or 1 enoer ounts. The torque is mesure t 4 points per revolution. For the -phse 12/8 motor, the experimentl torquengle hrterist for [, 22.5 o ] is extrte from Figure 6. The resulting look-up tle for (, i is 1 25 mtrix. Figure 7 give the 2-D plot of this look-up tle. FIG. 6 HEE A omprtive stuy etween severl methos hs een one with the experimentl 12/8 motor in fig. 7. Figure 7 ( shows the torque ontrol with onventionl sinusoil ontrol while figure 7 ( is the torque result when metho from [9] is implemente in the sme motor. In this lst se the ontroller is opte for the ske of performne omprison. It n lerly see how the propose instntneous torque ontrol reues the torque ripple. FIG. 7 HEE V. CONCLUION The torque ripple of the M is ue to the ouly slient struture of the mhine. The existene of the torque ip etween two susequent phses tes the existene of torque ripples. The ie of the ontrol metho implemente in this work is to efine the ommuttion ngle, t whh two ent phses n proue the sme torque for sme urrent. Bse on the efine, speif urrent referenes for ommuttion re esigne, whh is theoretlly le to eliminte the torque ripple ue to the torque ip. Beuse the ontrol metho ssigns the strong phse to proue esire torque s muh s possle, it ssures low urrents in phses other thn the strong phse, whh hieves seonry oetive of minimizing the opper losses. The ontrol metho les to reution in the verge torque. The mximum ommne torque of the strong phse must e less thn ertin level whh is less thn the pek of the torque profile, to voi the torque ripple ue to the shpe of the torque profile (see Figure 7. Therefore, the verge torque uner this ontroller hs to e less thn the rte verge torque. In the future, it will e interesting to otin roust ontrollers in orer to minimize the non esire torque ripple (ue to its non-linerity whh let use this kin of motors s rive trins for prototype eletr rs. This is the suet of our urrent reserh. ACKNOWLEDGMENT This work ws supporte in prt y the Universi Politén e Mri. EFEENCE [1] T.J.E. Miller, withe elutne Motors n their Control, Mgn Physs Pulishing, 199. [2] T.J.E. Miller,.Optiml esign of swithe relutne motors, IEEE Trnstions on Inustrl Eletrons, vol. 49, no. 1, 22, pp [] Dvi A. Torrey,.withe relutne genertor n their ontrol, IEEE Trnstions on Inustrl Eletrons, vol. 49, no. 1, 22, pp. -1. [4] oert B. Inerk, Mrus Menne, n ik W.A.A. De Donker, Control of swithe relutne rives for eletr vehle ppltions, IEEE Trnstions on Inustrl Eletrons, vol. 49, no. 1, 22, pp [5] Mehr Ehsni n Bk Fhimi,.Elimintion of position sensors in swithe relutne rives: tte of the rt n future trens, IEEE Trnstions on Inustrl Eletrons, vol. 49, no. 1, 22, pp [6] Chng-Hwn Kim n In-Joong H,.A new pproh to feeklinerizing ontrol of vrle relutne motors for iret-rive ppltions, IEEE Trnstions on Control ystems Tehnology, vol. 4, no. 4, 1996, pp [7] Ptrk L. Chpmn n ott D. uhoff,.design n preise reliztion of optimize urrent wveforms for n 8/6 swithe relutne rive, IEEE Trnstions on Power Eletrons, vol. 17, no. 1, 22, pp [8].. Wlle n D.G. Tylor,.A lne ommuttor for swithe relutne motors to reue torque ripple,. IEEE Trnstions on Power Eletrons, vol. 7, no. 4, Otoer [9].-K. Chung, H.-. Kim, C.-G. Kim, n M.-J. Youn, A new instntneous torque ontrol of PM synhronous motor for high performne iret rive ppltions, IEEE Trns. Power Eletron., vol. 1, no., pp. 88 4, My 1998.

4 7-P594 4 Fig. 1. Cross setion of 6/4 motor (Phse A is t Aligne Position. Fig. 4. Inutne n torque versus rotor otine with the simultion. Fig. 2. Inutne vs otor Position for onstnt urrent. Fig. 5. Exmple of the reue torque ripple ontrol. Fig.. Trnsient torque wveform of 12/8 M. Fig. 6. Experimentlly Mesure (, i of Phse A for o 22.5 o.

5 7-P594 5 Fig. 7. Torque response of M when it is ontrolle y: ( Conventionl sinusoil. ( The ske of performne omprison etile in [9]. ( The propose instntneous torque ontrol.