TORQUE-SPEED ADAPTIVE OBSERVER AND INERTIA IDENTIFICATION WITHOUT CURRENT TRANSDUCERS FOR CONTROL OF ELECTRIC DRIVES

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1 PUBLISHING HOUSE PROCEEDINGS OF THE ROMANIAN ACADEMY, Seres A, OF THE ROMANIAN ACADEMY Volume 4, Number 3/2003, pp TORQUE-SPEED ADAPTIVE OBSERVER AND INERTIA IDENTIFICATION WITHOUT CURRENT TRANSDUCERS FOR CONTROL OF ELECTRIC DRIVES Gheorghe Danel ANDREESCU *, Raul RABINOVICI ** * Poltehnca Unversty of Tmsoara, Dept. of Automaton an Inustral Informatcs, Tmsoara, Romana. ** Ben-Guron Unversty of the Negev, Dept. of Electrcal an Computer Engneerng, Beer-Sheva, Israel. Corresponng author: Gheorghe Danel ANDREESCU, B. V. Parvan 2, Tmsoara, tel: , fax: , e-mal: anre@aut.utt.ro Ths paper evelops a hgh ynamc an robust spee-torue control system for servo rves base on aaptve observer an self-tunng technues wth on-lne nerta entfcaton. Only the rotor poston s measure even for a low precson shaft encoer. The nstantaneous spee an the sturbance torue are accurately estmate by an extene Luenberger observer nerta aaptve. A current to voltage ecouplng an sturbance torue feeforwar compensaton realze a fast current sensorless torue control wth ynamc torue lmtaton. The mechancal nerta, use for the selftunng of both spee controller an Luenberger observer, s on-lne entfe by a screte tme recursve graent algorthm. Extensve smulaton results wth the propose control structure, apple to a permanent magnet synchronous motor (PMSM) rve, prove hgh-ynamc performances n we spee range. A goo robustness to :0 nerta varaton at rate loa torue s obtane. Key wors: Current sensorless, Aaptve state-sturbance observer, Recursve graent algorthm, Inerta entfcaton, Self-tunng controller, Feeforwar ecouplng, Torue control, PMSM rves.. INTRODUCTION The sensorless control s an mportant goal n nustral applcatons to obtan a goo performance per prce nces []. However, the robust an hgh-ynamc control of robots an machne tools reure precse poston control loop, thus the poston transucer s always present. Usually, the robust control of electrc rves comprses an nternal current-loop usng current sensors. In ths case, the power source operates as a current source an a torue control s expecte. However, real currents are affecte by a lot of noses, e.g., nverter swtchng, an thus they are ffcult to measure especally at no loa. Lnke sensor cables an ADC nterface consttute sources of falures. A promsng soluton s observer-base current sensorless control [2]. The sturbance torue estmaton an compensaton s use to obtan a robust moton control when the loa torue an parameters change. Moreover, auto-tunng technues base on parameter entfcatons are also employe []. Dfferent approaches to on-lne entfy the nerta were evelope n the last ten years for self-tunng spee controller. They coul be: least suare (LS) metho [], recursve extene least suares (RELS) metho [3-4], Lanau screte tme recursve algorthm [5]. To estmate the nstantaneous spee an sturbance torue the followng solutons coul be use: extene Kalman flter [3], aaptve extene Kalman flter [4], mnmal-orer Gopnath observer [5]. In all these cases, a current loop wth measure currents an a poston transucer are always present. In most cases, the computaton effort s ute heavy. Ths paper proposes a new robust current sensorless control for hgh-ynamc electrc rves usng only poston transucer. Ths soluton s base on: current sensorless torue control, spee-loa torue observer, auto-tunng spee controller an on-lne nerta entfcaton. A representatve applcaton s the robot axs control wth effcent compensaton of nerta varaton an euvalent complex couple-sturbance terms. Recommene by Ion DUMITRACHE, Member of the Romanan Acaemy

2 Gheorghe Danel ANDREESCU, Raul RABINOVICI 2 2. STRUCTURE OF CURRENT SENSORLESS SPEED-TORQUE CONTROL The propose current sensorless spee-torue control structure for electrc rves s presente n Fg.. Fg.. Structure of current sensorless spee-torue control base on aaptve observer an nerta entfcaton. where: PMSM wth poston transucer, voltage source nverter (VSI) wth space vector moulaton (SVM), current to voltage ecouplng (CVD Fg. 2) for torue control, ynamc correcton (Hc), sturbance torue feeforwar compensaton (T L^), aaptve extene Luenberger state-sturbance observer (Obs^ Fg. 3) for spee-loa torue estmaton, nerta entfcaton wth screte tme recursve graent algorthm (J^ estm Fg. 4), PI self-tunng spee controller wth ant-wnup (PI_arw Fg. 5). 3. TORQUE CONTROL CURRENT TO VOLTAGE DECOUPLING Electrc machnes moels can be separate nto two subsystems: an electromagnetc moel (EM) an a mechancal moel (M), couple by the electromagnetc torue (T e ) an by the mechancal rotor spee ω. The M moel s (), where: θ - mechancal rotor poston, J - mechancal nerta, B - ampng factor, T L - loa torue. θ 0 θ 0 = + T t ω 0 - B/J ω /J /J e T L, θ ω θ = ω 0 t= 0 0. () In a partcular case, e.g., for a salent-pole PMSM, the EM moel n, rotor reference s a nonlnear couple MIMO gven by (2) an (3). It s assume that the argap magnetc flux s snusoal strbute, there are no amper wnngs an the ron losses are neglecte [6]. u u = R = R e + L + L /t + /t pω L pω ( λ 0, + L ), (0) = (0) = 0 0, (2) T = 3/2 p [ λ0 ( L L ) ], L > L, (3) where: r (, ) - stator current vector, u r (u, u ) - stator voltage vector, p number of pole par, R - stator resstance, λ 0 - PM flux, L, L -, axs nuctances. Base on (2), a feeforwar current to voltage ecouplng control (4) s use to obtan a torue control. u u = R = R o o pl ˆ ˆ o ω + pωˆ ( λ + L 0o o, (4) ˆ )

3 3 Torue-spee aaptve observer an nerta entfcaton wthout current transucers for control electrc rves where: u r* (u *, u * ) - stator voltage reference, r* ( *, * ) - current vector reference, superscrpt ^ - estmate varables, subscrpt o - estmate parameters. The r* s gven by an optmal crtera from the torue reference T e * elvere by the moton controller [6]. For current vector control wth * = 0, therefore T e * = K To *, where K To = 3/2 p λ 0o. In ths case, the current to voltage ecouplng s presente n Fg. 2. Fg. 2. Current to voltage ecouplng. PMSM torue control wth * = 0. We antcpate the result from (5) ^ / * = / ( + st o ) that expresses the elay ue to the stator tme constant T o. The ecouplng proceure s senstve to PMSM electromagnetc parameters, exceptng L. For an eal VSI, u r = u r*. In the eal tune case,.e., the estmate parameters are eual to the PMSM parameters, a ecouplng between, axs s obtane from (2) an (4). The current transfer functons are euvalent to two frst-orer lag elements (5) wth tme constants T o = L o /R o an T o = L o /R o, respectvely. In the case * = 0, the torue transfer functon s: T e /T e * = / ( + st o ),.e., the reueste torue control. H ( s). (5) + st = =, H ( s) = = + sto Dynamc correcton Hc (Fg. ) s use to obtan a faster torue response T e /T e ** = / ( + st c ), T c < T o. Feeforwar euvalent sturbance-torue compensaton T L^ s realze for a fast torue control wth accurate ynamc-torue lmtaton (Fg. ). o 4. INSTANTANEOUS SPEED AND DISTURBANCE TORQUE OBSERVER The nstantaneous spee ω^ an sturbance torue T L^ estmatons (Fg. 3) are base on extene Luenberger observer nerta aaptve [2], [7] (6). The loa torue T L s consere to be practcal constant n a samplng nterval h. The man observer nput T e^ leas to a reuce phase lag. The compensator esgn uses the pole allocaton metho (7). Real negatve poles p, p 2, p 3 are chosen for fast convergence wthout oscllatons. Accorng to the Shannon samplng theorem: mn (/ p ) > 2h. θˆ ωˆ = t ˆ TL θˆ /Jˆ ωˆ + /J ˆ ˆ Te 0 0 ˆ 0 TL k + k k 2 3 ( θ θˆ), θˆ ωˆ ˆ TL θˆ 0 = ωˆ 0 ˆ TL t= 0 0. (6) k = (p + p 2 + p 3 ); k 2 = p p 2 + p 2 p 3 + p 3 p ; k 3 = p p 2 p 3. (7) Wth ecouplng an the ynamc correcton Hc, the estmate electromagnetc torue T e^ s gven by T e^ / T e ** = / ( + st c ). There are two ways ω^ an ω ^ to estmate the spee (Fg. 3). For hgh-ynamc response, the better choce s ω ^ estmaton because t has atonally a poston correcton term k.

4 Gheorghe Danel ANDREESCU, Raul RABINOVICI 4 Fg. 3. Extene Luenberger observer nerta aaptve to estmate: θ^, ω^, a^, T L^. 5. INERTIA IDENTIFICATION There are servo rves applcatons where the nerta has a large varaton, e.g., :0 range n robotcs. Both the Luenberger observer (6) an the spee controller are senstve to the nerta J evaton; thus ynamc performances are affecte. In ths case, the estmate euvalent sturbance torue T L^ contans to terms: the loa torue an the components generate from parameter varatons []. However, because the loa torue s not possble to be separately estmate, the electromagnetc torue T e ** (Fg. ) n transent an steay state regmes s not correctly lmte. To avo these savantages, an nerta on-lne entfcaton s propose to self-tune both the Luenberger observer an the spee controller. The basc euaton for nerta entfcaton s a smplfe screte-tme mechancal moel gven by (8), obtane from () usng the elaye Euler metho,.e., s = ( z ) / z. Assumng that rap changes n loa torue are not expecte n few samplng peros h, thus T L s practcally constant. The fference between two tme-consecutve of (8) gves the screte process (9), where the loa torue T L s mssng [], [5]. ω k = ωk / 2ωk k 2 e k ek e k e k 2 = ωk + b( Tek TL k ), b = h J, (8) ω + b T, T = T T. (9) The on-lne nerta entfcaton s base on a screte tme recursve graent algorthm n a moelreference aaptve approach [8]. Accorng to reference moel (9), where ω s replace by ω^, the precton aaptve moel ϖ s gven by (0) where a parameter aaptaton mechansm b^(j) wth aaptve correcton C () s use. The stablty s guarante for any gan f > 0. Notaton: any screte-tme varable x k s wrtng x k. ω ~ = 2ωˆ bˆ = bˆ + C e, e = ωˆ ω~, Tˆ b ˆ ˆ, (0) ωˆ 2 + T ˆ ˆ ˆ ˆ e, ω(0) = ω0, ω2 (0) = ω20 e C = = ( Tˆ e f Tˆ /( + Tˆ e e2 e f Tˆ ), 2 e ), Tˆ (0) = Tˆ e0, bˆ (0) = bˆ Tˆ e2 0 (0) = Tˆ e20. () The mplementaton of the screte-tme algorthm for nerta entfcaton J^ s presente n Fg. 4. A lmtaton an a gtal fst-orer lag flter s ae for J^ to reuce the noses. Fg. 4. Dscrete-tme recursve graent algorthm for nerta entfcaton.

5 5 Torue-spee aaptve observer an nerta entfcaton wthout current transucers for control electrc rves Wth a correct nerta entfcaton there s a ynamc ecouple control acton between the reueste electromagnetc torue components (Fg. ): ) the estmate torue T L^ that compensate the loa torue T L, an ) the transent torue from the spee controller T eω * that appears urng changes n the reueste spee ω * or n the real spee ω. An accurate ynamc lmtaton of the real electromagnetc torue T e can be realze. 6. SELF-TUNING SPEED CONTROLLER The smplfe transfer functon of the torue control system from Fg., for T L^ = 0 s gven by ω k H ( s) = = k = T = Tc T ω,,. s ( + st) J (2) e Fg. 5. Spee controller PI ant-wnup wth reference flter an nerta aaptve. The spee controller esgn s base on a generalzaton of the Kessler symmetrcal optmum metho [9]. There s a sngle parameter m to be chosen, an for each selecte soluton, the maxmum value for the phase margn s obtane. Accorng to ths metho apple n our case, the spee controller s proportonal ntegral (PI) type wth a frst orer-lag flter on the spee reference ω *. A ynamc lmtaton T emax of the reueste torue T e ** s obtane by usng an ant-wnup proceure apple to the ntegral component. The spee controller structure s gven n Fg. 5. The esgn relatons are: 2 k = / ( mtk ), T = m T, T = T. (3) p To obtan robust transent spee responses to nerta varaton an because only k p gan strongly epens on nerta J, the k p gan s self-tune usng the estmate nerta J^. fw 7. SIMULATION RESULTS The parameters of the control system are the followng: PMSM rate ata: T eo = 2.3 Nm, ω o = 000 rpm, I ao = 3 A, V co = 20 V, an parameters: p = 4, λ 0o = 0. Wb, L o = 0.02 H, L o = 0.02 H, R o =.8 Ohm, J o = kgm 2, B o = 0.00 Nms/ra. Luenberger observer: p = 300, p 2 = 400, p 3 = 500, an thus k = 200, k 2 = 470e3, k 3 = 60e6. recursve graent algorthm for nerta entfcaton: h = ms, f = 50, T f = 40 ms, a = 0.975, b = PI-arw spee controller: T o = ms, T c = 3.7ms, m = 2.5, T = T fw = 23ms, k aw = 5, T emax = 5Nm, kp/j o = 0. The theoretcal eas are well supporte by gtal smulatons. The smulatons are performe n contons of extreme nerta changes from 0J o to 0.5J o. The rve system performances are teste at step spee references at low spee of 20 rpm (Fgs. 6 an 7) an at hgh spee of 400 rpm (Fgs. 8 an 9). The spee s reverse at 0.35 s, an a step loa torue of 2 Nm s apple at 0.85 s. The Matlab-Smulnk package wth Runge-Kutta 3 an h = ms s use. The transent responses are stues as followng: ω - real spee, T e - real electromagnetc torue, T eω * - reference torue from the spee controller, T L^ - estmate sturbance torue, J^ - estmate nerta. In Fg. 6, n the frst 00 ms - when the nerta J^ s n transent entfcaton, the spee responses oscllates an the sturbance torue T L^ oes not estmate the real loa torue but the component ue to nerta varaton. That fact s so because both the spee controller an the Luenberger observer are etune. On the other han, the estmate nerta J^ converge n all cases an accurate estmate varables are obtane. In Fgs. 6 an 8, at step reverse spee, the loa torue T L^ s correctly estmate. Furthermore, there s a correct ecouplng between the loa torue estmaton T L^ an the transent torue T eω *. Therefore, a correct

6 Gheorghe Danel ANDREESCU, Raul RABINOVICI 6 lmtaton of the electromagnetc torue to 5 Nm n transent regmes s obtane. A ute fast spee response at loa torue changes s expecte. In Fgs. 7 an 9, for J = 0.5J o, the electromagnetc torue s not n lmtaton. Thus, robust fast speeresponses nvarants to reference spee are obtane. The nerta entfcaton algorthm s base on torue varatons. Therefore, when torue varatons are small values then the convergence tme s longer (Fg. 7). In Fg. 8, at a large step spee reference, the electromagnetc torue s lmte for a long tme. The spee response s naturally longer but wthout overshoot,.e., the spee controller ant-wnup faclty. Fg. 0 shows the robustness to electrc parameters uncertanty, use n Fg. 2,.e., stator resstance R o an PM flux λ 0o at hgh spee of 400 rpm. For a temperature rse of 50 C, the resstance ncreases by 20% an the PM flux ecreases by 0% n the case of ferrte magnet. The nuctances are not affecte by temperature. The estmate J^ = 0.03 kgm 2 s slghtly fferent from the real J = kgm 2. Fg. 6. Transent responses for ω * = ± 20 rpm, J = 0 J o. Fg. 8. Transent responses for ω * = ± 400 rpm, J = 5 J o.

7 7 Torue-spee aaptve observer an nerta entfcaton wthout current transucers for control electrc rves Fg. 7. Transent responses for ω * = ± 20 rpm, J = 0.5 J o. Fg. 9. Transent responses for ω * = ± 400 rpm, J = 0.5 J o. Fg. 0. Transent responses for ω * = ± 400 rpm, etune case: J = 5J o, R =.2R o, λ 0 = 0.9λ 0o. 8. CONCLUSIONS A new hgh-ynamc an robust spee-torue control structure base on aaptve observer wth on-lne nerta entfcaton usng only the poston transucer s evelope for the control of electrc rves, partcularly for PMSM. The man features are the followng. The nstantaneous spee an sturbance torue are estmate by an extene Luenberger observer nerta aaptve, wth fast convergence, usng the estmate motor torue an the measure poston. To obtan a hgh-ynamc current sensorless torue-control, a current to voltage feeforwar ecouplng (for PMSM or specfc for fferent motor types) an a ynamc correcton to reuce the electrc tme constant are apple. Also, a feeforwar compensaton of the sturbance torue s use for robustness. On-lne nerta entfcaton gven by a Lanau screte-tme recursve graent algorthm s use for robust aaptve tunng of both PI ant-wnup spee controller an extene Luenberger observer. Wth correct nerta entfcaton, there s a ynamc e-couple acton between the reueste electromagnetc torue components,.e., the torue from the spee controller an the torue to compensate the loa torue. Moreover, an accurate ynamc lmtaton of the real electromagnetc torue s obtane. Extensve smulaton results usng a PMSM rve prove hgh-ynamc performances an robustness of the propose control structure n we spee range, wth rate loa torue, an large :0 nerta varaton.

8 Gheorghe Danel ANDREESCU, Raul RABINOVICI 8 The applcaton area of the propose control structure covers hgh-ynamc ac or c servo rves, robust to parameter varatons an loa torue, n we spee range. A typcal example s a robot axs control wth effcent compensaton of nerta varaton an euvalent complex couple-sturbance terms. REFERENCES. OHNISHI, K. MATSUI N., HORI, Y. Estmaton, entfcaton, an sensorless control n moton control system, Proceengs of IEEE, 82, 8, pp , Aug ANDREESCU, G.D., RABINOVICI, R., Current sensorless control of c motors by torue an spee observer, Proc 8 th European Conf. on Power Electroncs an Applcatons EPE 99, Lausanne, Swtzerlan, CDROM, 086.pf, pp. -8, Sept JI, J.-K., SUL, S.-K., DSP-base self-tunng IP spee controller wth loa torue compensaton for rollng mll c rve, IEEE Transactons on Inustral Electroncs, 42, 4, pp , Aug KWEON, T.-J., HYUN, D.-S., Hgh-performance spee control of electrc machne usng low-precson shaft encoer, IEEE Transactons on Power Electroncs, 4, 5, pp , Sept FUJITA, K., SADO, K., Instantaneous spee etecton wth parameter entfcaton for ac servo systems, IEEE Transactons on Inustry Applcatons, 28, 4, pp , July/Aug BOLDEA, I., NASAR, S.A., Vector Control of AC Drves, Flora, CRC Press, SCHMIDT, P.B., LORENZ, R.D., Desgn prncples an mplementaton of acceleraton feeback to mprove performance of c rves, IEEE Transactons on Inustry Applcatons, 28, 3, pp , May/June LANDAU, I.D., Ientfcaton et Commane es Systemes, Pars, Etons Hermes, PREITL, S., PRECUP, R.-E., An extenson of tunng relatons after symmetrcal optmum metho for PI an PID controllers, Automatca 35, pp , 999. Receve October 20, 2003