SENSORLESS DIRECT TORQUE CONTROL OF RUSHLESS AC MACHINE USING LUENBERGER OBSERVER

5-8 JATIT. All right reerved. SENSORLESS DIRECT TORQUE CONTROL OF RUSHLESS AC MACHINE USING LUENBERGER OBSERVER 1 Khalil. Nabti, K. Abed, H. Benalla 1, Student, Prof. Department of Electrical Engineering, Faculty of Engineering Science, Ain El Bey, Contantine, 5ALGERIA E-mail: Idor6@yahoo.fr, Khoudir.abed@Lapote.net, benalladz@yahoo.fr ABSTRACT The enorle DTC of Bruhle AC (BLAC machine uing Luenberger oberver i propoed in thi paper. In Direct Torque Control (DTC, accurate rotor poition information i not eential. The peed i etimated by Luenberger oberver, which ued to improve the performance of dynamic tracking and accuracy of the whole ytem. The peed regulation i realized by a conventional PI regulator. Simulation reult how mall overhooting and good dynamic of the peed and torque, low ripple in torque and flux. So we verify the effectivene of the propoed oberver to monitor the drive. Keyword: Senorle BLAC, Direct Torque Control, Luenberger Oberver, PI regulator. 1. INTRODUCTION The PMSM control difficulty reide in the coupling of control variable uch a flux and electromagnetic torque. Two principal trategie were developed almot at the ame time in two different reearch center, Direct Torque Control trategy wa firt introduced by I. Takahahi, in 1986 [1]. M. Depenbrock, develop a imilar idea in 1988 under the name of Direct Self Control []. The DTC i one of the recent reearche control cheme which are baed on the decoupled control of tator flux and torque providing a quick and robut repone with a imple implementation in AC drive. DTC ha the advantage of implicity, good dynamic performance, and inenitive to motor parameter except the tator reitance. In DTC trategy the peed enor i not eential for the flux and torque etimation. Baically Direct Torque Control employ two hyterei controller to regulate the tator flux and torque, which reult in approximate decoupling between the flux and the torque control. The key iue of DTC deign i how to chooe the uitable tator voltage vector to keep the tator flux and torque in their hyterei band. The principal diadvantage of conventional DTC are: the high torque ripple and the low tranient repone during tart-up and during load diturbance. In mot control cheme; cloed-loop control i baed on the meaurement of peed or poition of the motor uing an encoder. However, in ome cae it i difficult to ue enor for peed meaurement. There are everal diadvantage of encoder uch a higher number of connection between motor and it driver, additional cot, uceptibility to noie and vibration, extra pace, volume and weight on the motor. Some technique were propoed in literature. Thee technique are generally baed on the tate oberver or Luenberger oberver [], MRAS method [4]-[5], and Kalman filter [6]-[7]. In Speed enorle trategie, the motor peed i etimated and ued a a feedback ignal for cloedloop peed control. In any control trategy we cannot obtain a much atifactory repone under the moment of inertia or load torque variation which generally happen, adding to enorle drive uing thi kind of oberver we can etimate the load torque and it variation which ued to ameliorate the performance of the whole ytem. Luenberger oberver i a pecial type of oberver which provide optimal etimation and high performance. Simulation reult howing that the method improve the Direct Torque Control ytem performance.. MOTOR EQUATIONS IN α,β REFERENCE FRAME In the tationary α-β reference frame, the motor model can be expreed a [8]: u u α β = R.i = R.i α β dψ + dψ + α β (1 75

5-8 JATIT. All right reerved. ψ α coθ r inθr ψ d =. ( ψ β inθ r coθr ψ q ψ d = Ld.i d + ψ m ( ψ = L.i q q q ψ α Ld.i α coθr = + ψ m. ψ β Lq.i β inθr The mechanical equation i given by: (4 dω 1 ( = p.i β L + ψ ω d Lq iα. m T L Bm J (5 If L d = L q, for mooth pole machine. The electromagnetic torque i given by: Tem = p.i β. ψ m (6 Where (uα, uβ, (iα, iβ and (ψα, ψβ are the tator voltage, tator current, and tator flux linkage in α, β reference frame, L d, L q are the d,q axe inductance, R i the tator reitance. ψ m i the flux linkage of permanent magnet, p i the number of pole pair, T em i the electromagnetic torque, T L i the load torque, B m i the damping coefficient, ω r i the rotor peed and J i the moment of inertia. From (7 we can etimate the tator flux a follow: ( v R.i ψ = + (1 ψ α β ψ = ψ + ψ (11 ψ i the tator flux vector, and ψ i it initial value. For implicity, it i aumed that the tator voltage drop R.i i mall and neglected, the tator flux variation can be expreed a: ψ V. t. The change of torque can be controlled by keeping the amplitude of the tator flux linkage contant and by controlling the rotating peed of the tator flux linkage a fat a poible. It' hown in thi ection that both the amplitude and rotating peed of the tator flux linkage can be controlled by electing a proper tator voltage vector a hown in figure 1. The primary voltage vector V, i defined by the equation (8. DIRECT TORQUE CONTROL PRINCIPLES Flux and torque etimation and control In tationary reference frame, the machine tator voltage pace vector i repreented a follow: dψ V = R i + (7 π 4π j = + = j + V + uα j.uβ VaN VbN e VcN e (8 Where: R, i, ψ tator reitance, current and flux repectively. V an, V bn, V cn the three phae voltage inverter output are given a follow: U c VaN = Va = ( C1 C C U c (9 VbN = Vb = ( C C1 C U c VcN = Vc = ( C C C1 Uc i the inverter DC upply voltage, C1, C, C are the witching table output, and they are relevant to the witching trategy. Figure.1. Stator flux variation in tationary (α, β frame In DTC technique, the inverter witche are controlled uing the flux and torque error, and the poition of the tator flux within the ix-region control of the motor. The flux and torque error are evaluated a follow: Δ ψ = ψ ref ψ (1 Δ T = T ref T em (1 1 ψ β θ = tg (14 ψ α Where θ i the angle between tator flux vector and α axi, ψ α, ψ β are the tator flux component in (α, β reference frame. Switching table: In order to determine the inverter witching pattern uing flux and torque error, for the flux and torque control two hyterei controller are employed. The inverter i witched baed on thee 76

5-8 JATIT. All right reerved. error and poition of the tator flux within the ixregion control a can be een from Table 1, in uch a way that the inverter output voltage vector minimize the flux and torque error and determine the out-put flux rotation direction of thee controller. Table.1. DTC witching table n 1 4 5 6 Flux Couple K Cem =1 V V V 4 V 5 V 6 V 1 K ψ =1 K Cem = V 7 V V 7 V V 7 V K ψ = K Cem =-1 V 6 V 1 V V V 4 V 5 K Cem =1 V V 4 V 5 V 6 V 1 V K Cem = V V 7 V V 7 V V 7 K Cem =-1 V 5 V 6 V 1 V V V 4 4. CONTROL STRUCTURE Figure ( illutrate the BLAC drive cheme conidered in thi invetigation. The drive conit of a Luenberger oberver for peed etimation, flux and torque controller, pace flux poition, and bruhle AC machine. The rotor peed w r i compared with the reference peed w ref. The reulting error i proceed in the PI peed controller for each ampling interval. The output of thi i conidered to be the reference torque T ref. Figure.. A direct torque control cheme 5. SPEED ESTIMATION USING CONVENTIONAL APPROACH Since a tator flux-linkage i required in order to implement direct torque control, the etimation of rotor peed from a tator flux-linkage i common. After calculating equation (1, the angular poition of the tator flux-linkage vector can be obtained a in [6] and [9]: ψ β θ = arctan (15 ψ α Therefore, the rotational peed of the tator flux linkage i given a: ( k θ ( k 1 dθ θ ω = (16 T Where θ(k and θ(k 1 repreent the poition of the tator flux-linkage vector at ample time t k and t k 1 repectively and T = (t k t k 1. 6. SPEED ESTIMATION USING LUENBERGER OBSERVER The objective here i to ue a peed oberver in order to delete all mechanical enor. We etimate the rotation peed and load torque uing the meaured current and voltage, and the peed etimated by claical method. In the tator flux reference frame, the developed torque i: [1]-[11] T em =.p. ψ m. i β (17 Where i β i the quadrate component of the tator current vector, ψ i the tator flux magnitude, and p i the number of pole pair. From (5 and (17 dω 1 =.p.( ψ i T B. m L m J β ω (18 dtl = The econd order Luenberger oberver (hown in Figure i given by: [1] X & = A.X + BU. + L( Y Y (19 Y = C.X With: ω Xˆ = l1 ; T L = ( L l We have finally: d ω f 1 l ω J 1 J d = l T + T L L pψ m l (i 1 J +. ω β l claic (1 77

5-8 JATIT. All right reerved..5. Stator flux (Wb.15.1.5 Figure.. Principle Oberver diagram The matrix L determine how fat the imulation error approache zero and hould be choen carefully to achieve good tability and a nice repone of the oberver. 7. SIMULATION RESULTS To verify the technique propoed, digital imulation baed on MATLAB/SIMULINK have been implemented. The PMSM ued for the imulation ha the following parameter (preented in table [8]: Uc = 5[V], f = 5[Hz], R =.[Ω], Ld =.66[mH], Lq =.66[mH], J = 1.8e-5[Kg/m ], Bm = [Nm/rad/], ψ m =.776[V/rad/], p = 5. Conventional PI regulator coefficient: ki =.55; kp =1.441. For propoed method and conventional DTC the dynamic repone of peed, flux, and torque for the tarting proce without load Tl=, we applied a load torque equal to Tl=7Nm at.6, at t=1.7 we remove the load torque. We Invere the peed at t=1. Electromagnetic torque (N.m 1 1 8 6 4 - Oberved load torque (N.m.1...4.5.6.7.8.9 1 T( 1 1 8 6 4 - Figure.5. Stator flux repone. -4.1...4.5.6.7.8.9 1 t( Figure.6. Oberved load torque uing Luenberger oberver. Real load torque (N.m 1 1 8 6 4 - -4.1...4.5.6.7.8.9 1 T( Figure.7. Real load torque. -4-6.1...4.5.6.7.8.9 1 T( Figure.4. Electromagnetic torque repone. 78

5-8 JATIT. All right reerved. Rotation peed (rad/ 15 1 5-5 -1-15.1...4.5.6.7.8.9 1 T( Figure.8. Rotation peed oberved uing Luenberger oberver. Figure 8 repreent the robutne and dynamic repone of the peed oberved uing Luenberger oberver with the tep change of reference. The comparion between claical etimated peed and the peed oberved i hown in figure 9. Rotation peed (rad/ 15 1 5-5 -1-15.1...4.5.6.7.8.9 1 T( Figure.9. Comparion between claical etimated peed and oberved Speed uing Luenberger oberver (dahed line. For Luenberger oberver method good dynamic repone in peed without overhooting in tarting and inverion, we oberve an influence of load diturbance and at the inverion in torque repone a hown in figure 4. No influence oberved in flux repone when load diturbance application and at the inverion a een in figure 5. The oberved load toque hown in figure 6 i imilar to the real load torque applied figure 7 with a mall overhooting in tranient repone. Figure 9 how that Luenberger oberver method give very fat repone and good dynamic comparing with claical method. 8. CONCLUSION In thi paper, Senorle direct torque control cheme uing two type of peed etimator, one i baed on the angle of the tator flux linkage; the other i baed on Luenberger oberver for peed and load torque etimation are preented. The imulation reult how that both method can well etimate the peed of the bruhle AC machine; the firt method make the elected voltage vector incorrect, the motor unteady. The peed etimator that i baed on Luenberger oberver can make the motor tart teadily and have good dynamic. Compared to the enorle baed on the angle of tator flux linkage, the econd method decreae coniderably the ripple of both torque and flux. The cheme of peed etimator baed on Luenberger oberver i proved by the imulation that it i imple and eay to implement in enorle DTC ytem of uper high-peed of BLAC machine. REFERENCES [1] I. Takahahi, and T. Noguchi, A new quickrepone and high- efficiency control trategy of an induction machine. IEEE Tranaction on Indutry Application. (5, 8-87, 1986. [] M. Depenbrock. Direct elf-control (DSC of inverter-fed induction machine. IEEE Tranaction on Power Electronic. (4, 4-49, 1988. [] C. Youn-Ok; L. Kang-Yeon; S. Kang-Sung; K. Gi-Bum; J. Byung-Ho; C. Geum-Bae; B. Hyung-Lae; J. Sam-Yong. Performance analyi of the DTC uing a cloed loop tator flux oberver for induction motor in the low peed range. Electrical Machine and Sytem, ICEMS 1. Proceeding of the Fifth International Conference on Volume 1, 18- Aug. 1 Page(:89-9. [4] T. Zhuohui; L. Yongdong; J.Zhiyan. Speed enorle DTC and parameter etimation of induction motor baed on a full-order MRAS method. Power Electronic and Motion Control Conference. Proceeding IPEMC. Volume, 15-18 Aug. Page(:1 16. [5] L. Zhen, L. Xu. Senorle field orientation control of induction machine baed on a mutual MRAS cheme. Indutrial Electronic, IEEE Tranaction on Volume 45, Iue 5, Oct. 1998 Page(:84 81. 79

5-8 JATIT. All right reerved. [6] L. Yong, Z. Zi-Qiang, H. David. Simplified EKF Baed Senorle Direct Torque Control of Permanent Magnet Bruhle AC Drive. International Journal of Automation and Computing Volume 1, Number 1/ October 4. [7] K.L. Shi; T.F. Chan; Y.K. Wong; S.L. Ho. Speed etimation of an induction motor drive uing extended Kalman filter. Power Engineering Society Winter Meeting,. IEEE, Volume 1, Iue, Page(:4 48. [8] Xi Zhu, Z. Zi-Qiang., and H. David. Application of full-order and implified EKF to enorle PM bruhle AC machine. International journal of automation and computing, 179-186, 5. [9] B. Chunyuan R, Shuangyan M, Liangyu. Senorle DTC of Super High-peed PMSM. Automation and Logitic, 7 IEEE STATES OF THE ARTS In thi table we preent the tate of the art of enor le control, and no paper tudied enorle DTC International Conference on, Publication Date 18-1 Aug. 7, page(: 6-64 [1] L. Critian, T. Andrzej. M. Combining the Principle of Sliding Mode, Direct Torque Control, and Space-Vector Modulation in a High-Performance Senorle AC Drive. Indutry Application Conference,. 7th IAS Annual Meeting. Conference Record of the Volume, Iue 1, Page(: 7 79. [11] L. Critian, B. Ion, B. Frede. Direct Torque Control of Senorle Induction Motor Drive: A Sliding-Mode Approach. Indutry Application, IEEE Tranaction on Volume 4, Iue, March-April 4 Page(: 58 59. [1] R. Ghon (1. Contrôle vectoriel de la machine aynchrone à rotor bobiné à double alimentation. Thei for a doctoral degree, LEEI-INSEEIHT, Touloue. of BLAC machine uing Luenberger oberver which confirm the originality of thi idea. [1] R. Ghon (1. Contrôle vectoriel de la machine aynchrone à rotor bobiné à double alimentation. Thei for a doctoral degree, LEEI-INSEEIHT, Touloue. [] L. Yong, Z. Zi-Qiang, H. David. Simplified EKF Baed Senorle Direct Torque Control of Permanent Magnet Bruhle AC Drive. International Journal of Automation and Computing Volume 1, Number 1/ October 4. [] A.R. Haron, N.R.N. Idri,. ''Simulation of MRASbaed peed enorle etimation of induction motor drive uing MATLAB/SIMULINK''. Power and Energy Conference, 6 PECon '6 IEEE International 8-9 Nov. 6 Page(:411 415. [4] B. Chunyuan R, Shuangyan M, Liangyu. Senorle DTC of Super High-peed PMSM. Automation and Logitic, 7 IEEE International Conference on, Publication Date 18-1 Aug. 7, page(: 6-64. In thi thei, peed enorle control of indirect field oriented for doubly fed induction machine drive i tudied. Several kind of peed etimator are preented; one i baed on the angle of the rotor flux linkage. In the econd method the tator flux baed MRAS (SF- MRAS i ued for etimating the rotor peed. nd order Leunberger oberver i the third method tudied, in where the reference peed i etimated by SF-MRAS method. A implified extended Kalman filter (EKF baed enorle direct torque control technique for bruhle AC machine i preented. It performance i compared with that obtained with other enorle method for etimating the rotor peed and poition from a tator flux-linkage. In thi work, the performance of the rotor flux baed MRAS (RF-MRAS and back e.m.f baed MRAS (BEMF-MRAS for etimating the rotor peed wa tudied. The object tudied in thi invetigation i the uper high-peed permanent magnet ynchronou microturbine generator. Two kind of peed etimator are preented, one i baed on the angle of the tator flux linkage; the other i baed on the angle of the rotor flux linkage. 7