978-1-4244-2800-7/09/$25.00 ©2009 IEEE ICIEA 2009
PMSM Speed Sensorless Direct Torque Control
Based on EKF
Yingpei Liu, Ji...
white noise with covariance of R and Q , respectively and
independent from each other.
Both the optimal state and its cova...
Figure 1. Schematic diagram of speed sensorless DTC control for SPMSM
based on EKF
TABLE I. SWITCH VOLTAGE VECTOR SELECTIO...
(b) Traditional DTC method
Figure 4. Rotor speed wave
(a) DTC-based on EKF method
(b) Traditional DTC method
Figure 5. A p...
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17.pmsm speed sensor less direct torque control based on ekf

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17.pmsm speed sensor less direct torque control based on ekf

  1. 1. 978-1-4244-2800-7/09/$25.00 ©2009 IEEE ICIEA 2009 PMSM Speed Sensorless Direct Torque Control Based on EKF Yingpei Liu, Jianru Wan, Hong Shen, Guangye Li, Chenhu Yuan School of Electric Engineering and Automation Tianjin University Tianjin, 300072, China Email:liuyingpei_123@126.com Abstract— System with mechanical speed sensor has lower reliability and higher cost. Traditional direct torque control method has disadvantages of big ripples on current and flux linkage and torque. To solve these problems, the Extended Kalman Filter is established to estimate both stator flux linkage and rotor speed. Therefore, speed sensorless direct torque control for surface permanent magnet synchronous motor is realized. Simulation results have shown that the advantage of direct torque control method such as rapid torque response is maintained, at the same time, the system based on EKF is robust to motor parameters and load disturbance. The dynamic and static performances are dramatically improved. Index Terms—Direct torque control, Permanent magnet synchronous motor (PMSM), Extended kalman filter (EKF), Stator flux linkage observation, Speed sensorless control I. INTRODUCTION Direct torque controlled permanent magnet synchronous motor (PMSM) has rapid response and good static and dynamic performance; so many scholars have conducted research to this field and achieved certain results [1-4]. In the direct torque control method, the observation accuracy of stator flux linkage directly determines the performance of the entire system. System with mechanic speed sensor has lower reliability and higher system cost. So how to get stator flux linkage and speed information has become the research hotspot. In the traditional DTC control, flux linkage is observed through pure voltage integration. The model is very simple, but in practical applications, the disadvantages impact of integrator such as the sensitivity to initial value and DC offset has influenced stator flux linkage observation accuracy. In order to solve these problems, in literature [5], an improved integration is applied to observe stator flux linkage in induction motor, which could only get accurate phase information. In literature [6], low-pass filter is applied instead of integrator to observe flux linkage, which results in flux linkage phase ahead and its amplitude smaller. Amplitude and phase compensation is researched in literature [7], which can not fundamentally resolve the shortcomings of pure integrator. Aiming at speed sensorless DTC controlled surface permanent magnet synchronous motor (SPMSM), Extended This paper is supported by National Science Foundation of China (60874077) and Specialized Research Fund for the Doctoral Program of Higher Education of China (20060056054). Kalman filter (EKF) observer is researched to estimate both stator flux linkage and rotor speed in the paper. The disadvantage of pure integrator has been overcome, and the advantages of DTC method such as rapid torque response and strong robustness are still maintained. In the meantime, the problems resulting from mechanical speed sensor has been resolved. II. MODEL OF SPMSM βα − Coordinate is chosen in order to design EKF observer. The voltage equation of SPMSM is as following. sin cos s s r r r s s r r r di u R i L dt di u R i L dt α α α β β β ωψ θ ωψ θ ⎧ = + −⎪⎪ ⎨ ⎪ = + + ⎪⎩ (1) Equation (2) is gotten from (1). s s d u R i dt d u R i dt α α α β β β ψ ψ ⎧ = +⎪⎪ ⎨ ⎪ = + ⎪⎩ (2) Where uα and uβ are stator voltage ,α β coordinate components, iα 、 iβ are stator current components, αψ and βψ are stator flux linkage components, sR is stator resistance, sL is stator inductance, rω is rotor speed, rθ is rotor position angle. III. DESIGN OF EKF OBSERVOR The state and output equations of discrete linear system with random interference is as following [8]. 1k k k k k k k k k k x A x B u w y C x v + = + +⎧ ⎨ = +⎩ (3) Where system noise ( )kw takes into account the system disturbances and model errors, while ( )kv represents the measurement noise, which takes into account all measure noise and measure errors. Both ( )kv and ( )kw are zero-mean 3581
  2. 2. white noise with covariance of R and Q , respectively and independent from each other. Both the optimal state and its covariance are computed in a two-step loop. The first one (prediction step) performs a prediction of both quantities based on the previous estimates. The equations are as the following: / 1 1/ 1 / 1 1k k kk k k k kx A x B U ∧ ∧ − −− − −= + (4) / 1 / 1 1 / 1 T k k k k k k kP A P A Q ∧ − − − −= + (5) The second step (innovation step) corrects the predicted state and estimation and its covariance matrix through a feedback correction scheme that makes use of the actual measured quantities, which are realized by the following equations. 1 / 1 / 1 T T k k k kk k k kK P C C P C R −∧ ∧ − − ⎛ ⎞= +⎜ ⎟ ⎝ ⎠ (6) / / 1 / 1k k k k k kk k kx x K y C x ∧ ∧ ∧ − − ⎛ ⎞ = + −⎜ ⎟ ⎝ ⎠ (7) ( ) / 1/ k kk k k kP I K C P ∧ −= − (8) The flux linkage equation of SPMSM is as the following. s s cos sin f r f r i i α α β β ψ ψ θ ψ ψ θ +⎧⎪ ⎨ +⎪⎩ =L =L (9) Combined with (2), (10) can be obtained. cos sin s s f r s s s s f r s s d R R u dt L L d R R u dt L L α α α β β β ψ ψ ψ θ ψ ψ ψ θ ⎧ = − + +⎪ ⎪ ⎨ ⎪ = − + + ⎪⎩ (10) Compared to the dynamic process of SPMSM, sampling interval time is so small that speed can be considered unchanged, which is 0= dt dω . Also, we have the equation 0= dt d rθ . ( ) [ ]T rrtx θωψψ βα= is selected as state variable, [ ]T uuu βα= and [ ]T iiy βα= are chosen as input and output variable respectively which can easily obtained from the measurements. Thus the dynamic state model for SPMSM was as following. ( ) ( )⎪⎩ ⎪ ⎨ ⎧ = += • xgy Buxfx (11) Where ( ) cos sin 0 s s f r s s s s f r s s r R R L L R R f x L L α β ψ ψ θ ψ ψ θ ω ⎡ ⎤ − +⎢ ⎥ ⎢ ⎥ ⎢ ⎥ − += ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ , ( ) ( ) ( ) 1 cos 1 sin f r s f r s L g x L α β ψ ψ θ ψ ψ θ ⎡ ⎤ −⎢ ⎥ ⎢ ⎥= ⎢ ⎥ −⎢ ⎥ ⎣ ⎦ , 1 0 0 1 0 0 0 0 B ⎡ ⎤ ⎢ ⎥ ⎢ ⎥= ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ Equation (12) is obtained by linearization and discretization of (11). ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) 1x k A k x k H k u k w k y k C k x k v k + = + +⎧⎪ ⎨ = +⎪⎩ (12) Where 0 0 sin 0 0 cos 0 0 0 0 0 0 1 0 s s f r s s s s f r s s R R L L R R A L L ψ θ ψ θ ⎡ ⎤ − −⎢ ⎥ ⎢ ⎥ ⎢ ⎥ −= ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ , ( ) 0 0 0 0 0 0 T T H k BT ⎡ ⎤ ⎢ ⎥ ⎢ ⎥≈ = ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ 1 0 0 sin 1 0 0 cos f r s s f r s s L L C L L ψ θ ψ θ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥= ⎢ ⎥ −⎢ ⎥ ⎢ ⎥⎣ ⎦ System noise ( )kw represents the error caused by parameters changes and linearization and discretization, while ( )kv represents errors caused by input and output measurements. Given system initial state, state estimates can be got through recursive operation according to (4) to (8). IV. SPEED SENSORLESS DTC CONTROL Schematic diagram of speed sensorless DTC control for SPMSM based on EKF is shown as Figure 1. Switch voltage vector selection is shown as TABLE Ⅰ. 3582
  3. 3. Figure 1. Schematic diagram of speed sensorless DTC control for SPMSM based on EKF TABLE I. SWITCH VOLTAGE VECTOR SELECTION TABLE △ ψ △ T ① ② ③ ④ ⑤ ⑥ 1 1 Us2 Us3 Us4 Us5 Us6 Us1 0 Us7 Us8 Us7 Us8 Us7 Us8 -1 Us6 Us1 Us2 Us3 Us4 Us5 -1 1 Us3 Us4 Us5 Us6 Us1 Us2 0 Us8 Us7 Us8 Us7 Us8 Us7 -1 Us5 Us6 Us1 Us2 Us3 Us4 V.SIMULATION RESULT Simulation model is established using MATLAB/SIMULINK tools. EKF algorithm is achieved by S- function. Parameters of SPMSM are shown is TABLE Ⅱ. TABLE II. MOTOR PARAMETERS Motor Parameters value Ω/sR 1.26 nP 4 HLs / 6.5 Wbr /ψ 0.175 )./( 2 mkgJ 0.0008 Parameters of EKF are as following to ensure filter not divergent. ( ) ( ) 0.3 0 0 0 0 0.3 0 0 0.2 0 ; ; 0 0 3 0 0 0.2 0 0 0 0.3 0.1 0 0 0 0 0 0.1 0 0 0 0 ; 0 0 0 200 0 0 0 0 0 10 0 Q R P x ⎡ ⎤ ⎢ ⎥ ⎡ ⎤⎢ ⎥= = ⎢ ⎥⎢ ⎥ ⎣ ⎦ ⎢ ⎥ ⎣ ⎦ ⎡ ⎤ ⎡ ⎤ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥= = ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎢ ⎥ ⎣ ⎦ ⎣ ⎦ (1) Given rotor speed is 500rpm, at 0.2 seconds, load torque decreases from 30N.m to 0N.m. Corresponding stator flux linkage and electromagnetic torque waves using traditional DTC method and DTC-based on EKF method are respectively shown in Figure 2-3. Flux linkage under traditional DTC is not smooth and has sharp fluctuation especially in the start-up, while, under DTC-based on EKF flux linkage has no obvious ripples due to more accurate EKF observer. Torque dynamic response time is basically the same, which indicates EKF control method do not affect the DTC dynamic performance. The torque ripples using DTC-based on EKF method is significantly reduced and steady performance has been greatly improved. (a) DTC-based on EKF method (b) Traditional DTC method Figure 2. Stator flux linkage wave (a) DTC-based on EKF method (b) Traditional DTC method Figure 3. Electromagnet torque wave (2) Given rotor speed is 100rpm, at 0.1 seconds, load torque increases from 0N.m to 6N.m. Corresponding rotor speed and current waves using traditional DTC method and DTC-based on EKF method are respectively shown in Figure 4-5. The system robustness to the load disturbance using DTC-based on EKF method has been greatly enhanced. When disturbance occurred, speed and current is regulated fast to avoid large overstrike and oscillation. Their waves are more smoothing, especially in the start-up. (a) DTC-based on EKF method 3583
  4. 4. (b) Traditional DTC method Figure 4. Rotor speed wave (a) DTC-based on EKF method (b) Traditional DTC method Figure 5. A phase current wave (3) At 0.5 seconds, given rotor speed increases from 1000rpm to 1600rpm, and Load torque is 5N.m. Corresponding rotor speed and rotor angle waves are shown in Figure 6-7. The estimated speed and rotor angle lag behind real speed and angle respectively when motor starts and given speed mutates, but it also satisfies performance demand for motor control, while, at steady operation the estimated speed follows up real speed only with small error, which reflects EKF algorithm has good filtering effect. Figure 6. Estimated speed and real speed waves (a) Real rotor angle wave (b) Estimated rotor angle wave Figure 7. Rotor angle wave VI. CONCLUSION Speed sensorless DTC control based on EKF for SPMSM is proposed. For a relatively accurate SPMSM model, flux linkage and rotor speed and rotor position can be estimated more precisely by EKF algorithm. Ripples on torque and stator flux are reduced. The motor start problems are solved as EKF do not need accurate initial rotor position information to achieve observer stability convergence. DTC control for PMSM based on EKF has just begun. Many places are imperfect and need for further study. REFERENCES [1] L.Zhong, M.F.Rahman, W.Y. Hu , K.W.Lim, “Analysis of direct torque control in permanent magnet synchronous motor drives,” IEEE Trans. on Power Electronics, 1997, 13(5), pp:528-536. [2] Jun Hu, Bin Wu. “New integration algorithms for estimating motor flux over a wide speed range,” IEEE Trans. on Power Electronics, 1998, 13(5),pp:969-977. [3] Cenwei Shi, Jianqi Qiu, Mengjia Jin, “Study on the performance of different direct torque control methods for permanent magnet synchronous machines,” Proceeding of the Csee, 2005, 25(16),pp:141- 146. [4] Limei Wang, Yanping Gao. “Direct torque control for permanent magnet synchronous motor based on space voltage vector pulse width modulation,” Journal of Shenyang University of Technology, 2007,29(6), pp:613-617. [5] Zhiwu Huang, Yi Li, Xiaohong Nian, “Simulation of direct torque control based on modified integrator,” Computer Simulation, 2007,24(02),pp:149-152. [6] Liyong Yang, Zhengxi Li, Rentao Zhao, “Stator flux estimator based programmable cascaded digital low-pass filter,” Electric Drive,2007,37(10),pp:25-28. [7] NRN.Klris, AHM. Yatim, “An improved stator flux estimation in steady-state operation for direct torque control of induction machine,” IEEE Trans on Industry Applications, 2002, 38(1),pp: 110-116. [8] Yingpei Liu. Research on PMSM speed sensorless control for elevator drive [D]. Tianjin University: 2007.6 3584

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