40220140506003

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40220140506003

  1. 1. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME 30 STATE ESTIMATION OF PERMANENT MAGNET SYNCHRONOUS MOTORS USING EXTENDED KALMAN FILTER Siddharth Kaul1 , Raosaheb Pawar2 , Shailendra Sahu3 1, 2, 3 (Control and Automation, VIT University, Vellore Tamil Nadu India) ABSTRACT The estate estimation of Permanent Magnet Synchronous Motor (PMSM) is based on the study of sensorless control using Extended Kalman filter (EKF). The sensorless control system possesses accurate Dynamic estimation by reducing the size and increasing the efficiency of PMSM. Similar projects have attracted many researchers’ interests. This paper would present the application of Extended Kalman Filter (KF) in PMSM speed control system. The project worked on the areas of the mathematical model of PMSM and will estimate the angular speed (ω) using EKF algorithm The simulation results is expected to show that the control system will work smoothly in various speeds with load. The project would mainly focus on the study of Permanent magnet synchronous motor and extended Kalman filter to achieve the state estimation of PMSM. Keywords: Extended Kalman Filter (EKF), Modeling and Simulation, Permanent Magnet Synchronous Motors (PMSM), Sensorless Control. I. INTRODUCTION Permanent magnet synchronous motor (PMSM) drives are replacing dc and induction motors drives in a variety of industrial applications, such as industrial robots and machine tools. PMSM possesses many good performances such as simple structure, small size, high efficiency, high power factor and low moment of inertia compared with traditional electrical synchronous motors. Because of these advantages, PMSM are excellent for use in High-performance servo drives where a fast and accurate torque response is required. The main drawback of a PMSM is the position sensor. The use of such direct speed/position sensors implies additional electronics, extra wiring, extra space, frequent maintenance and careful mounting which detracts from the inherent robustness and reliability of the drive. For these reasons, the development of alternative indirect methods has become an important research topic. PMSM INTERNATIONAL JOURNAL OF ELECTRICAL ENGINEERING & TECHNOLOGY (IJEET) ISSN 0976 – 6545(Print) ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME: www.iaeme.com/ijeet.asp Journal Impact Factor (2014): 6.8310 (Calculated by GISI) www.jifactor.com IJEET © I A E M E
  2. 2. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME 31 drive research is concentrated on the elimination of the mechanical sensors at the motor shaft without weakening the dynamic performances of the drive. Many advantages of sensorless ac drives such as reduced hardware complexity, low cost, reduced size, cable elimination, reduce IR2 loss, increased noise immunity; increased reliability and decreased maintenance can be achieved. Sensorless motor drives are also preferred in hostile environments, and high speed applications. The main objective of this paper is to propose an effective Sensorless PMSM drive by using EKF. The proposed EKF is applied to the field oriented control of the PMSM and no mechanical parameters are involved. As a result, the EKF achieves the precise position and speed estimation of PMSM against other parameter deviations. II. MATHEMATICAL MODEL OF PERMANENT MAGNET SYNCHRONOUS MOTOR (PMSM) The mathematical model of PMSMS can be divided into three kinds of representation by the axis systems, including the three-phase stationary coordinate system (A-B-C shafting coordinate system), the stator phase stationary coordinate system (α-β coordinate system) and the rotor two- phase rotating coordinate system (d-q coordinate system). The mathematical model utilized for EKF estimation is the α-β coordinate system. Therefore, this coordinate system is represented as follow. The voltage equations of PMSM in the α and β -coordinate system are equations (1) and (2): ܷఈ ൌ ܴ௦݅ఈ ൅ ‫ܮ‬௦ ݀݅ఈ ݀‫ݐ‬ െ ߱௥ܰ௣ߣ௥‫ߠ݊݅ݏ‬௥ ሺ1ሻ ܷఉ ൌ ܴ௦݅ఉ ൅ ‫ܮ‬௦ ݀݅ఉ ݀‫ݐ‬ ൅ ߱௥ܰ௣ߣ௥ܿ‫ߠݏ݋‬௥ ሺ2ሻ From equations (1) and (2), we have ݀݅ఈ ݀‫ݐ‬ ൌ െ ܴ௦ ‫ܮ‬௦ ݅ఈ ൅ ߱௥ ܰ௣ߣ௥ ‫ܮ‬௦ ‫ߠ݊݅ݏ‬௥ ൅ ܷఈ ‫ܮ‬௦ ሺ3ሻ ݀݅ఉ ݀‫ݐ‬ ൌ െ ܴ௦ ‫ܮ‬௦ ݅ఉ ൅ ߱௥ ܰ௣ߣ௥ ‫ܮ‬௦ ܿ‫ߠݏ݋‬௥ ൅ ܷఉ ‫ܮ‬௦ ሺ4ሻ In digital systems, the sampling cycle is very short and each samling period can be considered as constant so we have next equation (5) and (6): ݀߱௥ ݀‫ݐ‬ ൌ 0 ሺ5ሻ ݀ߠ௥ ݀‫ݐ‬ ൌ ߱௥ ሺ6ሻ
  3. 3. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME 32 III. CONTROL SYSTEM STRUCTURE OF PERMANENT MAGNET SYNCHRONOUS MOTOR (PMSM) Figure 1: Vector Control System Structure of PMSM The operation of a brushless PM motor relies on the conversion of electrical energy to magnetic energy and then from magnetic energy to mechanical energy. It is possible to generate a magnetic rotating field by applying sinusoidal voltages to the 3 stator phases of a 3 phase motor. A resulting sinusoidal current flows in the coils and generates the rotating stator flux. The rotation of the rotor shaft is then created by attraction of the permanent rotor flux with the stator flux. Through a series of coordinate transforms, we can indirectly determine and control the time invariant values of torque and flux with classic PI control loops. The process begins by measuring the 3-phase motor currents. In practice, the instantaneous sum of the three current values is zero. Therefore, by measuring only two of the three currents, we can determine the third. Because of this fact, hardware cost can be reduced by the expense of the third current sensor. Vector control system structure of PMSM is shown in Fig. 1, including Proportional Integral (PI) modulator, Space Vector Pulse Width Module (SVPWM), EKF estimation module, Clark-Park transform module, three-phase inverter and PMSM module. PMSM adopts Field Oriented Control (FOC) controlling method with dual closed-loop control scheme of speed and current regulated by PI modulator. System estimates rotation angle and rotation speed from EKF in real time. Here, is the feedback variable of speed control loop and is the parameter of the Park transform and inverse transform to implement relevant calculation. IV. SIMULATION ANALYSIS AND EXPECTED OUTPUT The simulation is done by understanding the system parameters and understanding the algorithms of the Extended Kalman filter. MATLAB code was written inorder to get the expected output as shown in the figure below.
  4. 4. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME 33 In the Fig. 2 shown below, the red curve presents the actual measurements from speed sensor. As can be seen from the figure, there are system disturbances emerging in the process of system starting and state transition. Also we can observe that the transient to stable state is very quick. In Fig. 3, blue curve denotes the estimation of speed with EKF in sensorless condition. Comparing with the actual speed measurements and estimations from EKF, there is a slight lag in the process of system starting and speed transition. Figure 1: Actual Speed Measured with Sensor Figure 2: Estimation of Speed with Extended Kalman Filter
  5. 5. International Journal of Electrical Engineering and Technology (IJEET), ISSN 0976 – 6545(Print), ISSN 0976 – 6553(Online) Volume 5, Issue 6, June (2014), pp. 30-34 © IAEME 34 V. REFERENCES [1] Tao Xu, Zhengbin Zhang, “Simulation of Permanent Magnet Synchronous Motor Control System with Extended Kalman Filter”, Journal of Theoretical and Applied Information Technology Vol. 51 No. 1. [2] Wang Jian, “Overview Of The Modern AC Servo System Technology and the Market Development”, Servo Contol, Vol. 12, No. 9, June 2008, pp. 22-26. [3] Wang Chengyuan, Xia JiaKuan, Yang Junyou and et al, “Modern Moter Control Technology”, Beijing: Machinery Industry Press, August 2006, pp. 238-304 [4] S Bolognani, L Tubiana and M Zigliotto. “Extended Kalman Filter Tuning in Sensorless PMSM Drives”, IEEE Transactions on Industry Applications, 2003, Vol. 6, No. 39, November 2003, pp. 1741-1747. [5] Jiang Jun, Shen Yanxia and Ji Zhicheng, “Speed and Roter Positoin Estimation for PMSM Based on EKF”, Acta Simulata Systematic Sinica, Vol. 17, No. 7, July 2005, pp. 1704-1707 [6] Wang Chenchen and Li Yongdong, “A Speed Sensorless Vector Control Method of IM Using Extended Kalman Filter”, Journal of Tsinghua University (Science and Technology), Vol. 48, No. 10, October 2008, pp. 1545-1548. [7] Fu Mengyin, Deng Zhihong and Yan Liping, “Kalman Filter Principle and its Application in Navigation System”, Beijing: Science Press, April 2010, Second Edition, pp. 163-165. [8] An Quntao, Sun Li and Li Bo, “Variable Paramters EKF for Speed Estimation of PMSM”, Electric Machines and Control, Vol. 11, No. 6, June 2007, pp. 559-563. [9] T.S. Viswanath and Dr.Subhash S K, “A Graphical-Based Acceleration Stabilization in PMSM using Controller”, International Journal of Electrical Engineering & Technology (IJEET), Volume 2, Issue 2, 2011, pp. 21 - 31, ISSN Print: 0976-6545, ISSN Online: 0976-6553. [10] Vishal Rathore and Dr. Manisha Dubey, “Speed Control of Asynchronous Motor using Space Vector PWM Technique”, International Journal of Electrical Engineering & Technology (IJEET), Volume 3, Issue 3, 2012, pp. 222 - 233, ISSN Print: 0976-6545, ISSN Online: 0976-6553. [11] Pooja Agrawal and Ritesh Diwan, “Sensorless Control of Surface-Mount Permanent-Magnet Synchronous Motors”, International Journal of Electrical Engineering & Technology (IJEET), Volume 4, Issue 2, 2013, pp. 112 - 119, ISSN Print: 0976-6545, ISSN Online: 0976-6553.

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