Estimation of Angular Velocity and Position of a Permanent Magnet Synchronous Motor Using Discrete-Time Extended Kalman Filter and Hybrid Extended Kalman Filter

Document Type : Original Article


1 Malek Ashtar University of Technology (MUT), Tehran, Iran

2 Sharif University of Technology, Tehran, Iran


In this paper we analyze the permanent magnet synchronous motor. The state equations governing the permanent magnet synchronous motor are nonlinear, so the angular position and velocity of its rotor are estimated using nonlinear filters. Since the current passing through the armature is measurable, this measurement is used to estimate system states (i.e. angular position and angular velocity). Discrete extended Kalman filter and hybrid extended Kalman filter algorithms are presented. The comparison between simulation results of rotor’s position and velocity estimation using discrete extended Kalman filter and hybrid Kalman filter shows that hybrid Kalman filter estimator has better performance.


Chretien, L. (2006). Position Sensorless Control Of Non-Salient Permanent Magnet Synchronous Machine (Doctoral Dissertation, University Of Akron).
Vaidyanathan, C., Kettle, P., Moynihan, F., & Lehman, B. (1999). Highly Flexible Motor Control Possible for the Appliance Market. In EPE.
Bolognani, S., Zigliotto, M., & Zordan, M. (2001). Extended-range PMSM sensorless speed drive based on stochastic filtering. IEEE transactions on power electronics, 16(1), 110–117. doi:10.1109/63.903995
Jones, L. A., & Lang, J. H. (1989). A state observer for the permanent-magnet synchronous motor. IEEE transactions on industrial electronics (1982), 36(3), 374–382. doi:10.1109/41.31500
Matsui, N. (2002). Sensorless operation of brushless DC motor drives. Proceedings of IECON ’93 - 19th Annual Conference of IEEE Industrial Electronics. Maui, HI, USA. doi:10.1109/iecon.1993.338989
Aydogmus, O., & Sünter, S. (2012). Implementation of EKF based sensorless drive system using vector controlled PMSM fed by a matrix converter. International Journal of Electrical Power & Energy Systems, 43(1), 736–743. doi:10.1016/j.ijepes.2012.06.062
Bolognani, S., Tubiana, L., & Zigliotto, M. (2003). Extended Kalman Filter Tuning In Sensorless PMSM drives. IEEE transactions on industry applications, 39(6), 1741–1747. doi:10.1109/tia.2003.818991
Huang, M. C., Moses, A. J., Anayi, F., & Yao, X. G. (2006). Linear Kalman filter (LKF) sensorless control for permanent magnet synchronous motor based on orthogonal output linear model. International Symposium on Power Electronics, Electrical Drives, Automation and Motion, 2006. SPEEDAM 2006. Taormina, Italy. doi:10.1109/speedam.2006.1649983
Jang, J.-S., Park, B.-G., Kim, T.-S., Lee, D. M., & Hyun, D.-S. (2008). Parallel reduced-order Extended Kalman Filter for PMSM sensorless drives. 2008 34th Annual Conference of IEEE Industrial Electronics. Orlando, FL. doi:10.1109/iecon.2008.4758146
Yim, D.-H., Park, B.-G., & Hyun, D.-S. (2010). Sensorless control strategy of IPMSM based on a parallel reduced-order EKF. IECON 2010 - 36th Annual Conference on IEEE Industrial Electronics Society. Glendale, AZ, USA. doi:10.1109/iecon.2010.5675070
Quang, N. K., Hieu, N. T., Hunter, G. P., & Ha, Q. P. (2012). FPGA-based sensorless PMSM drive using parallel reduced-order Extended Kalman Filter. 2012 International Conference on Control, Automation and Information Sciences (ICCAIS). Saigon, Vietnam. doi:10.1109/iccais.2012.6466579
Quang, N. K., Hieu, N. T., & Ha, Q. P. (2014). FPGA-based sensorless PMSM speed control using reduced-order extended Kalman filters. IEEE transactions on industrial electronics (1982), 61(12), 6574–6582. doi:10.1109/tie.2014.2320215.