Stability analysis of the extended Kalman filter for Permanent Magnet Synchronous Motor

  • Djamel Taibi MSE Laboratory, University of Biskra, B.P.145, 07000, Biskra, Algeria
  • Abdenacer Titaouine MSE Laboratory, University of Biskra, B.P.145, 07000, Biskra, Algeria
  • Fateh Benchabane MSE Laboratory, University of Biskra, B.P.145, 07000, Biskra, Algeria
  • Ouafae Bennis PRISME Institute, University of Orléans, 21 rue Loigny La Bataille, 28000 Chartres, France


This paper presents a sensorless direct field oriented control fed interior permanent magnet synchronous motor (IPMSM) by using a known mathematical tool. The Kalman filter is an observer for linear and non-linear systems and is based on the stochastic intromission, in others words, noise. It is a question of studying the state and measurement noise covariance matrices Q and R on the stability of the Extended Kalman Filter. This last is used for the d, q stator current, mechanical speed, rotor position, stator resistance and the load torque estimation. The simulation tests carried out on Matlab Simulink showed that the matrix R improves much more quality of the estimated states while the matrix Q allows the improvement of the estimation process convergence.

Author Biography

Abdenacer Titaouine, MSE Laboratory, University of Biskra, B.P.145, 07000, Biskra, Algeria
Corresponding author:
Prof. Abdenacer Titaouine
MSE Laboratory, University of Biskra, B.P.145, 07000, Biskra, Algeria
E-mail address:



Achour, A.Y., B. Mendil (2009) Passivity-based current controller design for a permanent-magnet synchronous motor. ISA Transactions 48 (3) 336-346.
Aissa, A., B. Mokhtari (2012) Extended Kalman filter for speed sensorless direct torque control of a PMSM drive based stator resistance estimator, Journal of Electrical and Control Engineering 2(6): 33-39.
Alonge, F. (2014) Sensorless control of induction-motor drive based on robust kalman filter and adaptive speed estimation. IEEE Transactions on Industrial Electronics 61(3) 1444-1453.
Barut, M., O.S. Bogosyan, M. Gokasan (2003) An Extended Kalman Filter Based Sensorless Direct Vector Control of Induction Motors. Industrial Electronics Society, IECON '03, the 29th Annual Conference of the IEEE, 2003, 318-322.
Barut, M., S. Bogosyan (2005) Speed sensorless direct torque control of IMs with rotor resistance estimation. Energy Conversion and Management 46(3): 335-349.
Belkacem, S., B. Zegueb (2010) Robust non-linear direct torque and flux control of adjustable speed sensorless pmsm drive based on svm using a pi predictive controller. Journal of Engineering Science and Technology Review 3 (1): 168-175.
Benchabane, F., A. Titaouine, O. Bennis (2011) Systematic fuzzy sliding mode approach combined with extended Kalman filter for permanent magnet synchronous motor control, Mediterranean Journal of Measurement and Control 7(1): 183-189.
Benchabane, F., A. Titaouine (2011) Influence des matrices de bruits d’état et de mesure sur la stabilité du filtre de Kalman étendu. Application au MSAP, Revue Sciences, Technologies et Développement ANDRU 7: 99-109.
Benchabane, F., A. Titaouine (2012a) Sensorless fuzzy sliding mode control for permanent magnet synchronous motor fed by AC/DC/AC converter. International Journal of Systems Assurance Engineering and Management 3(3) 221–229.
Benchabane, F., A. Titaouine (2012b) Sensorless direct torque control for salient-pole PMSM based on extended Kalman filter fed by AC/DC/AC converter. Frontiers In Eneergy 6(3) 247–254.
Bolognani, S., L. Tubiana (2003) Extended Kalman filter tuning in sensorless PMSM drives, IEEE Transactions on Industry Applications 39: 1741-1747.
Chikh, K., A. Saad (2011) A novel drive implementation for pmsm by using direct torque control with space vector modulation. Canadian Journal on Electrical and Electronics Engineering 2(8) 400-408.
Deng, Z.L. (2005) Information fusion in Kalman filter weighted by diagonal matrices. Control Theory and Applications 22(6): 870-874.
Dhaouadi, R., N. Mohan (1991) Design and implementation of an extended Kalman filter for the state estimation of a permanent magnet synchronous motor. IEEE Transactions on Power Electronics 6: 491–497.
Guohan, L., W. Qin (2012) Estimation of rotor resistance of induction motor based on extended Kalman filter. Journal of Advances in CSIE, Vol. 2: 193–198.
He, Y.Y., W. Jiang (2007) A new variable structure controller for direct torque controlled interior permanent magnet synchronous motor drive, Proceedings of the IEEE International Conference on Automation and Logistics, 2007, 2349-2354.
Janiszewski, D. (2000) Extended Kalman filter based speed sensorless pmsm control with load reconstruction, Kalman filter, Publisher InTech.
Khan, M.R. (2009) Experimental investigation of five-phase induction motor drive using extended kalman-filter. Asian Power Electronics Journal 3(1) 1-7.
Samosir, A.S., A.H.M. Yatim (2010) Dynamic evolution control for synchronous buck DC–DC converter. Simulation Modelling Practice and Theory 18(5): 663–676.
Sturtzer, G., E. Smigiel (2000) Modélisation et commande des moteurs triphasés, commande vectorielle des moteurs synchrones, commande numérique par contrôleurs DSP, Edition Ellipses.
Yahia, K., S.E. Zouzou (2006) Indirect vector control of induction motor with on line rotor resistance identification. Asian Journal of Information Technology 5: 1410-1415.
Yahia K., S.E. Zouzou (2009) Comparative study of an adaptive Luenberger observer and extended Kalman filter for a sensorless direct vector control of induction motor. Acta Electrotehnica 50(2): 99-107.
How to Cite
TAIBI, Djamel et al. Stability analysis of the extended Kalman filter for Permanent Magnet Synchronous Motor. Journal of Applied Engineering Science & Technology, [S.l.], v. 1, n. 2, p. 51-60, mar. 2015. ISSN 2352-9873. Available at: <>. Date accessed: 24 feb. 2024.
Section A: Electrical, Electronics and Automatic Engineering


Permanent magnet synchronous machine, Direct filed oriented control, Extended Kalman filter, Estimation

Most read articles by the same author(s)

Obs.: This plugin requires at least one statistics/report plugin to be enabled. If your statistics plugins provide more than one metric then please also select a main metric on the admin's site settings page and/or on the journal manager's settings pages.