doi: 10.17586/2226-1494-2015-15-1-40-45


A. A. Bobtsov, A. A. Pyrkin, R. Ortega

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Article in Russian

For citation: Bobtsov A.A., Pyrkin A.A., Ortega R. Аdaptive flux observer for permanent magnet synchronous motors. Scientific and Technical Journal of Information Technologies, Mechanics and Optics, 2015, vol. 15, no. 1, pp. 40–45 (in Russian)


The paper deals with the observer design problem for a flux in permanent magnet synchronous motors. It is assumed that some electrical parameters such as resistance and inductance are known numbers. But the flux, the angle and the speed of the rotor are unmeasurable. The new robust approach to design an adaptive flux observer is proposed that guarantees globally boundedness of all signals and, moreover, exponential convergence to zero of observer error between the true flux value and an estimate obtained from the adaptive observer. The problem of an adaptive flux observer design has been solved with using the trigonometrical properties and linear filtering which ensures cancellation of unknown terms arisen after mathematical calculations. The key idea is the new parameterization of the dynamical model containing unknown parameters and depending on measurable current and voltage in the motor. By applying the Pythagorean trigonometric identity the linear equation has found that does not contain any functions depending on angle or angular velocity of the rotor. Using dynamical first-order filters the standard regression model is obtained that consists of unknown constant parameters and measurable functions of time. Then the gradient-like estimator is designed to reconstruct unknown parameters, and it guarantees boundedness of all signals in the system. The proposition is proved that if the regressor satisfies the persistent excitation condition, meaning the “frequency-rich” signal, then all errors in observer exponentially converges to zero. It is shown that observer error for the flux explicitly depends on estimator errors. Exponential convergence of parameter estimation errors to zero yields exponential convergence of the flux observer error to zero. The numerical example is considered. 

Keywords: synchronous motor, flux, adaptive observer, robustness. 

Acknowledgements. Работа выполнена при государственной финансовой поддержке ведущих университетов Российской Федерации (субсидия 074-U01, Проект 14.Z50.31.0031).


1. Acarnley P.P., Watson J.F. Review of position-sensorless operation of brushless permanent-magnet machines. IEEE Transactions on Industrial Electronics, 2006, vol. 53, no. 2, pp. 352–362. doi: 10.1109/TIE.2006.870868

2. Shah D., Espinosa-Perez G., Ortega R., Hilairet M. An asymptotically stable sensorless speed controller for non-salient permanent magnet synchronous motors. International Journal on Robust and Nonlinear Control, 2014, vol. 24, pp. 644–668. doi: 10.1002/rnc.2910

3. Dib W., Ortega R., Malaize J., Sensorless control of permanent-magnet synchronous motor in automotive applications: estimation of the angular position. IECON Proceedings (Industrial Electronics Conference), 2011, art. 6119400, pp. 728–733. doi: 10.1109/IECON.2011.6119400

4. Ortega R., Nam K., Praly L., Astolfi A., Hong J., Lee J. Sensorless control method and system for SPMSM using nonlinear observer. Korean Patent N 10-1091970, 2009.

5. Lee J., Hong J., Nam K., Ortega R., Praly L., Astolfi A. Sensorless control of surface-mount permanentmagnet synchronous motors based on a nonlinear observer. IEEE Transaction on Power Electronics, 2010, vol. 25, no. 2, pp. 290–297. doi: 10.1109/TPEL.2009.2025276

6. Nam K.H. AC Motor Control and Electric Vehicle Applications. CRC Press, 2010, 449 p.

7. Ortega R., Praly L., Astolfi A., Lee J., Nam K Estimation of rotor position and speed of permanent magnet synchronous motors with guaranteed stability. IEEE Transaction on Control Systems Technology, 2011, vol. 19, no. 3, pp. 601–614.

8. Pillai H., Ortega R., Hernandez M., Devos T., Malrait F. Robustness analysis of a position observer for surface-mount permanent magnet synchronous motors vis-a-vis rotor saliency. Proc. 9th IFAC Symposium on Nonlinear Control Systems, NOLCOS 2013. Toulouse, France, 2013, vol. 9, part 1, pp. 353–358. doi: 10.3182/20130904-3-FR-2041.00074

9. Malaize J., Praly L., Henwood N. Globally convergent nonlinear observer for the sensorless control of surface-mount permanent magnet synchronous machines. Proc. 51st IEEE Conference on Decision and Control, CDC 2012. Maui, USA, 2012, pp. 5900–5905. doi: 10.1109/CDC.2012.6426415

10. Tomei P., Verrelli C. Observer-based speed tracking control for sensorless permanent magnet synchronous motors with unknown torque. IEEE Transactions on Automatic Control, 2011, vol. 56, no. 6, pp. 1484–1488. doi: 10.1109/TAC.2011.2121330

11. Middleton R.H., Goodwin G.C. Adaptive computed torque control for rigid link manipulations. Systems and Control Letters, 1988, vol. 10, no. 1, pp. 9–16. doi: 10.1016/0167-6911(88)90033-3

12. Miroshnik I.V., Nikiforov V.O., Fradkov A.L. Nelineinoe i Adaptivnoe Upravlenie Slozhnymi Dinamicheskimi Sistemami [Nonlinear and Adaptive Control of Complex Dynamic Systems]. St. Petersburg, Nauka Publ., 2000, 549 p.

13. Ioannou P.A., Sun J. Robust Adaptive Control. Upper Saddle River, Prentice Hall, 1996, 825 p.

14. Khalil H. Nonlinear Systems. 3rd ed. Upper Saddle River, Prentice Hall, 2002, 750 p.

15. Ichikawa S., Tomita M., Doki S., Okuma S. Sensorless control of permanent magnet synchronous motors using online parameter identification based on system identification theory. IEEE Transactions on Industrial Electronics, 2006, vol. 53, no. 2, pp. 363–372. doi: 10.1109/TIE.2006.870875

16. Piippo A., Hinkkanen M., Luomi J. Adaptation of motor parameters in sensorless PMSM drives. IEEE Transactions on Industry Applications, 2009, vol. 45, no. 1, pp. 203–212. doi: 10.1109/TIA.2008.2009614 

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