Observer design for induction motor: an approach based on the mean value theorem

Abstract

In this paper, observer design for an induction motor has been investigated. The peculiarity of this paper is the synthesis of a mono-Luenberger observer for highly coupled system. To transform the nonlinear error dynamics for the induction motor into the linear parametric varying (LPV) system, the differential mean value theorem combined with the sector nonlinearity transformation has been used. Stability conditions based on the Lyapunov function lead to solvability of a set of linear matrix inequalities. The proposed observer guarantees the global exponential convergence to zero of the estimation error. Finally, the simulation results are given to show the performance of the observer design.

Keywords

observer design / differential mean value theorem (DMVT) / sector nonlinearity transformation / linear matrix inequalities (LMI) / induction motor

References

[1] Gomez-Gutierrez D, Ramirez-Prado G, Ramirez Trevino A, Ruiz-Leon J. Joint state-mode observer design for switched linear systems. In: Proceedings of IEEE International Conference on Emerging Technologies and Factory Automation. Hamburg, Germany, 2008, 1408-1415

[2] Sadaka H, Shafai B, Sipahi R. Robust PI observer design for linear time-delay systems. In: Proceedings of IEEE International Conference on Control Applications, (CCA) & Intelligent Control. Saint Petersburg, Russia, 2009, 1209-1213

[3] Guerra R M, Luviano-Juarez A. Rincon-Pasaye J J. On nonlinear observers: A differential algebraic approach. In: Proceedings of American Control Conference. New York, USA, 2007, 1682-1686

[4] .Babaali M, Egerstedt M, Kamen W E. An observer for linear systems with randomly-switching measurement equations. In: Proceedings of American Control Conference. Arlington, USA, 2003, 1879-1884

[5] Rafaralahy H, Zasadzinski M, Boutayeb M, Darouach M. State observer design for descriptor bilinear systems. In: Proceedings of UKACC International Conference on Control. Institution of Engineering and Technology, UK, 1996, 843-848

[6] Ball A A. Khalil H K. High-gain observers in the presence of measurement noise: A nonlinear gain approach. In: Proceedings of IEEE Decision and Control Conference, Cancun, Mexico, 2008, 2288-2293

[7] Sayem H, Braiek N B, Hammouri H. Trajectory tracking of bilinear systems using high gain observer. In: Proceedings of International Conference on Electrical Engineering and Software Applications, Hammamet, Tunisia, 2013, 1-6

[8] Hasegawa M. Robust-adaptive-observer design based on γ-positive real problem for sensorless induction-motor drives. IEEE Transactions on Industrial Electronics, 2006, 53(4): 76-85

[9] Proca A B, Keyhani A. Sliding mode flux observer with online rotor parameter estimation for induction motors. IEEE Transactions on Industrial Electronics, 2007, 54(2): 716-723

[10] Shi H, Feng Y. A hybrid sliding mode flux observer for induction motor drive. In: Proceedings of the 30th Chinese Control Conference. Yantai, China, 2011, 762-767

[11] Joen S H, Oh K K, Choi J Y,. Flux observer with online tuning of stator and rotor resistances for induction motor. IEEE Transactions on Industrial Electronics, 2002, 49(3): 653-664

[12] Savoia A, Mengoni M, Zarri L, Casadei D. A nonlinear luenberger observer for sensorless vector control of induction motors. In: Proceedings of 2011 International Aegean Conference on Electrical Machines and Power Electronics, İstanbul, Turkey2011, 544-549

[13] Park C W, Lee S. Nonlinear observer based control of induction motors. Electrical Engineering, 2007, 92(2): 107-113

[14] Besançon G. Nonlinear Observers and Applications. Springer, 2007

[15] Besançon G, Ticlea A. An immersion-based observer design for rank-observable nonlinear systems. IEEE Transactions on Automatic Control, 2007, 52(1): 83-88

[16] Wang Y, Chai T, Zhang Y. State observer-based adaptive fuzzy output-feedback control for a class of uncertain nonlinear systems. Information Sciences, 2010, 180(24): 5029-5040

[17] Takagi T, Sugeno M. Fuzzy identification of system and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 1985, 15(1): 116-132

[18] Tanaka K, Wang H O. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. New York: Wiley-Interscience, 2001

[19] Allouche M, Chaabane M, Souissi M, Mehdi D, Tadeo F. State feedback tracking control for indirect field-oriented induction motor using fuzzy approach. International Journal of Automation and Computing, 2013, 10(2): 99-110

[20] Pourgholi M, Majd V J. A nonlinear adaptive resilient observer design for a class of Lipschitz systems using LMI. Circuits, Systems, and Signal Processing, 2011, 30(6): 1401-1415

[21] Zemouche A, Boutayeb M, Bara G I. Observer design for nonlinear systems: an approach based on the differential mean value theorem. In: Proceedings of 44th IEEE Conference on Decision and Control, and the European Control Conference. Seville, Spain, 2005, 12-15

[22] Zemouche A, Boutayeb M, Bara G I. Observer for a class of Lipschitz systems with extension to H∞ performance analysis. Systems & Control Letters, 2008, 57(1): 18-27

[23] Shen Z, Zhao J, Xu J, Gu X S. Nonlinear unknown input observer design by LMI for lipschitz nonlinear systems. In: Proceedings of the 8th World Congress on Intelligent Control and Automation, Jinan, China, 2010, 3450-3454

[24] Ichalal D, Arioui H, Mammar S. Observer design for two-wheeled vehicle: A Takagi-Sugeno approach with unmeasurable premise variables. In: Proceedings of 19th Mediterranean Conference on Control and automation. Corfu, Greece, 2011, 934-939

[25] Ichalal D, Marx B, Maquin D, Ragot J. On observer design for nonlinear Takagi-Sugeno systems with unmeasurable premise variable. In: Proceedings of International Symposium on Advanced Control of Industrial Processes. Hangzhou, China, 2011, 353-358

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