1. MSE Laboratory, Department of Electrical Engineering, University of Biskra, BP 145, Biskra 07000, Algeria 2. FCLab, University of Technology of Belfort-Montbéliard, CNRS 3539, Femto-ST UMR 6174, Belfort 90010, France 3. LBMS, University of Brest, Kergoat street, CS 93837, 29238 Brest Cedex 3, France 4. Ecole militaire polytechnique, UER ELT, Algiers 1611, Algeria
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.
. [J]. Frontiers in Energy, 2014, 8(4): 426-433.
Mohamed Yacine HAMMOUDI,Abdelkarim ALLAG,Mohamed BECHERIF,Mohamed BENBOUZID,Hamza ALLOUI. Observer design for induction motor: an approach based on the mean value theorem. Front. Energy, 2014, 8(4): 426-433.
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
https://doi.org/10.1109/TIE.2005.862311
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
https://doi.org/10.1109/TIE.2007.891786
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
https://doi.org/10.1109/TIE.2002.1005393
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, ?stanbul, Turkey2011, 544-549
Besan?on G. Nonlinear Observers and Applications. Springer, 2007
15
Besan?on G, Ticlea A. An immersion-based observer design for rank-observable nonlinear systems. IEEE Transactions on Automatic Control, 2007, 52(1): 83-88
https://doi.org/10.1109/TAC.2006.889867
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
https://doi.org/10.1016/j.ins.2010.08.046
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
https://doi.org/10.1109/TSMC.1985.6313399
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
https://doi.org/10.1007/s11633-013-0702-4
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
https://doi.org/10.1016/j.sysconle.2007.06.012
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