Functional diagnosis and state estimation for nonlinear systems represented by Takagi-Sugeno multi-models
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DOI:
https://doi.org/10.5281/zenodo.14897898Keywords:
Nonlinear System, Takagi-Sugeno Multi-Model, Multi-Observer, Diagnosis, Identification, Levenberg-Marquardt Algorithm, State Estimation, Linear Matrix Inequalities (LMI)Abstract
In this paper, a method of state estimation and diagnostics is implemented for the non-linear
systems. These systems are modeled using a Takagi-Sugeno multi-model with measurable decision
variables in order to be able to use a classical technique of bank of observers. First, we present the
approximation of the nonlinear model by a multi-model, and then the development of a multi-observer
allows estimating the states of the system. This type of observer is then used in bank of observers which
generate residues its analysis makes it possible to reveal the occurrence of sensor defects. Finally, this
diagnostic strategy is applied to a hydraulic system to illustrate the effectiveness of the proposed method.
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References
R. Rajamani. Observers for Lipschitz nonlinear systems. IEEE Transactions on Automatic Control, 43 :397–401, March 1998.
S. Raghavan and J. K. Hedrick. Observer design for a class of nonlinear systems. International Journal of Control, 59(2) :515–528, 1994.
A.M. Pertew, H.J. Marquez, and Q. Zhao. LMI-based sensor fault diagnosis for nonlinear lipschitz systems. Automatica, 43 :1464–1469, 2007.
G. Balas, J. Bokor, and Z. Szabo. Failure detection for LPV systems - a geometric approach. In Proceedings of the American Control Conference, 2002.
T. Takagi and M. Sugeno. Fuzzy identification of systems and its applications to modeling and control. IEEE Transactions on Systems, Man, and Cybernetics, 15 :116–132, 1985.
K. Tanaka, T. Ikeda, and H.O. Wang. Fuzzy regulators and fuzzy observers: Relaxed stability conditions and lmi-based designs. IEEE Transactions on Fuzzy Systems, 6(2) :250–265, 1998.
K. Tanaka and H.O. Wang. Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach. Hardcover, 2001.
T.M. Guerra, A. Kruszewski, L. Vermeiren, and H. Tirmant. Conditions of output stabilization for nonlinear models in the Takagi-Sugeno’s form. Fuzzy Sets and Systems, 157(9) :1248–1259, May 2006.
A. Kruszewski. Lois de commande pour une classe de mod`eles non lin´eaires sous la forme Takagi-Sugeno : Mise sous forme LMI. PhD thesis, Universit´e de Valenciennes et du Hainaut-Cambresis, 2006, (In french).
M. Chadli. Analyse des systèmes non linéaires décrits par des multi-modèles. PhD thesis, Institut National Polytechnique de Lorraine, 2002.
R. Murray-Smith et T.A. Johansen. Multiple model approaches to modelling and control. Taylor & Francis, London, 1997.
R. J. Patton et J. Chen, Observer-based fault detection and isolation: Robustness and applications, Control Engineering Practice, Vol. 5 (5), pp. 671-682, 1997.
3R. J. Patton et J. Chen ,Neural networks in nonlinear dynamic systems fault diagnosis, Engineering simulation, Vol. 13 (6), pp. 905-924, 1996.
A. Akhenak, Conception d’observateurs non linéaires par approche multimodèle, Doctorat de L’Institut National Polytechnique de Lorraine, 2003
S. Boyd, L. El Ghaoui, E. Feron et V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, Philadelphia : SIAM, 1994.
