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Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach

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Abstract

This paper deals with the design of a robust fault detection observer for a Takagi-Sugeno (T-S) fuzzy model affected by sensor and actuator faults and unknown bounded disturbances simultaneously. An observer based on the technique of descriptor systems is studied. Indeed, by considering faults as auxiliary state variables, both states and faults are estimated simultaneously. In order to guarantee the best robustness to disturbances and sensitivity to faults, the developed observer combine the H /H performances. Then, based on Lyapunov method, asymptotic stability conditions are given to design the observer parameters. In order to get convenient and reliable faults estimator in computations, an iterative linear matrix inequality (LMI) algorithm is developed. This algorithm, solved easily using existing numerical tools, allows to minimize influences of disturbances and maximize the ones of faults. Finally, a numerical example is proposed to illustrate the effectiveness of the result.

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Correspondence to Mohammed Chadli.

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Recommended by Editorial Board member Bin Jiang under the direction of Editor Young Il Lee.

Maha Bouattour was born in Sfax, Tunisia, in 1981. She received her Master degrees in Electrical Engineering from the National Engineering School of Sfax, Tunisia, in 2005, and her Ph.D. degree in Electrical Engineering from the University of Picardie Jules Verne, France, and the National Engineering School of Sfax, in 2010. She is an assistant with the Preparatory Engineering Institute of Sfax, since 2009. Her current research interests include fuzzy control and fault tolerant control.

Mohammed Chadli was born in Oued-Zem, Morocco. He received his Master degree (DEA) from INSA of Lyon, France in 1999 and his Ph.D. thesis from CRAN-INPL of Nancy-France in 2002. From 1999 to 2004, he was an associate researcher in CRAN-INPL. Since 2004, he has been an Associate Professor at the University of Picardie Jules Verne and a researcher in the ‘Modélisation, Information et Systèmes’ Laboratory (MIS) in Amiens, France. His research interests include, on the theoretical side, analysis and control of singular (switched) systems, analysis and control of fuzzy/multiple model approach, robust control, model-based diagnosis, fault detection and isolation (FDI), fault tolerant control (FTC), analysis and control via LMI optimization techniques and Lyapunov methods. On the application side he is mainly interested in automotive control.

Mohamed Chaabane is working as a professor in automatic control at National School of Engineers of Sfax (ENIS), Tunisia. He received his Doctorate degree in Electrical Engineering from the University of Nancy, France in 1991. He was an Associate Professor at the University of Nancy and was a researcher at Center of Automatic Control of Nancy (CRAN) from 1988–1992. Since 1997, he is holding a research position at Automatic Control Unit, ENIS. The main research interests are in the filed of robust and optimal control, delay systems, descriptor systems. Currently, he is an associate editor of journal IJ-STA International Journal on Sciences and Techniques of Automatic control & computer engineering (www.statn.com).

Ahmed El Hajjaji received his Ph.D. and “Habilitation à diriger les recherches” degrees in automatic control from the University of Picardie Jules Verne, France, in 1993 and 2000, respectively. He was an Associate Professor in the same university from 1994 to 2003. He is currently a Full Professor and Director of the Electrical Engineering department in University of Picardie Jules Verne. Since 2001, he has also been also the head of the research team of control and vehicle of Modeling, Information and Systems (MIS) laboratory. His current research interests include fuzzy control, vehicle dynamics, Fault Tolerant Control (FTC), neural networks, maglev systems, and renewable energy systems.

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Bouattour, M., Chadli, M., Chaabane, M. et al. Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach. Int. J. Control Autom. Syst. 9, 973–979 (2011). https://doi.org/10.1007/s12555-011-0519-2

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