Fault tolerant control for Takagi-Sugeno systems with unmeasurable premise variables by trajectory tracking

This paper presents a new method for fault tolerant control of nonlinear systems described by Takagi-Sugeno fuzzy systems with unmeasurable premise variables. The idea is to use a reference model and design a new control law to minimize the state deviation between a healthy reference model and the eventually faulty actual model. This scheme requires the knowledge of the system states and of the occurring faults. These signals are estimated from a Proportional-Integral Observer (PIO) or Proportional-Multi-Integral Observer (PMIO). The fault tolerant control law is designed by using the Lyapunov method to obtain conditions which are given in Linear Matrix Inequality formulation (LMI). Finally, an example is included.

[1]  Didier Georges,et al.  Robust fault-tolerant control for descriptor systems , 2004, IEEE Transactions on Automatic Control.

[2]  B. Marx,et al.  Design of observers for TakagiߝSugeno descriptor systems with unknown inputs and application to fault diagnosis , 2007 .

[3]  Youmin Zhang,et al.  Active Fault Tolerant Control Systems: Stochastic Analysis and Synthesis , 2003 .

[4]  Michio Sugeno,et al.  Fuzzy identification of systems and its applications to modeling and control , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[5]  Thierry-Marie Guerra,et al.  Nonquadratic Stabilization Conditions for a Class of Uncertain Nonlinear Discrete Time TS Fuzzy Models: A New Approach , 2008, IEEE Transactions on Automatic Control.

[6]  Panos J. Antsaklis,et al.  Reconfigurable control system design via perfect model following , 1992 .

[7]  D. Luenberger.  An introduction to observers , 1971 .

[8]  Didier Theilliol,et al.  Fault-tolerant control in dynamic systems: application to a winding machine , 2000 .

[9]  J. Ragot,et al.  Nonquadratic stability analysis of Takagi-Sugeno models , 2002, Proceedings of the 41st IEEE Conference on Decision and Control, 2002..

[10]  B. M. Arx.  Design of observers for Takagi-Sugeno descriptor systems with unknown inputs and application to fault diagnosis , 2008 .

[11]  Thierry-Marie Guerra,et al.  Conditions of output stabilization for nonlinear models in the Takagi-Sugeno's form , 2006, Fuzzy Sets Syst..

[12]  M. Oudghiri.  Commande multi-modèles tolérante aux défauts : Application au contrôle de la dynamique d'un véhicule automobile. , 2008 .

[13]  Steven X. Ding,et al.  Actuator fault robust estimation and fault-tolerant control for a class of nonlinear descriptor systems , 2007, Autom..

[14]  J. Ragot,et al.  Fault detection and isolation using sliding mode observer for uncertain Takagi-Sugeno fuzzy model , 2008, 2008 16th Mediterranean Conference on Control and Automation.

[15]  José Ragot,et al.  Model structure simplification of a biological reactor , 2009 .

[16]  Kazuo Tanaka,et al.  Fuzzy Control Systems Design and Analysis: A Linear Matrix Inequality Approach , 2008 .

[17]  M. Darouach,et al.  Full-order observers for linear systems with unknown inputs , 1994, IEEE Trans. Autom. Control..

[18]  Marcel Staroswiecki.  Fault tolerant control : The pseudo-inverse method revisited , 2005 .