Design of a proportional integral observer based on sliding mode principle for uncertain Takagi-Sugeno fuzzy systems: applications to a turbo-reactor

Abstract

This work deals with the problem of state and fault estimation for systems described by Takagi-Sugeno fuzzy systems. The state and fault estimation is made using a proportional integral observer based on the sliding mode principle. Only sensor faults are considered in this work. In order to estimate this kind of fault, a particulate mathematical transformation is used. The application of this mathematical transformation to the initial system output allows to conceive an augmented system where the initial sensor fault appears as an unknown input. An adaptive mathematical form is used for the sign function to facilitate the determination of the proportional gains of the conceived observer. The observer convergence conditions are formulated in the form of linear matrix inequalities (LMI) allowing computing the observer gains and the Lyapunov theory is used to guarantee the system stability with faults. The proposed proportional integral sliding mode observer is applied to turbo-reactor showing the efficiency of the fault and state estimation.