Observer design and active fault tolerant control for Takagi-Sugeno systems affected by sensors faults

Abstract

This paper deals with the problem of active fault tolerant control strategy for nonlinear systems described by Takagi-Sugeno models. The proposed control law uses the estimated fault. The considered systems are affected by sensor faults. A mathematical transformation is used in order to conceive an augmented system in which the sensor faults affecting the initial system appear as unknown inputs. A proportional integral observer with unknown inputs is conceived in order to estimate simultaneously states and sensor faults. The stability of the system with the proposed fault tolerant control strategy is formulated using Lyapunov theory and the observer gains are obtained by solving linear matrices inequalities. To illustrate the proposed method, it is applied to the three columns.Keywords: Takagi-Sugeno model; proportional integral observer with unknown inputs; sensor faults; active fault tolerant control strategy.Reference to this paper should be made as follows: Jamel, W., Khedher, A. and Ben Othman, K. (2017) 'Observer design and active fault tolerant control for Takagi-Sugeno systems affected by sensors faults', Int.

Adaptive Proportional Integral Observer Design for Interval Type 2 Takagi–Sugeno Fuzzy Systems

“…Elementary Background on Type 1 Takagi-Sugeno Fuzzy Systems. Takagi-Sugeno fuzzy systems are an appropriate tool which permits to model large class of complex and nonlinear systems with a mathematical model which can be used for analysis [32,33], control [34,35], and observer design [1,8,13,36]. is approach is based on a decomposition of the system operating space into a finite number of operating zones.…”

“…Sensor networks are considered in [12] more precisely in the case of nonfragile distributed filters with Takagi-Sugeno models. In this context, the problem of state and fault estimation is studied in [2,4,5,8,13]. In [4], a sliding mode observer with unknown input for the case of uncertain Takagi-Sugeno models is proposed.…”

“…It is possible to estimate simultaneously the system state and the fault affecting the system using the proportional integral observer. is kind of observer is composed of two estimators (proportional and integral) [4,5,8,13]. In practice, the design of the proportional integral observer is reduced to the computation of the two gains (proportional and integral) where the proportional term lets to estimate the system state and the integral term permits to estimate the fault [4,5,8,13].…”

“…is kind of observer is composed of two estimators (proportional and integral) [4,5,8,13]. In practice, the design of the proportional integral observer is reduced to the computation of the two gains (proportional and integral) where the proportional term lets to estimate the system state and the integral term permits to estimate the fault [4,5,8,13]. Works presented in [4,5,8,13] are interested in state and fault estimation in the context of Takagi-Sugeno systems using proportional integral observers which are composed of two estimators; the first one called proportional terms is used to estimate the system state and the second one called integral term allows estimating the fault affecting the system.…”

“…is paper shows that it is possible to adapt this observer to estimate, simultaneously, the system state, the actuator, and the sensor faults. Indeed, the mathematical transformation proposed in [2], for the case of linear systems and extended to the case of systems described by Takagi-Sugeno models in [4,8,13], is adapted to interval type 2 Takagi-Sugeno models in this paper. Based on the adapted form of this transformation, an augmented system state is obtained.…”