SUMMARYThis work concerns robust sensor fault detection observer (SFDO) design for uncertain and disturbed discrete‐time Takagi–Sugeno (T–S) systems using H −  ∕ H ∞ criterion. The principle of the proposed approach is based on simultaneously minimizing the perturbation effect and maximizing the fault effect on the residual vector. Furthermore, by introducing slack decision matrices and taking advantage of the descriptor formulation, less conservative sufficient conditions are proposed leading to easier linear matrix inequalities (LMIs). Moreover, the proposed (SFDO) design conditions allow dealing with unmeasurable premise variables. Finally, a numerical example and a truck–trailer system model are proposed to illustrate the efficiency of the SFDO design methodology. Copyright © 2013 John Wiley & Sons, Ltd.

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Abstract-This paper deals with the fault tolerant control (FTC) design for a Vertical Takeoff and Landing (VTOL) aircraft subject to external disturbances and actuator faults. The aim is to synthesize a fault tolerant controller ensuring trajectory tracking for the nonlinear uncertain system represented by Takagi-Sugeno (T-S) model. In order to design the FTC law, a proportional integral observer (PIO) is adopted which estimate both of the faults and the faulty system states. Based on Lyapunov theory and ℒ 2 optimization, the trajectory tracking performance and the stability of the closed loop system are analyzed. Sufficient conditions are obtained in terms of linear matrix inequalities (LMI). Simulation results show that the proposed controller is robust with respect to uncertainties on the mechanical parameters that characterize the model and secures global convergence.

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This paper investigates the problem of robust fault detection observer design for nonlinear Takagi-Sugeno models with unmeasurable premise variables subject to sensor faults and unknown bounded disturbance. The main idea is to synthesize a robust fault detection observer by means of a mixed H =H 1 performance index. The considered observer is used to estimate jointly states and faults. Using the technique of descriptor system representation, we proposed a new less-conservative approach in term of a linear matrix inequality (LMI) by considering the sensor fault as an auxiliary state variable. A solution of the problem is obtained by using an iterative LMI procedure.In the field of diagnosis, this assumption forces to design observers with weighting functions depending on the input u.t /, for the detection of the sensors faults, and on the output y.t /, for the detection of actuator faults. Indeed, if the decision variables are the inputs, for example, in a bank of observer, even if the i th observer is not controlled by the input u i , this input appears indirectly in the weighting function and it cannot be eliminated. For this reason, it is interesting to consider the case of weighting functions depending on unmeasurable premise variables, such as the state of the system. This case makes it possible to handle a large class of physical systems [21][22][23].Using descriptor approach, this work dealt with the problem of fault detection observer for Takagi-Sugeno (T-S) model affected by both sensor faults and bounded disturbances. Although many papers have dealt with the problem of observer design for descriptor systems, only a few works have been carried out for simultaneous disturbance rejection and fault detection algorithms [1]. Compared with existing fault estimation schemes [24,25], the given descriptor observer approach leads to more suitable observer design, which is applicable to diagnosis of more general faults. The proposed procedure has the advantage, over the ones proposed on [26,27], to estimate different faults types, whereas the proposed method in [26] is only able to estimate step faults. The problem formulation in a descriptor form allows also to estimate state and sensor faults simultaneously.This paper aims to extend the results proposed in [4] to T-S models with unmeasurable premise variables. The present work illustrates the design of a fault detection observer for T-S model affected by sensor faults and unknown bounded disturbances. The observer gains and the residual weighting matrix are obtained through the minimization of an H 1 norm and the maximization of an H norm. The main objective is to design a fault detection observer such that the resulting residual has the best robustness to disturbances and the best sensitivity to faults. Sufficient conditions are expressed in terms of linear matrix inequalities (LMIs), and an iterative algorithm is provided to get the solution. This algorithm can be solved effectively using numerical optimization techniques.This paper is organized as follows. In ...

This study deals with the design of a robust fault estimation and fault-tolerant control for vehicle lateral dynamics subject to external disturbance and unknown sensor faults. Firstly, a descriptor state and fault observer is designed to achieve the system state and sensor fault estimates simultaneously. Secondly, based on the information of on-line fault estimates, a robust fault-tolerant controller based on static output-feedback controller (SOFC) design approach is developed. To provide linear matrix inequalities of less conservatism, the results are conducted in the non-quadratic framework dealing with unmeasurable premise variables case. Simulation results show the effectiveness of the proposed control approach when the vehicle road adhesion conditions change and the sideslip angle is unavailable for measurement. © The Institution of Engineering and Technology 2014

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