Abstract
This paper presents a state and fault observer design for a class of Takagi-Sugeno implicit models (TSIMs) with unmeasurable premise variables satisfying the Lipschitz constraints. The fault variable is constituted by the actuator and sensor faults. The actuator fault affects the state and the sensor fault affects the output of the system. The approach is based on the separation between dynamic and static relations in the TSIM. Firstly, the method begins by decomposing the dynamic equations of the algebraic equations. Secondly, the fuzzy observer design that satisfies the Lipschitz conditions and permits to estimate simultaneously the unknown states, actuator and sensor faults is developed. The aim of this approach for the observer design is to construct an augmented model where the fault variable is added to the state vector. The exponential convergence of the state estimation error is studied by using the Lyapunov theory and the stability condition is given in term of only one linear matrix inequality (LMI). Finally, numerical simulation results are given to highlight the performances of the proposed method by using a TSIM of a single-link flexible joint robot.
Highlights
Due to the growth of the industrial demand for high reliability and safety, the field of the observer design for many chemical and physical processes by using different approaches has attracted much attention of the researchers for a long time
In this paper, based on the T-S approach, we study the problem of observer design for simultaneous state and fault estimation for a class of continuous-time TakagiSugeno implicit models (TSIMs) in presence of actuator and sensor faults
This paper develops a new methodology of fuzzy observer design, as a new contribution to simultaneously estimate fault variables as well as system states variables, for a class of TSIMs with unmeasurable premise variables satisfying the Lipschitz constraints in presence of the actuator and sensor faults
Summary
Due to the growth of the industrial demand for high reliability and safety, the field of the observer design for many chemical and physical processes by using different approaches has attracted much attention of the researchers for a long time. Fuzzy control systems based on the Takagi-Sugeno (T-S) approach has been received great attention in researches and recognized as a powerful tool to describe the global behaviors of nonlinear systems The interest of this formalism is to apprehend the global behavior of a nonlinear process by a set of local linear models, [7, 8]. Simultaneous state and fault estimation for Takagi-Sugeno implicit models with Lipschitz constraints system model and to design controller and observer in different areas of research. In this paper, based on the T-S approach, we study the problem of observer design for simultaneous state and fault estimation for a class of continuous-time TSIMs in presence of actuator and sensor faults.
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