Simultaneous state and fault estimation for Takagi-Sugeno implicit models with Lipschitz constraints

¹ Laboratory of High Energy Physics and Condensed Matter, Faculty of Science Hassan II University of Casablanca, B.P 5366, Maarif, Casablanca, Morocco

² ECPI, Department of Electrical Engineering, ENSEM Hassan II University of Casablanca, B.P 8118, Oasis, Casablanca Morocco

IJOCTA 2021, 11(1), 100–108; https://doi.org/10.11121/ijocta.01.2021.00877

Submitted: 15 October 2019 | Accepted: 10 May 2020 | Published: 3 January 2020

© 2020 by the Author(s). This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution -Noncommercial 4.0 International License (CC-by the license) ( https://creativecommons.org/licenses/by-nc/4.0/ )

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Abstract

This paper presents a state and fault observer design for a class of TakagiSugeno 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.

Keywords

Takagi-Sugeno implicit model

Estimation of actuator

and sensor faults

Fuzzy Observer design

Lyapunov method

LMI technique

Lipschitz constraints

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