H&lt;inf&gt;&amp;#x221E;&lt;/inf&gt; sensor faults estimation for T-S models using descriptor techniques: Application to fault diagnosis

Bouattour, Maha; Chadli, Mohammed; Chaabane, Mohamed

doi:10.1109/fuzzy.2009.5277179

Cited by 20 publications

(19 citation statements)

References 18 publications

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“…Proof: See for example [10]. The following result derived in LMI terms guarantees robustness against disturbance.…”

Section: H ∞ Robustness Conditionsmentioning

confidence: 95%

“…as disturbances rejected by H ∞ performance [10,16]. In the sequel only the case of T-S fuzzy systems with common output matrix, i.e., 1…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

“…LMI synthesis conditions to design observer for T-S models have been given (See for example [7,10,18,22]). Thus, methods for detecting and also estimating faults using different techniques such as unknown input observers [19,20], sliding mode technique [21], and descriptor system technique [10,16] have been proposed. However, to the best of our knowledge, very few effort has been made to compute residual generator as sensitive as possible to faults and as robust as possible to unknown disturbances for T-S models.…”

Section: Introductionmentioning

confidence: 99%

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Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach

Bouattour

Chadli

Chaabane³

et al. 2011

Int. J. Control Autom. Syst.

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This paper deals with the design of a robust fault detection observer for a Takagi-Sugeno (T-S) fuzzy model affected by sensor and actuator faults and unknown bounded disturbances simultaneously. An observer based on the technique of descriptor systems is studied. Indeed, by considering faults as auxiliary state variables, both states and faults are estimated simultaneously. In order to guarantee the best robustness to disturbances and sensitivity to faults, the developed observer combine the H -/H ∞ performances. Then, based on Lyapunov method, asymptotic stability conditions are given to design the observer parameters. In order to get convenient and reliable faults estimator in computations, an iterative linear matrix inequality (LMI) algorithm is developed. This algorithm, solved easily using existing numerical tools, allows to minimize influences of disturbances and maximize the ones of faults. Finally, a numerical example is proposed to illustrate the effectiveness of the result.

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“…Proof: See for example [10]. The following result derived in LMI terms guarantees robustness against disturbance.…”

Section: H ∞ Robustness Conditionsmentioning

confidence: 95%

“…as disturbances rejected by H ∞ performance [10,16]. In the sequel only the case of T-S fuzzy systems with common output matrix, i.e., 1…”

Section: Preliminaries and Problem Formulationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach

Bouattour

Chadli

Chaabane³

et al. 2011

Int. J. Control Autom. Syst.

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“…Hence, the study of the simultaneous state/disturbance estimation problem will enrich the theory of 2D system, particularly the analysis and design of 2D observers. On the other hand, for 1D systems, the problem of simultaneous estimation of system states and disturbances (or faults) has attracted significant attention with numerous published results [15][16][17][18][19].There are mainly two kinds of schemes to deal with disturbances and/or unknown inputs in a system: the passive scheme and the active scheme. The passive scheme usually obtains a limited performance in terms of an index, for example, the H ∞ index [20].…”

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confidence: 98%

Integrated state/disturbance observers for two‐dimensional linear systems

Zhao

Lin

Wang

2015

IET Control Theory & Applications

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In this study, the problem of simultaneous estimation of system states and disturbances is addressed for twodimensional (2D) linear systems. The considered 2D systems can be described as Fornasini-Marchesini second local state-space model coupled with unknown disturbances in the measurement equation. Asymptotically stable and uniformly ultimately bounded integrated state/disturbance observers are proposed as solutions to the simultaneous estimation problem under different system conditions. For the asymptotically stable integrated state/disturbance observer, a necessary and sufficient condition for its existence is presented and proved. For the uniformly ultimately bounded integrated state/disturbance observer, a sufficient condition for its existence is given and proved, and it can be designed such that its estimation error has arbitrarily small upper bound. Moreover, some constructive design methods are given for the proposed integrated state/disturbance observers. Finally, a thermal process plant and another numerical example are provided to illustrate the effectiveness of the proposed methods. IntroductionObserver synthesis and estimation problems in the context of two-dimensional (2D) systems have received substantial attention during the past several decades. In the early 1980s, Bisiacco conducted fundamental studies on 2D observers [1,2]. He presented both necessary and sufficient conditions for state reconstruction and the structure of observers for 2D systems on the basis of polynomial matrix theory. In the same period, other basic results concerning 2D observers have been reported, such as the minimal order state observer given by Kaczorek (see [3] and the references therein). Since then, a series of studies on 2D observers have been reported, particularly during the past ten years. Bisiacco and Valcher discussed the unknown input observer (UIO) problem for 2D systems in the frequency domain, where the design of a 2D linear system dead-beat UIO was considered on the basis of polynomial matrix method [4]. This kind of UIO can be used for fault detection and isolation [5,6]. By extending the concept of the Luenberger observer to 2D state-space models and replacing the original observer by two interconnected linear 2D systems, Bisiacco and Valcher introduced a generalised Luenberger observer [7] with less conservative existence condition. Xu et al. [8] presented an asymptotic UIO in the time domain with a sufficient existence condition in terms of rank conditions, and a constructive design method was also proposed based on linear matrix inequalities (LMIs). With a similar design and analysis method as that for asymptotic UIOs, Xu et al. [9] successfully solved the functional observer problem for 2D systems. On the basis of an early study on 2D non-linear digital filters [10] and by utilising a method similar to a study reported for functional observers [9], Wang et al. [11] studied the asymptotic UIO problem for a class of 2D nonlinear systems. In addition, Zou et al. [12], Wang and Zou [13] and Kaczorek [...

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“…Several methods have been developed to detect and identify sensor faults when they appear [2,11,13,14,16,17]. Among these techniques, Takagi-Sugeno (TS) fuzzy model has been used to represent the nonlinear systems [21,22,23].…”

Section: Introductionmentioning

confidence: 99%

Robust fault detection for Takagi-Sugeno discrete models: Application for a three-tank system

Ghorbel¹,

Souissi²,

Chaabane³

et al. 2012

IJCA

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In this paper, we present a fuzzy observer based on TakagiSugeno (TS) models, to estimate simultaneously the system state and the sensors faults of discrete time nonlinear systems. The method uses the technique of descriptor systems, by considering the sensor faults as auxiliary states variables. More precisely, This paper addresses the problem of index fault detection observer to ensure the sensitivity against the faults. The proposed method is based on the use of the Lyapunov theory to ensure the stability of the system. Necessary and sufficient conditions are obtained in terms of Linear Matrix Inequalities (LMIs), in order to determine the observer gains. An application of the fault estimation method on an hydraulic process with three tanks, using TS models is realized. Simulation and experimental results show the effectiveness of the proposed method. General TermsTakagi-Sugeno model, observer design.

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H<inf>∞</inf> sensor faults estimation for T-S models using descriptor techniques: Application to fault diagnosis

Cited by 20 publications

References 18 publications

Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach

Design of robust fault detection observer for Takagi-Sugeno models using the descriptor approach

Integrated state/disturbance observers for two‐dimensional linear systems

Robust fault detection for Takagi-Sugeno discrete models: Application for a three-tank system

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