Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation

Koenig, Damien

doi:10.1109/tac.2004.841889

Cited by 234 publications

(163 citation statements)

References 13 publications

(28 reference statements)

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“…For a given Z, Θ is deduced from (32), the matrices N i , M i and L i are derived from (19), (23) and (24) respectively. This result unifies the results obtained, on the one hand, in the field of the descriptor systems with UI [6], [9], [10] and, on the other hand, in the field of the TS systems with UI [1]. It is useful because a TSDS cannot be reduced, either to a single singular system (it would not handle the nonlinearities due to the weighting functions h i ), or to a regular TS system (it would not handle the algebraic relation between the state variables).…”

Section: Corollarysupporting

confidence: 90%

“…It is useful because a TSDS cannot be reduced, either to a single singular system (it would not handle the nonlinearities due to the weighting functions h i ), or to a regular TS system (it would not handle the algebraic relation between the state variables). The existence condition (9) can be linked to previous works concerning single descriptor systems [9], [10]. Considering (9) for a single descriptor system, would lead to the condition…”

Section: Corollarymentioning

confidence: 94%

“…Then (28) is equivalent to (9). In the discrete-time case, the proof is very similar, thus it is omitted.…”

Section: Lemmamentioning

confidence: 99%

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Design of observers for Takagi–Sugeno descriptor systems with unknown inputs and application to fault diagnosis

Marx

Koenig

Ragot

2007

IET Control Theory Appl.

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177

139

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This paper presents a method for state-estimation of Takagi-Sugeno descriptor systems (TSDS) affected by unknown inputs (UI). For ease of implementation's sake, the proposed observers are not in descriptor form but in usual form. Sufficient existence conditions of the unknown input observers are given and strict linear matrix inequalities (LMI) are solved to determine the gain of the observers. If the perfect unknown input decoupling is not possible, the UI observer is designed in order to minimise the L2-gain from the UI to the state estimation error. The two previous objectives can be mixed in order to decouple the estimation to a subset of the UI, while attenuating the L2 gain from the other UI to the estimation. The proposed UI observers are used for robust fault diagnosis. Fault diagnosis for TSDS is performed by designing a bank of observers. A simple decision logic and thresholds setting allow to determine the occurring fault. The results are established for both the continuous and the discrete time cases.The proposed method is illustrated by a numerical example. Index TermsTakagi-Sugeno systems, singular systems, state estimation, unknown input observers, fault diagnosis. I. INTRODUCTIONThe Takagi-Sugeno (TS) model proposed by [14] is a well-known structure to represent nonlinear systems into several linear fuzzy models. In the last two decades, the control and the observation of TS systems have become challenging problems that received a considerable amount of attention. In The descriptor formalism is very attractive for system modelling, as pointed out in [4], since it describes a wider class of systems including physical systems with non dynamic constraints (e.g. algebraic relations induced in interconnected systems such as power transfer networks or water distribution networks) or jump behaviour. The enhancement of the modelling ability is due to the structure of the dynamic equation which encompasses not only dynamic equations, but also algebraic relations.Since both TS and descriptor formalisms are attractive in the field of modelling, the TS representation has been generalised to descriptor systems. The stability and the design of state-feedback controllers for TS descriptor systems to the authors' knowledge, the design of UIO has not been treated in the generic case of TSDS. The aim of this paper is not only to generalise the existing works on UIO design to TSDS, but also to apply this new observer in the field of fault diagnosis of TSDS which has not been treated so far. This paper gives a simple extension to TSDS of the design of observers for the state estimation in the presence of unknown inputs (UI). Under some sufficient conditions, the design of the observer is reduced to the determination of a matrix. The choice of this parameter is performed by solving strict LMIs. If the estimation error cannot be decoupled from the UI, an L 2 observer is proposed to minimise the influence of the UI on the state estimation. The two design objectives can be mixed by decoupling the state estimatio...

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Section: Corollarysupporting

confidence: 90%

Section: Corollarymentioning

confidence: 94%

See 1 more Smart Citation

Design of observers for Takagi–Sugeno descriptor systems with unknown inputs and application to fault diagnosis

Marx

Koenig

Ragot

2007

IET Control Theory Appl.

Self Cite

177

139

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show abstract

“…Fault diagnosis is also a necessary part of active fault-tolerant control (Blanke et al, 2016). In recent years, significant research effort have been dedicated to fault diagnosis for descriptor systems, such as H − /H ∞ fault detection methods for nonlinear descriptor systems have been studied in López Estrada et al (2015); Boulkroune et al (2013), fault estimation of nonlinear descriptor systems (Koenig, 2005;Gao and Ding, 2007). In an uncertain control system, system disturbances and measurement noise have an important effect on the fault diagnosis result.…”

Section: Introductionmentioning

confidence: 99%

Zonotopic Fault Estimation Filter Design for Discrete-time Descriptor Systems

Wang

Puig

et al. 2017

IFAC-PapersOnLine

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This paper considers actuator-fault estimation for discrete-time descriptor systems with unknown but bounded system disturbance and measurement noise. A zonotopic fault estimation filter is designed based on the analysis of fault detectability indexes. To ensure estimation accuracy, the filter gain in the zonotopic fault estimation filter is optimized through the zonotope minimization. The designed zonotopic filter not only can estimate fault magnitudes, but it also provides fault estimation results in an interval, i.e. the upper and lower bounds of fault magnitudes. Moreover, the proposed fault estimation filter has a non-singular structure and hence is easy to implement. Finally, simulation results are provided to illustrate the effectiveness of the proposed method.

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“…An eigenstructure approach was used to design a UIO by Duan et al (2002). A UIO was proposed by Yeu et al (2005) for fault detection and isolation, and a UIO was designed for fault estimation by Koenig (2005). A singular UIO and a fault detection filter for diagnosis purposes in these systems were designed respectively by Share Pasand et al (2010) and Yao et al (2011).…”

Section: Introductionmentioning

confidence: 99%

Robust fault detection of singular LPV systems with multiple time–varying delays

Hassanabadi

Shafiee²,

Puig

2016

International Journal of Applied Mathematics and Computer Science

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In this paper, the robust fault detection problem for LPV singular delayed systems in the presence of disturbances and actuator faults is considered. For both disturbance decoupling and actuator fault detection, an unknown input observer (UIO) is proposed. The aim is to compute a residual signal which has minimum sensitivity to disturbances while having maximum sensitivity to faults. Robustness to unknown inputs is formulated in the sense of the H∞-norm by means of the bounded real lemma (BRL) for LPV delayed systems. In order to formulate fault sensitivity conditions, a reference model which characterizes the ideal residual behavior in a faulty situation is considered. The residual error with respect to this reference model is computed. Then, the maximization of the residual fault effect is converted to minimization of its effect on the residual error and is addressed by using the BRL. The compromise between the unknown input effect and the fault effect on the residual is translated into a multi-objective optimization problem with some LMI constraints. In order to show the efficiency and applicability of the proposed method, a part of the Barcelona sewer system is considered.

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Unknown input proportional multiple-integral observer design for linear descriptor systems: application to state and fault estimation

Cited by 234 publications

References 13 publications

Design of observers for Takagi–Sugeno descriptor systems with unknown inputs and application to fault diagnosis

Design of observers for Takagi–Sugeno descriptor systems with unknown inputs and application to fault diagnosis

Zonotopic Fault Estimation Filter Design for Discrete-time Descriptor Systems

Robust fault detection of singular LPV systems with multiple time–varying delays

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