Observer-based controller synthesis for LPV descriptor systems using dilated LMI conditions

Halalchi, Houssem; Bara, Gabriela Iuliana; Laroche, Édouard

doi:10.1109/cacsd.2011.6044556

Cited by 5 publications

(5 citation statements)

References 20 publications

(28 reference statements)

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“…Following the LPV descriptor system formulation given in , consider a system with sensor and actuator faults given as

E \overset{x}{true} = A (θ (t)) x + Bu + Rd

where

x \in {double-struckR}^{n}, u \in {double-struckR}^{m}

and

d \in {double-struckR}^{d}

are the state vector, the input vector and disturbance vector or modelling uncertainties, respectively. It should be noted that d denotes the ‘lumped total effect’ of exogenous disturbance and modelling uncertainties.…”

Section: Baseline Controller For Lpv Descriptor Systemsmentioning

confidence: 99%

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Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Shi

Patton

2014

Intl J Robust & Nonlinear

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Starting with the baseline controller design, this paper proposes an integrated approach of active fault tolerant control based on proportional derivative extended state observer (PDESO) for linear parameter varying descriptor systems. The PDESO can simultaneously provide the estimates of the system states, sensor faults, and actuator faults. The L 2 robust performance of the closed-loop system to bounded exogenous disturbance and bounded uncertainty is achieved by a two-step design procedure adapted from the traditional observerbased controller design. Furthermore, an LMI pole-placement region and the L 2 robustness performance are combined into a multiobjective formulation by suitably combing the appropriate LMI descriptions. A parameter-varying system example is given to illustrate the design procedure and the validity of the proposed integrated design approach.

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“…Following the LPV descriptor system formulation given in , consider a system with sensor and actuator faults given as

E \overset{x}{true} = A (θ (t)) x + Bu + Rd

where

x \in {double-struckR}^{n}, u \in {double-struckR}^{m}

and

d \in {double-struckR}^{d}

Section: Baseline Controller For Lpv Descriptor Systemsmentioning

confidence: 99%

“…Consider the following descriptor system example modified from :

E \dot{x} = A (θ) x + B u + F_{a} f_{a} + Rd

y = C x

E = [\begin{matrix} 1 & 0 & 0 \\ 0 & 1 & 0 \\ 0 & 0 & 0 \end{matrix}], A (θ) = [\begin{matrix} θ & 2 & 1 \\ 1 & - 1 & 0 \\ θ & - θ & - 2 - θ \end{matrix}], C = [\begin{matrix} 1 & 1 & 0 \\ 0 & 0 & 1 \end{matrix}]

B = {[\begin{matrix} 2 & 1 & 0 \end{matrix}]}^{T}, F_{a} = {[\begin{matrix} 2 & 1 & 0 \end{matrix}]}^{T}, R = {[\begin{matrix} normal0 . 1 & normal0 . 1 & 0 \end{matrix}]}^{T}

where

θ \in ([], \begin{matrix} - 1.5 & 1.5 \end{matrix})

. In this study, only an actuator fault is considered to illustrate of the design procedure.…”

Section: Case Studymentioning

confidence: 99%

Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Shi

Patton

2014

Intl J Robust & Nonlinear

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“…The LPV descriptor system formulation can have powerful analysis and design properties and is a suitable way of representing real systems . However, few studies have been concerned with LPV approaches to the joint problems of state reconstruction and fault detection and diagnosis or fault estimation for descriptor systems .…”

Section: Introductionmentioning

confidence: 99%

Fault diagnosis based on sliding mode observer for LPV descriptor systems

Hamdi

Rodrigues

Mechmeche

et al. 2019

Asian Journal of Control

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This paper considers the problem of fault detection and reconstruction of actuator faults for linear parameter varying descriptor systems. A polytopic sliding mode observer (PSMO) is constructed to achieve simultaneous reconstruction of LPV polytopic descriptor system states and actuator faults. Sufficient conditions for the existence and design algorithm of the proposed polytopic sliding mode observer are provided. In addition, the design of the PSMO is formulated in terms of linear matrix inequalities that can be suitably solved using convex optimization techniques. This PSMO can force the output estimation error to converge to zero in a finite time when the actuators faults are bounded through the reinjection of the output estimation error via a nonlinear switching term. The effectiveness of the design technique is illustrated through a simulation of an anaerobic bioreactor.

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“…Fault detection and isolation problems have been investigated for a long time, and significant results have been developed for general systems, including descriptor systems . For descriptor linear parameter varying systems (D‐LPV) systems, however, still remain a challenge, and only a little work can be found in the literatures . For instance, proposed an actuator fault estimation method for D‐LPV systems based on an adaptive polytopic observer; however, it needed to satisfy the strictly positive real condition and the convergence domain depended on the norm of fault.…”

Section: Introductionmentioning

confidence: 99%

Simultaneous actuator and sensor fault estimation for descriptor LPV system based on H _∞ reduced-order observer

Zhu

2015

Optim. Control Appl. Meth.

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SUMMARYThis paper addresses the problems of simultaneous actuator and sensor fault estimation for a class of descriptor linear parameter varying systems. By extending the sensor fault as an auxiliary state, the original system can be transformed into a descriptor one. Then, by the using of H 1 optimization technique, a reduced-order observer is developed with a new defining variable. The proposed approach is based on the parameterizations of the obtained algebraic constraints from the error equation. By using the designed reduced-order observer and super twisting algorithm, the actuator fault can be reconstructed via a polytopic algebraic method. Finally, a simulation example of electric network is given to illustrate the validation of the proposed method.

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Observer-based controller synthesis for LPV descriptor systems using dilated LMI conditions

Cited by 5 publications

References 20 publications

Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Fault diagnosis based on sliding mode observer for LPV descriptor systems

Simultaneous actuator and sensor fault estimation for descriptor LPV system based on H _∞ reduced-order observer

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Observer-based controller synthesis for LPV descriptor systems using dilated LMI conditions

Cited by 5 publications

References 20 publications

Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Fault estimation and active fault tolerant control for linear parameter varying descriptor systems

Fault diagnosis based on sliding mode observer for LPV descriptor systems

Simultaneous actuator and sensor fault estimation for descriptor LPV system based on H ∞ reduced-order observer

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Simultaneous actuator and sensor fault estimation for descriptor LPV system based on H _∞ reduced-order observer