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A fault estimation and fault-tolerant control based sliding mode observer for LPV descriptor systems with time delay

Hamdi Habib, Rodrigues Mickael, Rabaoui Bouali, Benhadj Braiek Naceur

International Journal of Applied Mathematics and Computer Science

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2021

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Vol. 31, no. 2

247--258

EN

This paper considers the problem of fault-tolerant control (FTC) and fault reconstruction of actuator faults for linear parameter varying (LPV) descriptor systems with time delay. A polytopic sliding mode observer (PSMO) is synthesized to achieve simultaneous reconstruction of LPV polytopic descriptor system states and actuator faults. Exploiting the reconstructed actuator faults and state estimates, a fault-tolerant controller is designed to compensate the impact of actuator faults on system performance by stabilizing the closed-loop LPV delayed descriptor system. Besides, the controller and PSMO gains are obtained throughout the resolution of linear matrix inequalities (LMIs) using convex optimization techniques. The developed PSMO could 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. Simulation results applied to a given numerical system are presented to highlight the superiority and effectiveness of the proposed approach.

2

Distributed fault estimation of multi-agent systems using a proportional-integral observer: A leader-following application

Farrera Beltrán, López-Estrada Francisco-Ronay, Chadli Mohammed, Valencia-Palomo Guillermo, Gómez-Peñate Samuel

International Journal of Applied Mathematics and Computer Science

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2020

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Vol. 30, no. 3

551--560

EN

This paper proposes a methodology for observer-based fault estimation of leader-following linear multi-agent systems subject to actuator faults. First, a proportional-integral distributed fault estimation observer is developed to estimate both actuator faults and states of each follower agent by considering directed and undirected graph topologies. Second, based on the proposed quadratic Lyapunov equation, sufficient conditions for the asymptotic convergence of the observer are obtained as a set of linear matrix inequalities. Finally, a numerical example is provided to illustrate the proposed approach.

3

Robust multiple sensor fault-tolerant control for dynamic non-linear systems: Application to the aerodynamical twin-rotor system

Pazera M., Buciakowski M., Witczak M.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 2

297--308

EN

The paper deals with the problem of designing sensor-fault tolerant control for a class of non-linear systems. The scheme is composed of a robust state and fault estimator as well as a controller. The estimator aims at recovering the real system state irrespective of sensor faults. Subsequently, the fault-free state is used for control purposes. Also, the robust sensor fault estimator is developed in a such a way that a level of disturbances attenuation can be reached pertaining to the fault estimation error. Fault-tolerant control is designed using similar criteria. Moreover, a separation principle is proposed, which makes it possible to design the fault estimator and control separately. The final part of the paper is devoted to the comprehensive experimental study related to the application of the proposed approach to a non-linear twin-rotor system, which clearly exhibits the performance of the new strategy.

4

Data-driven techniques for the fault diagnosis of a wind turbine benchmark

Simani S., Farsoni S., Castaldi P.

International Journal of Applied Mathematics and Computer Science

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2018

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Vol. 28, no. 2

247--268

EN

This paper deals with the fault diagnosis of wind turbines and investigates viable solutions to the problem of earlier fault detection and isolation. The design of the fault indicator, i.e., the fault estimate, involves data-driven approaches, as they can represent effective tools for coping with poor analytical knowledge of the system dynamics, together with noise and disturbances. In particular, the proposed data-driven solutions rely on fuzzy systems and neural networks that are used to describe the strongly nonlinear relationships between measurement and faults. The chosen architectures rely on nonlinear autoregressive models with exogenous input, as they can represent the dynamic evolution of the system along time. The developed fault diagnosis schemes are tested by means of a high-fidelity benchmark model that simulates the normal and the faulty behaviour of a wind turbine. The achieved performances are also compared with those of other model-based strategies from the related literature. Finally, a Monte-Carlo analysis validates the robustness and the reliability of the proposed solutions against typical parameter uncertainties and disturbances.

5

On fault tolerant control structures incorporating fault estimation

Krokavec D., Filasová A., Liščinský P.

Archives of Control Sciences

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2016

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Vol. 26, no. 4

453--469

EN

The paper provides the minimal necessary modifications of linear matrix inequality conditions for the mixed H2/H∞ control design as well as for the augmented observer-based fault estimation to be mutually compatible in joint design of integrated fault estimation and fault tolerant control. To be possible, within this integration, to design the controller which guarantees a pre-specified H∞ norm disturbance attenuation level, the design conditions has to be regularized using the H2 performance index and, moreover, augmented fault observer must be of enforced dynamics. Analyzing the ambit of performances given on the mixed H2/H∞ design, the joint design conditions are formulated as a minimization problem subject to convex constraints expressed by a system of LMIs. The feasibility of the conditions is demonstrated by a numerical example.

6

Adaptive observer-based fault estimation for a class of Lipschitz nonlinear systems

Oucief N., Tadjine M., Labiod S.

Archives of Control Sciences

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2016

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Vol. 26, no. 2

245--259

EN

Fault input channels represent a major challenge for observer design for fault estimation. Most works in this field assume that faults enter in such a way that the transfer functions between these faults and a number of measured outputs are strictly positive real (SPR), that is, the observer matching condition is satisfied. This paper presents a systematic approach to adaptive observer design for joint estimation of the state and faults when the SPR requirement is not verified. The proposed method deals with a class of Lipschitz nonlinear systems subjected to piecewise constant multiplicative faults. The novelty of the proposed approach is that it uses a rank condition similar to the observer matching condition to construct the adaptation law used to obtain fault estimates. The problem of finding the adaptive observer matrices is formulated as a Linear Matrix Inequality (LMI) optimization problem. The proposed scheme is tested on the nonlinear model of a single link flexible joint robot system.

7

Systematic fault tolerant control based on adaptive Thau observer estimation for quadrotor UAVs

Cen Z., Noura H., Younes Y. A.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 1

159--174

EN

A systematic fault tolerant control (FTC) scheme based on fault estimation for a quadrotor actuator, which integrates normal control, active and passive FTC and fault parking is proposed in this paper. Firstly, an adaptive Thau observer (ATO) is presented to estimate the quadrotor rotor fault magnitudes, and then faults with different magnitudes and time-varying natures are rated into corresponding fault severity levels based on the pre-defined fault-tolerant boundaries. Secondly, a systematic FTC strategy which can coordinate various FTC methods is designed to compensate for failures depending on the fault types and severity levels. Unlike former stand-alone passive FTC or active FTC, our proposed FTC scheme can compensate for faults in a way of condition-based maintenance (CBM), and especially consider the fatal failures that traditional FTC techniques cannot accommodate to avoid the crashing of UAVs. Finally, various simulations are carried out to show the performance and effectiveness of the proposed method.

8

Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

López-Estrada F. R., Ponsart J. C., Theilliol D., Astorga-Zaragoza C. M., Camas-Anzueto J. L.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 2

233--244

EN

This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.

9

An H∞ sliding mode observer for Takagi–Sugeno nonlinear systems with simultaneous actuator and sensor faults

Ben Brahim A., Dhahri S., Ben Hmida F., Sellami A.

International Journal of Applied Mathematics and Computer Science

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2015

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Vol. 25, no. 3

547--559

EN

This paper considers the problem of robust reconstruction of simultaneous actuator and sensor faults for a class of uncertain Takagi–Sugeno nonlinear systems with unmeasurable premise variables. The proposed fault reconstruction and estimation design method with H∞ performance is used to reconstruct both actuator and sensor faults when the latter are transformed into pseudo-actuator faults by introducing a simple filter. The main contribution is to develop a sliding mode observer (SMO) with two discontinuous terms to solve the problem of simultaneous faults. Sufficient stability conditions in terms linear matrix inequalities are achieved to guarantee the stability of the state estimation error. The observer gains are obtained by solving a convex multiobjective optimization problem. Simulation examples are given to illustrate the performance of the proposed observer.

10

Novel optimal recursive filter for state and fault estimation of linear stochastic systems with unknown disturbances

Khémiri K., Ben Hmida F., Ragot J., Gossa M.

International Journal of Applied Mathematics and Computer Science

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2011

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Vol. 21, no 4

629-637

EN

This paper studies recursive optimal filtering as well as robust fault and state estimation for linear stochastic systems with unknown disturbances. It proposes a new recursive optimal filter structure with transformation of the original system. This transformation is based on the singular value decomposition of the direct feedthrough matrix distribution of the fault which is assumed to be of arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance criteria. Two numerical examples are given in order to illustrate the proposed method, in particular to solve the estimation of the simultaneous actuator and sensor fault problem and to make a comparison with the existing literature results.