The main contribution of this paper is the design of a polytopic unknown inputs proportional integral observer (UIPIO) for linear parameter-varying (LPV) descriptor systems. This observer is used for actuator fault detection and isolation. The proposed method is based on the representation of the LPV descriptor systems in a polytopic form. Its parameters evolve in an hypercube domain. The designed polytopic UIPIO is also able to estimate both the states and the unknown inputs of the LPV descriptor system. Stability conditions of such observer are expressed in terms of linear matrix inequalities. An example illustrates the performances of such polytopic UIPIO.
This paper presents an Adaptive Polytopic Observer (APO) design in order to develop an actuator fault estimation method dedicated to polytopic Linear Parameter Varying (LPV) descriptor systems. This paper extends a fault diagnosis method developed for regular LTI systems to polytopic LPV descriptor systems.Here, time-varying actuator faults are also considered, whereas in many papers, actuator faults are generally assumed to be constant. The design and convergence conditions of this APO are provided. The design is formulated through LMI techniques under equality constraints. The performances of the proposed actuator fault estimation scheme are illustrated using an electrical circuit. By using (31) and substituting (40) into Equation (38), one can obtain ² u 1 .t / D 12 sin.2:5t / u 2 .t / D 5
This paper addresses the robust fault detection and estimation problem of nonlinear descriptor system with unknown inputs observers. The considered nonlinear descriptor system is transformed into an equivalent multi-models form by using the Takagi-Sugeno (T-S) approach. Two cases are considered: the first one deals with the multi-models with measurable decision variables and the second one assumes that these decision variables are unmeasurable. Then, a residual generator based on an unknown observer is designed for fault detection and estimation. Stability analysis and gain matrices determination are performed by resolving a set of Linear Matrices Inequalities (LMIs) for both cases. The performances of the proposed fault detection and estimation method is successfully applied to an electrical circuit.
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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