Zonotopic fault detection observer for discrete-time descriptor systems considering ₋ fault sensitivity

Abstract

This paper addresses a zonotopic fault detection (FD) observer for discrete-time descriptor systems subject to additive actuator faults. The considered descriptor systems are also perturbed by unknown-but-bounded uncertainties including state disturbances and measurement noise. Under a set-based framework, the effects of uncertainties and faults are separated into two state zonotopes. Based on this decomposition, the FD observer gain is designed to be robust against uncertainties and meanwhile sensitive to faults based on a H − index in a finite-frequency domain. Then, two linear matrix inequality (LMI) conditions are obtained to design an observer that achieves robustness and fault sensitivity at the same time. The generalised KYP lemma is applied to address the fault sensitivity condition. The optimal FD observer gain can be obtained via an offline design procedure. Finally, the proposed fault detection method is applied to a chemical mixing system and the effectiveness is shown.

Advances in State Estimation, Diagnosis and Control of Complex Systems

“…This chapter presents set-based FDI strategies for discrete-time descriptor systems. The contributions of this chapter have been submitted in [149] and [151]. In this chapter, we apply the set-based framework proposed in Chapter 2 into FDI for discrete-time descriptor systems.…”

Union and Intersection Operators for Thick Ellipsoid State Enclosures: Application to Bounded-Error Discrete-Time State Observer Design

“…needs to be found. An optimization of this solution is possible by a minimization of trace P I k+1 , (replacing the optimization task involving the logarithm of the shape matrix determinant according to [45] Appendix C), where for a polytopic representation of the domain [N k+1 ] according to (21) the entry-wise defined vertices of the matrix inverse…”

“…Computations of ellipsoidal enclosures inherently have the property of a constant complexity if they are applied recursively. In addition, their enclosure quality enhances automatically for reducing domain sizes which is in contrast to the propagation of polytopic and zonotopic domains [21,22]. There, the number of vertices of the solution setsespecially after intersecting the results of measurement-based innovation steps with the outcome of state prediction stages-tends to increase in each time step.…”