Fault Diagnosis Observer Design For Descriptor Systems

Descriptor system which consists in dynamic characteristics and static constraints is more general than the state-space model. It is known that the study of descriptor systems is more complicated than of state-space systems because the former has a more complex structure. Currently, although much effort has been made in the analysis and design of descriptor systems, there are few results on fault diagnosis for descriptor systems. There-fore, this thesis focuses on model-based fault diagnosis methods for descriptor systems. The main contributions of this thesis consist in the following aspects.The problem of Observer design for descriptor systems is studied. For linear de-scriptor systems, we propose a new observer structure, present a design method based on Linear Matrix Inequality (LMI), and give the existence condition of the observer. The proposed observer provides some fundamental results in the fault diagnosis methods for descriptor systems. Moreover, note that descriptor observer is an effective fault diagnosis approach for state-space systems, the proposed observer is also applied to fault diagnosis for discrete-time state-space systems.Adaptive fault diagnosis observer design is studied for continuous-time descriptor systems. An LMI-based method is proposed to design adaptive fault diagnosis observer for linear descriptor systems, and the existence condition for the adaptive observer is also discussed. Furthermore, the proposed method is extended to a class of Lipschitz nonlinear descriptor systems.Robust fault diagnosis for continuous-time descriptor systems is investigated based on augmented observer. First, we propose an augmented observer-based fault diagnosis method for linear descriptor systems and give the existence condition for the augmented observer. Then, a multi-objective approach is presented to design augmented observer for linear descriptor systems with unknown disturbances. This method attenuates the effect of disturbances on fault estimation by using H∞technique, and the fault estimation speed is also considered in this method. The proposed robust augmented observer design is formulated as a feasibility problem of LMIs. Based on this fundamental result, we further investigate the fault diagnosis method in Lipschitz nonlinear descriptor systems.Fault diagnosis for discrete-time descriptor systems is also addressed in this thesis. For discrete linear descriptor systems with actuator fault, we present an observer-based fault diagnosis filter design method. No assumption on fault dynamics is required in this method and the fault can be estimated fast and accurately. Then, the proposed method is extended to discrete linear descriptor systems with sensor fault. Moreover, the dedicated observer scheme is used to achieve fault isolation.For discrete Linear Parameter-Varying (LPV) descriptor systems with actuator fault, we propose a fault diagnosis approach based on augmented observer. In this method, all parameter matrices of the fault diagnosis observer can be determined simultaneous-ly by solving a set of LMIs. Considering the fault variation, unknown disturbance and measurement noise in practical systems, a robust augmented observer design method is further proposed to improve the robustness of the fault diagnosis observer.