Actuator fault diagnosis for uncertain linear systems using a high-order sliding-mode robust differentiator (HOSMRD)

Many observer-based fault diagnosis strategies proposed for linear systems, subject to unknown inputs, operate based on three assumptions. The first assumption is that the system under consideration is at least detectable. The second one is that the unknown inputs satisfy certain matching conditions. The third one, which is often implicit, is that the relative degrees from the generalized input vector, including both known and unknown inputs, to the outputs are no larger than one. If none of these assumptions are met, little result exists on how to carry out fault diagnosis. The purpose of this paper is to develop a novel actuator fault diagnosis scheme for a general class of linear systems subject to unknown inputs that can work without the mentioned three assumptions. Four actuator fault diagnosis problems related to fault detection, isolation, and estimation are formulated and studied. In order to solve these problems, an input-output relation, which involves only the outputs and their higher-order derivatives, is derived. The posed problems are solved based on this relation via utilizing both the outputs and their higher-order derivatives. Because only the outputs are measured, higher-order output derivatives are estimated using the recently developed high-order sliding-mode robust differentiators (HOSMRDs). The first two fault detection and isolation problems are answered in terms of a concept called Generalized Actuator Fault Isolation IndeX (GAFIX), and it is proved that, under the condition that the derived input-output relation is used for fault diagnosis, actuator faults are detectable if and only if GAFIX >= 1, and l actuator faults can be isolated if and only if GAFIX >= l + 1. A method which can be used to estimate the faults is proposed for the fault estimation problem. To solve the last problem, an actuator fault diagnosis scheme is designed using both the measured outputs and their estimated derivatives obtained by HOSMRDs, and is presented in steps. Finally, an example is provided to show the effectiveness of our fault diagnosis scheme in terms of fault detection, isolation, and estimation. Copyright (C) 2007 John Wiley & Sons, Ltd.