High-order Sliding-mode Differentiator Based Actuator Fault Diagnosis For Linear Systems with Arbitrary Relative Degree and Unmatched Unknown Inputs

Many existing fault diagnosis schemes require two either implicit or explicit assumptions. An 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. The other is that the unknown inputs, if present, satisfy certain matching conditions. Little result exists for systems with relative degree not necessarily less than one and with unmatched unknown inputs. In this paper, in order to remove the relative degree assumption and to allow the presence of unmatched unknown inputs, four actuator fault diagnosis problems are studied for a general class of linear systems. These are: P1) Under what conditions can actuator faults be detected?; P2) Is actuator fault isolation possible, and if yes, how many actuator faults can be isolated simultaneously?; P3) Is it possible to estimate the shape of the actuator faults?; P4) What is the design approach for accomplishing these objectives? The above problems are solved via using both the outputs and their high-order derivatives. Because only the outputs are measured, higher-order output derivatives are estimated using the recently developed high-order sliding-mode robust differentiators (HSMRDs). The solutions for the first two problems are based on a concept called actuator fault isolation index (AFIX). Using this concept, it is proved that, under some conditions, actuator faults are detectable if and only if AFIX ges 1, and l actuator faults can be isolated if and only if AFIX ges l + 1. For the third problem, a method which can be used to estimate the faults is proposed. To solve the fourth problem, an actuator fault diagnosis scheme is designed using both the measured outputs and their estimated derivatives obtained by HSMRDs. Finally, an example is given to show the effectiveness of our fault diagnosis scheme in terms of fault detection, isolation and estimation