Fault Diagnosis of Linear Singularly Perturbed Systems

In this paper, the singular perturbation approach is used to study the diagnosability of linear two-time scale systems. Based on a power series expansion of the slow manifold aroundε = 0, higher order corrected models for both slow and fast subsystems are obtained. The diagnosability of the decomposed subsystems vary with respect to different corrected-order models. It is shown that if the original singularly perturbed system is fault diagnosable, a composite observer-based residual generator for the original system with actuator faults can be synthesized from the observers of the two separate subsystems. An example of a liner singularly perturbed system is worked out to illustrate the methodology.