Abstract

Singular perturbations technique is a means of taking into account neglected high-frequency and parasitic phenomena into modeling systems by decoupling the representation into separate slow and fast time-scales. The practical advantages of a singular perturbation in model order are significant, since the order of every real dynamical system is higher than that of the model used to represent the system. This thesis focus is emphasized on the fault diagnosis of two time-scaled singularly perturbed systems. By decoupling the original full-order system into higher-order slow and fast subsystem models, our goal is to design a composite diagnoser based on diagnosers designed for the two subsystems to detect and isolate the faults in the original full-order system. Based on a power series expansion of the exact slow manifold associated with the original model around [varepsilon] = 0 , higher-order corrections of the manifold are obtained. Conditions are formulated for which a composite diagnoser can be designed for the original full-order system. Satisfying the conditions of a geometric approach, this composite diagnoser is used to diagnose the faults in the original full-order system. The illustrated methodology is applied to a two time-scale aircraft longitudinal dynamical model as well as the four degree of freedom gyroscope.