Robust Fault Detection for Uncertain Discrete-Time Systems

Abstract

The fault detection problem under structured uncertainties in the system matrices is considered. The sensitivity of robust fault detection is one of the important issues considered in the fault detection and isolation development. To enhance this characteristic, an unconstrained optimization approach is taken to design a robust fault detection observer. The approach aims at enhancing the fault detection robustness to uncertainties without sacrie cing the faultdetectionsensitivity,whichwasseldomaddressedbefore.Furthermore,otherobjectivesrelatedtotheobserver gain and the eigenstructure conditioning of the observer system are also taken into account. The gradient-based optimization approach is facilitated by the explicit gradient expressions derived. Numerical simulation has also demonstrated the tradeoffs between different objectives as well as the effectiveness of the present methodology. I. Introduction T HE research and application of fault detection and isolation in automated processes has received considerable attention during thelast twodecades, 1i6 both ina research contextandalsointhe domain of application studies on real processes. One area of active research isthe developmentofmodel-basedfaultdetection systems. There are a great variety of methods in the literature to construct model-based fault detection systems. One of them, using observer techniques, has received much attention in the past. Modern technology has increasingly led to the creation of highly complex dynamic systems that have demanding performance requirements in a variety of environments. These systems must be capable of meeting stringent specie cations for reliability and operational safety over long periods of time, while operating under a great deal of uncertainty. However, in practice, such as in chemical processes or aerospace systems, fully accurate mathematical models of the systems cannot be obtained. There is always a mismatch between the actual process and its mathematical model even if there is no fault in the process. Such inaccuracies may give rise to false alarms and, thus, corrupt the performance of the fault detection system, which may even render it useless. To overcome this dife culty, the fault detection system has to be made robust, that is, insensitive or even invariant to such modeling errors. More specifically, a mere reduction of the sensitivity to modeling errors does