Analysis of set-theoretic unknown input observer and interval observer in robust fault detection

Abstract

This paper focuses on comparing fault detection (FD) performance of two robust FD approaches, namely the set-theoretic unknown input observer-based approach and the interval observer-based approach. The former is implemented using the set theory and the unknown input observer (UIO), where the set theory and the UIO are used to decouple the effect of unknown inputs in passive and active ways, respectively. The latter is based on the set theory and the Luenberger observer, which completely relies on the set-based passive decoupling to obtain FD robustness. The former is a new method recently proposed by the authors, while the latter is a well-known robust FD method. The objective of this paper is to analyze these two FD approaches in a systematic way and to compare their FD sensitivity based on mathematical analysis. Eventually, an explicit criterion used to choose which method is better for FD of a system is given by using invariant sets. At the end of this paper, an example is used to illustrate the obtained results.