On the design of an unknown input observer to fault detection, isolation, and estimation for uncertain multi-delay nonlinear systems

Abstract

In this article, an unknown input observer (UIO) is proposed for fault detection and isolation (FDI) for uncertain nonlinear time-delay systems with multiple discrete delays. The presented UIO can be able to isolate both actuator and sensor faults and estimate them to identify the shape, time of occurrence, amplitude, and other features of the faults. Furthermore, the proposed FDI method is robust to both input/state and output disturbances. At first, the system dynamics and faults are augmented and then UIO is driven. A delay-independent Lyapunov–Krasovskii functional is utilized to guarantee the stability of the proposed UIO-based FDI method. The terms of stability and UIO gains are obtained by solving some feasible linear matrix inequalities (LMI). The proposed method is simulated on two interconnected well-mixed non-isothermal continuous stirred tank reactors (CSTRs) with recycling where there are three parallel, irreversible elemental exothermic reactions. Two point-wise time delays in the output temperature and concentration in both CSTRs are considered. Furthermore, parametric uncertainties in the modeling are investigated. The simulation and numerical results show the superiority of the proposed UIO for fault detection, isolation, and estimation in the presence of multiple discrete time delays, model uncertainty, and input/state and output disturbances.