Set Invariance Approach for Fault Detection and Isolation in Lure Systems by LPV-embedding

Abstract

This paper analyses conditions for computing invariant sets for Lure-type nonlinear systems via two different approaches, by bounding the nonlinear terms and by embedding the nonlinear system in a linear parameter varying (LPV) model. Furthermore, we show that by an appropriate redefinition of the system's nonlinear terms, the sets obtained by both approaches can be made identical. These methods can be used to compute sets characterising faultless (nominal) and faulty system behaviour, which are applicable for fault diagnosis under specific conditions that guarantee their separation. We also present a simple mechanism for sensor fault estimation and controller compensation, thus resulting in a closed-loop fault tolerant control system. An example of a pendulum system is provided to illustrate the proposed approach.