Link between high-gain observer-based and parity space residuals for FDI

Abstract

This paper deals with residual generation methods for nonlinear model-based fault detection and isolation (FDI) systems. More specifically, a differential relationship between nonlinear parity space residuals (based on analytical redundancy relations) and high-gain observer-based residuals is emphasized. The first part of this paper presents the nonlinear affine state space model, which is considered to generate residuals in the following. In order to design the high-gain observer, a nonlinear transformation is used to put the model under its observable canonical form (OCF). The two residual generation approaches are detailed in the second part. The result of the paper is then established: we express explicitly a differential relationship between the two residuals and so extend in a more general framework the well known result that was established for linear and linearizable systems by input/output injection. A model of a series DC motor is considered to illustrate the theoretical result and simulations results are presented.