Design of Linear Residual Generators for Combined Fault Detection and Estimation in Nonlinear Systems

TL;DR

This paper presents a systematic method for designing linear residual generators that can detect and estimate faults in nonlinear systems, ensuring disturbance decoupling and verified through a chemical reactor case study.

Contribution

It introduces explicit design formulas for residual generators in nonlinear systems with necessary and sufficient conditions, advancing fault detection and estimation techniques.

Findings

Design formulas for residual generators are explicitly derived.

Residual generators effectively detect and estimate faults in nonlinear systems.

Method validated on a chemical reactor case study.

Abstract

A systematic method for the design of linear residual generators for combined fault detection and estimation in nonlinear systems is developed. The proposed residual generator is a linear functional observer built for an extended system that incorporates the fault dynamics from a linear exo-system, and in addition possesses disturbance-decoupling properties. Necessary and sufficient conditions for the existence of such residual generators for nonlinear systems are derived. As long as these conditions are satisfied, we obtain explicit design formulas for the residual generator. The results are illustrated through a chemical reactor case study, which demonstrates the effectiveness of the proposed methodology.