Closed-loop Optimal Fault Detection for Uncertain Systems

Abstract

Faults compromise the reliability and safety of complex engineering systems. The aim of this article is to address the problem of robust fault detection filter design for continuous-time linear time-invariant uncertain systems in open-loop or closed-loop configurations. The developed method offers a unified approach to handle parametric and dynamic uncertainties by solving a single Riccati equation, based on a worst-case disturbance and uncertainty model. This worst-case model is obtained by nonlinear optimization and application of the boundary Nevanlinna-Pick method. The efficacy of the proposed approach is demonstrated using an uncertain model of an experimental reticle stage used in the lithography industry. The results illustrate that an optimal compromise is achieved between sensitivity to faults and rejection of modelling uncertainties and disturbances on the other hand. This capability enables the clear differentiation between faults and undesired effects in residuals, thereby enhancing fault detection reliability, ultimately contributing to improved safety and performance of machines.