Optimal Fault Detection for Closed-Loop Linear Uncertain Systems

Robust fault detection is crucial for ensuring the reliability and safety of complex engineering systems. However, distinguishing faults from disturbances and model uncertainty which are inherently present in any practical system remains remains a challenging task. This paper addresses the robust fault detection filter design problem for continuous-time linear time-invariant uncertain systems operating in open or closed-loop configurations. The proposed framework offers a unified approach to handle both parametric and dynamic uncertainties by solving a single Riccati equation, based on a worst-case disturbance and uncertainty scenario. The efficacy of the proposed approach is demonstrated on a numerical multivariable double mass-spring-damper system. The results illustrate that an optimal compromise is achieved between fault sensitivity and rejection of modelling uncertainties and disturbances. This capability enables the clear differentiation between faults and undesired effects in the residuals, thereby enhancing fault detection reliability, ultimately contributing to improved safety and performance.