Development of A Guaranteed Minimum Detectable Sensor Fault Diagnosis Scheme

The paper deals with the estimation of sensor faults for dynamic systems as well as the assessment of the uncertainty of the resulting estimates. For that purpose, it is assumed that the external disturbances are bounded within an ellipsoidal domain. This allows considering both stochastic and deterministic process and measurement uncertainties. Under such an assumption, a fault diagnosis scheme is developed with a prescribed convergence rate and accuracy. To achieve fault estimation, a conversion into an equivalent descriptor system is utilized. The paper provides a full stability and convergence analysis of the estimator including observability analysis. As a result, a set of complementary fault uncertainty intervals is obtained, which are minimized in such a way as to obtain a minimum detectable sensor fault. The final part of the paper exhibits a numerical example concerning fault estimation of a multi-tank system. The obtained results clearly confirm the performance of the proposed estimator expressed in the minimum detectable fault intervals.