Conservatism Comparison of State Estimation Error and Residual in Multiple Actuator Faults Detection

This paper focuses on analyzing and comparing the performance of two robust fault detection (FD) criteria for discrete-time linear parameter varying (LPV) systems with bounded uncertainties, namely the state estimation error-based criterion and the classical residual-based criterion. First, a new FD criterion for the detection of multiple multiplicative actuator faults is proposed by testing consistency between the state estimation errors and the healthy state estimation error sets on-line. Then, a guaranteed FD condition is established based on set-separation of healthy and faulty invariant sets of state estimation error. Moreover, the generalized minimum detectable fault (MDF) for multiple actuator faults is defined and computed in order to characterize the performance of the two FD criteria. Finally, a proof is provided to compare the conservatism of the FD criterion using state estimation errors with the classical one based on residuals. At the end of this paper, a numerical example is used to illustrate the effectiveness of the obtained results.