Guaranteed Disturbance Compensation and Robust Fault Detection Based on Zonotopic Evaluation

Abstract

In the context of model-based fault detection, it is crucial to achieve strong robustness against disturbance and noise. However, the existing robust fault detection methods typically address disturbance and noise in a centralized manner to enhance robustness, which may cause some conservatism since the dynamic characteristics of disturbance and noise are considerably different. In addition, most of the existing model-based fault detection method is implemented with constant thresholds, which may further introduce conservatism. In this context, this paper proposes a guaranteed disturbance compensation and robust fault detection method based on zonotopic evaluation for the discrete-time systems subject to unknown but bounded disturbance and noise. To this end, a disturbance compensation controller is developed based on $L_{\infty }$ technology to obtain guaranteed control performance. Moreover, the control performances with or without disturbance compensation are analyzed based on zonotopes. By considering the disturbance dynamic characteristics, an extended fault detection observer (EFDO) is created to pursue robustness to disturbance, noise, and sensitivity to fault simultaneously. Meanwhile, a multi-objective EFDO is devised by exploiting the $L_{\infty }$ index and $H_{-}$ index as the criteria within the finite-frequency domain. Furthermore, the zonotopic residual evaluation is further deployed to generate the residual boundary, which helps to reduce the conservatism of fault detection. The superiority of the proposed method is theoretically analyzed. Simulation results also validate the effectiveness and superiority of the proposed method in disturbance compensation fault detection.