Mixed Active/Passive Robust Fault Detection and Isolation Using Set-Theoretic Unknown Input Observers

Abstract

This paper proposes a robust fault detection and isolation (FDI) approach that combines active and passive robust FDI approaches. Standard active FDI approaches obtain robustness by using the unknown input observer (UIO) to decouple unknown inputs from residuals. Differently, standard passive FDI approaches achieve robustness by using the set theory to bound the effect of uncertain factors (disturbances and noises). In this paper, we combine the UIO-based and the set-based approaches to produce a mixed robust FDI, which can mitigate the disadvantages and exert the advantages of the two robust FDI approaches. In order to emphasize the role of set theory, the UIO design based on the set theory is named as the set-theoretic UIO (SUIO). A quadrotor subsystem is used to illustrate the effectiveness of the proposed FDI approach. Note to Practitioners —The proposed SUIO-based approach achieves robustness in FD against disturbances, noises, and modeling uncertainties (e.g., linearization errors) either by decoupling or by bounding their effect on the residuals. Moreover, this approach allows FI by generating a set of structured residuals decoupling the effect of faults. The authors think that this method can be used for processes that operate around equilibrium points. In this case, we can linearize the nonlinear systems into linear systems with bounded unknown inputs and then apply the proposed method. Moreover, an important feature of this method is that it can overcome the design condition of the standard UIO approach, which means that it could be applied to a larger number of applications.