Combining set-theoretic UIO and invariant sets for optimal guaranteed robust fault detection and isolation. (June 2019) - Xu, Feng; Tan, Junbo; Wang, Ye; Puig, Vicenç; Wang, Xueqian
Highlights: A method to establish invariant set separation-based guaranteed FDI conditions for single optimal SUIO is proposed, which reduces the FDI conservatism of single observer but simultaneously obtains robust FDI guarantees. A method to design an optimal observer configuration for a bank of SUIOs is proposed, which aims to minimize the effect of all unknown inputs on guaranteed robust FDI to reduce the conservatism of a bank of observers. Abstract: This paper proposes an optimal guaranteed robust fault detection and isolation (FDI) method combing the set-theoretic unknown input observer (SUIO) and the robust positively invariant (RPI) sets for linear time-invariant (LTI) systems. The optimality of the proposed FDI method is achieved under a two-layer framework. The first layer allows to design a single optimal FDI-oriented SUIO with RPI set separation-based guaranteed FDI conditions to reduce the FDI conservatism of single observer. The second layer consists in designing an optimal observer configuration for a bank of optimal SUIOs to reduce the FDI conservatism of all the SUIOs together. Finally, the effectiveness of the proposed guaranteed robust FDI method is illustrated by using a four-tank system.