Active Fault Diagnosis for LPV Systems with Unknown Disturbances: A Two-Step-Based Set-Membership Observer Approach

The active fault diagnosis (AFD) problem is investigated for linear parameter-varying (LPV) systems subject to unknown disturbances, including both bounded and unbounded types. In this paper, a two-step-based set-membership observer approach is presented by integrating an unknown input observer with reachability analysis. This approach decouples partial unknown disturbances from the state error dynamics and further mitigates their impact on the error reachable sets. Then, the observer gain is derived based on the F-W -radius criterion of zonotopes in order to minimize the size of the error reachable sets. Furthermore, an optimization problem is formulated to obtain the optimal auxiliary signal, and the event-triggered AFD scheme is designed to limit the frequency of the signal injection into the system. The main objective of this work is to achieve set-membership estimation for the system state via the designed observer, while separating the estimated state sets of different system modes with the aid of the auxiliary signal. Finally, the effectiveness of the proposed AFD method is illustrated through a numerical example and an industrial gas pipeline model. Note to Practitioners-In practical industrial systems, there are many unknown disturbances whose boundaries are unknown or difficult to determine in advance, caused by large-scale fluctuations of industrial loads, which are referred to as unbounded disturbances in this paper. However, most existing deterministic AFD methods assume that the system disturbances and noise are unknown but bounded. To address this issue, this paper proposes a novel AFD method based on a two-step set-membership observer. In step 1, an unknown input observer is designed to achieve the decoupling of unbounded disturbances from the state error dynamics. In step 2, the error reachable sets are derived through reachability analysis, thereby obtaining the state set-membership estimation results. Moreover, the event-triggered AFD scheme is developed to limit the frequency of the auxiliary signal injection into the system, thereby mitigating its impact on system operation. Experimental results from both a numerical example and an industrial gas pipeline model demonstrate the feasibility and effectiveness of the proposed method.