A generalized proportional‐integral observer for fault detection: An approximate input disturbance decoupling approach

Abstract

Summary This article proposes a generalized PI observer with approximate disturbance decoupling (ADD‐GPIO) for detecting incipient actuator faults of a system subject to periodic input disturbances. Robustness to disturbances and sensitivity to faults is achieved through dynamic configuration of the disturbance transmission zeros and pole‐optimization respectively. By incorporating the v$$ v $$‐gap metric with Hprefix−$$ {H}_{-} $$ index, a novel interpretable fault sensitivity optimization objective function is proposed. It is the first time in the fault detection observer design that the difference between the transfer function matrices (TFMs) relating fault detection residual to the disturbances and faults is quantified by the proposed v$$ v $$‐gap metric, which allows a more differentiated treatment of the disturbance and fault signals for better fault detection. Then, the optimal design of the ADD‐GPIO is modeled as a mixed‐integer optimization problem and the Lagrangian relaxation is adopted to find the near‐optimal parameters of the ADD‐GPIO at less computation costs in real application. Finally, both simulation and lab experiments of a two‐wheeled self‐balancing robot are carried out to validate the improved performance of the proposed method.