A Disturbance Decoupling Generalized Proportional–Integral Observer Design for Robust Sensor Fault Detection

This article presents a novel disturbance decoupling generalized proportional–integral observer (DD-GPIO) for the early detection of sensor faults in dynamic systems subject to external semistationary periodic disturbances. The focus is to reduce the adverse impacts caused by the disturbance whose spectrum is uneven with some dominant frequencies. This achieved in a two-stage design procedure. In the first stage of zero-assignment, the additional zeros introduced by the state transition matrix of GPIO are allocated near the disturbance frequencies to construct a rank-deficient disturbance transfer function matrix (DFTM) relating from the disturbances to the fault detection residuals. In the second stage, an additional gain matrix is applied to the output estimation error before the error is fed into the GPIO. The additional matrix can be designed by using the eigenvector of zero eigenvalue of the rank deficient DFTM, such that the periodic perturbations can be completely decoupled from the fault detection residual for better performance in fault detection. The conditions to achieve disturbance decoupling is given. Finally, a novel condition number-based sensitivity objective is proposed to optimize the DD-GPIO's poles. Simulation and a two-wheeled robot experiment illustrate the outperformance of the DD-GPIO in decoupling periodic disturbances and detecting minor sensor faults.