Zero-assignment and complex coefficient gain design of generalized proportional-integral observer for robust fault detection

• Published in: Journal of the Franklin Institute Vol. 359; no. 8; pp. 3831 - 3856
• Main Authors: Hu, Yuxiang, Dai, Xuewu, Cui, Dongliang, Jia, Zhian
• Format: Journal Article
• Language: English
• Published: Elmsford Elsevier Ltd 01.05.2022; Elsevier Science Ltd
• Subjects: Coefficients; Disturbances; Dynamical systems; Eigenvalues; Eigenvectors; Fault detection; Fault diagnosis; Optimization; Proportional integral; Robustness (mathematics); Signal processing; Transfer functions; Zero assignment
• ISSN: 0016-0032; 1879-2693; 0016-0032
• DOI: 10.1016/j.jfranklin.2022.03.021

•Zero assignment to make the transfer function matrix (TFM) from the disturbance to the residual rank-deficient at the disturbance frequencies.•Complex coefficient gain in residual evaluation is proposed to exploit the unique feature of rank-deficiency of the disturbance TFM.•A new optimization objective function based on the difference of the maximum singular value of the transfer function matrix is proposed. [Display omitted] Aiming at early detection of faults in dynamic systems subject to external periodic disturbances, this paper proposes a new generalized proportional-integral observer (GPIO) fault detection scheme with zero-pole joint optimization and novel complex coefficient gain (CCG) of residual evaluation. The focus of the proposed scheme is to reduce the adverse impacts caused by the semi-stationary periodic disturbance whose spectrum is uneven, with most energy being at some dominant frequencies. The proposed GPIO with a complex coefficient gain is designed in a two-stage procedure. In the first stage of zero assignment and pole optimization, the additional zeros introduced by the GPIO’s integration action are allocated to near the disturbance frequency. The gain of the transfer function matrix relating from the disturbances to the fault indicator signals is minimized by pole optimization. In the second stage of designing complex coefficient gain in residual evaluation, the unique feature of rank-deficient caused by the additional zeros assigned in stage one is further exploited to cancel the disturbances in the fault indicator signals (which is also referred to as the fault detection residual in this article). It is proved that, for an arbitrary periodic disturbance with a specific spectrum, the remnant components of the disturbance in the indicator signals generated by the GPIO can cancel each other by a complex gain vector, which can be determined by the zero eigenvalue’s left eigenvector of the rank-deficient of the disturbance transfer function matrix. The sufficient conditions for the convergence of the proposed fault detection filter are also given. Numerical examples illustrate the proposed method’s better performance in detecting minor faults.