Zero-assignment and complex coefficient gain design of generalized proportional-integral observer for robust fault detection |
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| Institution: | 1. College of Science, Hohai University, Nanjing 210098, China;2. National Research Base of Intelligent Manufacturing Service, Chongqing Technology and Business University, Chongqing, 400067, China;1. School of Artificial Intelligence and Automation, Beijing University of Technology, Beijing 100124, PR China;2. Engineering Research Center of Intelligent Perception and Autonomous Control, Ministry of Education, Beijing 100124, PR China;3. Key Laboratory for Precision and Non-traditional Machining Technology of Ministry of Education, Dalian University of Technology, Dalian 116024, PR China;1. Electrical Engineering Department, Faculty of Engineering, Cairo university, Egypt;2. Department of Mechatronics, Faculty of Engineering, Autonomous University Carmen, Cd. del Carmen 24180, Mexico;3. Departamento de Control Automatico, CINVESTAV, A.P. 14-740, Mexico D.F. CP 07000, Mexico;1. School of Mathematics and Statistics, Wuhan University, Wuhan 430072, China;2. School of Finance, Nanjing Audit University, Jiangsu 211815, China;3. School of Data Science & Engineering, South China Normal University, Guangdong 516600, China |
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| Abstract: | 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. |
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