Compensation for state‐dependent nonlinearity in a modified repetitive control system |
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| Authors: | Lan Zhou Jinhua She Shaowu Zhou Chaoyi Li |
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| Affiliation: | 1. School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China;2. School of Automation, China University of Geosciences, Wuhan, China;3. Hubei Key Laboratory of Advanced Control and Intelligent Automation for Complex Systems, Wuhan, China;4. School of Engineering, Tokyo University of Technology, Tokyo, Japan |
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| Abstract: | This paper presents an estimation and compensation of state‐dependent nonlinearity for a modified repetitive control system. It is based on the equivalent‐input‐disturbance (EID) approach. The nonlinearity is estimated by an EID estimator and compensated by incorporation of the estimate into the repetitive control input. A two‐dimensional model of the EID‐based modified repetitive control system is established that enables the preferential adjustment of control and learning actions by means of 2 tuning parameters. The singular‐value‐decomposition technique and Lyapunov stability theory are used to derive a linear‐matrix‐inequality–based asymptotic stability condition. Exploiting the stability condition and an overall performance evaluation index, a design algorithm is developed. Simulation results for the tracking control of a chuck‐workpiece system show that the method not only compensates state‐dependent nonlinearity but also improves the tracking performance for the periodic reference input, thereby demonstrating the validity of the method. |
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| Keywords: | repetitive control equivalent input disturbance disturbance rejecting two‐dimensional system linear matrix inequality |
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