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Compensation for state‐dependent nonlinearity in a modified repetitive control system
Author(s) -
Zhou Lan,
She Jinhua,
Zhou Shaowu,
Li Chaoyi
Publication year - 2017
Publication title -
international journal of robust and nonlinear control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.361
H-Index - 106
eISSN - 1099-1239
pISSN - 1049-8923
DOI - 10.1002/rnc.3865
Subject(s) - control theory (sociology) , repetitive control , nonlinear system , estimator , compensation (psychology) , exponential stability , stability (learning theory) , linear matrix inequality , singular value decomposition , lyapunov function , computer science , lyapunov stability , mathematics , control system , control (management) , engineering , mathematical optimization , algorithm , artificial intelligence , psychology , statistics , physics , quantum mechanics , machine learning , psychoanalysis , electrical engineering
Summary 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.