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Global convergence for two-pulse rest-to-rest learning for single-degree-of-freedom systems with stick-slip Coulomb friction

Published online by Cambridge University Press:  01 May 2006

Brian J. Driessen  and
Nader Sadegh
Brian J. Driessen*
Affiliation:
Mechanical Engineering Department, Wichita State University, Wichita, KS 67260, USA.
Nader Sadegh
Affiliation:
Department of Mechanical Engineering, Georgia Institute of Technology, Atlanta, GA 30332, USA.
*
*Corresponding author. E-mail: brian.driessen@wichita.edu
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Summary

In this paper, we consider the problem of rest-to-rest maneu-ver learning, via iterative learning control (ILC), for single-degree-of-freedom systems with stick-slip Coulomb friction and input bounds. The static coefficient of friction is allowed to be as large as three times the kinetic coefficient of friction. The input is restricted to be a two-pulse one. The desired input's first pulse magnitude is required to be five times the largest possible kinetic (sliding) friction force. The theory therefore allows the stiction force to be as large as the desired second input pulse. Under these conditions, we prove global convergence of a simple iterative learning controller. To the best of our knowledge, such a global-convergence proof has not been presented previously in the literature for the rest-to-rest problem with stick-slip Coulomb friction.

Keywords

Rest-to-rest maneuverIterative learning control (ILC)Coulomb frictionConvergence theoryInput bounds/limitsSingle-degree-of-freedom system
Type
Article
Information
Robotica , Volume 25 , Issue 3 , May 2006 , pp. 307 - 313
Copyright
Copyright © Cambridge University Press 2006

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