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Journal of Vibration and Control
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Article

Vibration Control on a Pulse and Ramp Driven System with Friction

Kuo-Kai Shyu1, Yun-Yao Lee2*, and Ruh-Hua Wu3

1 Department of Electrical Engineering, National Central University, Taiwan, Republic of China
2 Department of Electrical Engineering, National Central University, and Lecturer, Chin-Yun University of Technology, Taiwan, R.O.C.
3 Actuation System, Chung-Shan Institute of Science and Technology, Taiwan, Republic of China

* To whom correspondence should be addressed.


  Abstract

This paper investigates the sufficient stability condition of a three-phase proportional gain, pulse, and ramp (PPR) controller for pointing systems under the influence of friction. With the ramp and pulse schemes integrated, the PPR controller has been demonstrated to be an effective control strategy for fast and precise pointing applications. In this paper the LuGre model is used to derive the upper bounds of the ramp slope Sr for the sufficient stability condition to suppress vibrations around the [–0.5, +0.5] µm target region. Our study reveals that the frictional stiffness {sigma}0 and the micro viscous damping coefficient {sigma}1 in the LuGre model are required for the bounds of Sr. With the derived bounds of Sr, the Lyapunov direct method is applied to prove the stability of the PPR controller.

Key Words: nonlinear system, friction, pointing control, Lyapunov stability.

First published on March 31, 2009, doi:10.1177/1077546309102671

Journal of Vibration and Control 2009;15:1763.

A more recent version of this article appeared on December 1, 2009

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