Vibration control on a pulse and ramp driven system with friction

Kuo Kai Shyu, Yun Yao Lee, Ruh Hua Wu

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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 [ĝ€"0.5, +0.5] 1/4m target region. Our study reveals that the frictional stiffness σ0 and the micro viscous damping coefficient σ1 in the LuGre model are required for the bounds of S r. With the derived bounds of Sr , the Lyapunov direct method is applied to prove the stability of the PPR controller.

Original languageEnglish
Pages (from-to)1763-1781
Number of pages19
JournalJVC/Journal of Vibration and Control
Issue number12
StatePublished - Dec 2009


  • Friction
  • Lyapunov stability.
  • Nonlinear system
  • Pointing control


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