Brief paper: Analysis of undercompensation and overcompensation of friction in 1DOF mechanical systems

  • Authors:

  • Devi Putra;Henk Nijmeijer;Nathan van de Wouw

  • Affiliations:

  • School of Electrical Engineering and Informatics, Institut Teknologi Bandung, Jl. Ganesha 10, Bandung 40132, Indonesia;Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands;Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB Eindhoven, The Netherlands

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2007

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Abstract

This paper investigates the effects of undercompensation and overcompensation of friction in PD controlled 1DOF mechanical systems. The friction force that is acting on the mechanical system and the friction compensation term in the feedback loop are described by a class of discontinuous friction models consisting of static, Coulomb and viscous friction, and including the Stribeck effect. Lyapunov's stability theorem and LaSalle's invariance principle are applied to prove that undercompensation of friction leads to steady-state errors and the properties of the @w-limit set of trajectories of a two-dimensional autonomous differential inclusion are used to show that overcompensation of friction may induce limit cycling. Furthermore, the analysis also indicates that the limit cycling effect can be eliminated by tuning the PD controller gains.