Brief Friction induced hunting limit cycles: A comparison between the LuGre and switch friction model

  • Authors:

  • R. H. A. Hensen;M. J. G. Van De Molengraft;M. Steinbuch

  • Affiliations:

  • Integrated Dynamics Engineering, Schoutlaan 4b, 6002 EA, Weert, Netherlands;Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, Netherlands;Control Systems Technology Group, Department of Mechanical Engineering, Eindhoven University of Technology, P.O. Box 513, 5600 MB, Eindhoven, Netherlands

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2003

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Abstract

In this paper, friction induced limit cycles are predicted for a simple motion system consisting of a motor-driven inertia subjected to friction and a PID-controlled regulator task. The two friction models used, i.e., (i) the dynamic LuGre friction model and (ii) the static switch friction model, are compared with respect to the so-called hunting phenomenon. Analysis tools originating from the field of nonlinear dynamics will be used to investigate the friction induced limit cycles. For a varying controller gain, stable and unstable periodic solutions are computed numerically which, together with the stability analysis of the closed-loop equilibrium points, result in a bifurcation diagram. Bifurcation analysis for both friction models indicates the disappearance of the hunting behavior for controller gains larger than the gain corresponding to the cyclic fold bifurcation point.