Control of mechanical motion systems with non-collocation of actuation and friction: A Popov criterion approach for input-to-state stability and set-valued nonlinearities

  • Authors:

  • J. C. A. de Bruin;A. Doris;N. van de Wouw;W. P. M. H. Heemels;H. Nijmeijer

  • Affiliations:

  • Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, NL 5600 MB Eindhoven, The Netherlands;Shell International Exploration and Production B.V., Keslerpark 1, 2288 GS Rijswijk, The Netherlands;Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, NL 5600 MB Eindhoven, The Netherlands;Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, NL 5600 MB Eindhoven, The Netherlands;Eindhoven University of Technology, Department of Mechanical Engineering, P.O. Box 513, NL 5600 MB Eindhoven, The Netherlands

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2009

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Abstract

The presence of friction in mechanical motion systems is a performance limiting factor as it induces stick-slip vibrations. To appropriately describe the stiction effect of friction, we adopt set-valued force laws. Then, the complete motion control system can be described by a Lur'e system with set-valued nonlinearities. In order to eliminate stick-slip vibrations for mechanical motion systems, a state-feedback control design is presented to stabilize the equilibrium. The proposed control design is based on an extension of a Popov-like criterion to systems with set-valued nonlinearities that guarantees input-to-state stability (ISS). The advantages of the presented controller is that it is robust to uncertainties in the friction and it is applicable to systems with non-collocation of actuation and friction where common control strategies such as direct friction compensation fail. Moreover, an observer-based output-feedback design is proposed for the case that not all the state variables are measured. The effectiveness of the proposed output-feedback control design is shown both in simulations and experiments for a typical motion control system.