Brief paper: Tracking and disturbance rejection for fully actuated mechanical systems

  • Authors:
  • Bayu Jayawardhana;George Weiss

  • Affiliations:
  • Department of Discrete Technology and Production Automation, The University of Groningen, 9747 AG Groningen, The Netherlands;Department of Electrical Engineering-Systems, Tel Aviv University, Ramat Aviv 69978, Israel

  • Venue:
  • Automatica (Journal of IFAC)
  • Year:
  • 2008

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Abstract

In this paper, we solve the tracking and disturbance rejection problem for fully actuated passive mechanical systems. We assume that the reference signal r and its first two derivatives r@?,r@? are available to the controller and the disturbance signal d can be decomposed into a finite superposition of sine waves of arbitrary but known frequencies and an arbitrary L^2 signal. We combine the internal model principle with the ideas behind the Slotine-Li adaptive controller. The internal model-based adaptive controller that we propose causes the closed-loop state trajectories to be bounded, and the tracking error and its derivative to converge to zero, without any prior knowledge of the plant parameters. An important part of our results is that we prove the existence and uniqueness of the state trajectories of the closed-loop system.