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Closed-Loop Control of the Motion of a Sphere Rolling on a Moving Horizontal Plane

Author

Listed:
  • Y. Yavin

    (University of Pretoria)

  • G. W. Ehlers

    (University of Pretoria)

  • C. Frangos

    (University of Pretoria)

Abstract

A uniform sphere is rolling without slipping on a horizontal plane. The motion of the sphere is controlled via the control of the acceleration of the plane. At the time t=0, the sphere and the plane are stationary and the center of the sphere is located at a point A in the plane. Given a time interval [0, t f], the problem dealt with here is: Find a closed-loop strategy for the acceleration of the moving plane such that, at the time t=t f, the plane and the sphere will be nearly at rest and the center of the sphere will be in a given neighborhood of the origin. By introducing the concept of path controllability, a closed-loop strategy for the solution of the above-mentioned problem is proposed and its efficiency is demonstrated by solving numerically some examples.

Suggested Citation

  • Y. Yavin & G. W. Ehlers & C. Frangos, 1997. "Closed-Loop Control of the Motion of a Sphere Rolling on a Moving Horizontal Plane," Journal of Optimization Theory and Applications, Springer, vol. 92(2), pages 377-391, February.
  • Handle: RePEc:spr:joptap:v:92:y:1997:i:2:d:10.1023_a:1022663331512
    DOI: 10.1023/A:1022663331512
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