Closed-Loop Control of the Motion of a Sphere Rolling on a Moving Horizontal Plane |
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| Authors: | Yavin Y Ehlers G W Frangos C |
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| Institution: | (1) Laboratory for Decision and Control, Department of Electrical and Electronic Engineering, University of Pretoria, Pretoria, South Africa;(2) Laboratory for Decision and Control, Department of Electrical and Electronic Engineering, University of Pretoria, Pretoria, South Africa;(3) Laboratory for Decision and Control, Department of Electrical and Electronic Engineering, University of Pretoria, Pretoria, South Africa |
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| 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. |
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| Keywords: | Rolling sphere nonholonomic constraints path controllability closed-loop control |
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