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Feedback Controller Stabilizing Vibrations of a Flexible Cable Related to an Overhead Crane

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  • Abdelhadi Elharfi

Abstract

The problem of stabilizing vibrations of flexible cable related to an overhead crane is considered. The cable vibrations are described by a hyperbolic partial differential equation (HPDE) with an update boundary condition. We provide in this paper a systematic way to derive a boundary feedback law which restores in a closed form the cable vibrations to the desired zero equilibrium. Such a control law is explicitly constructed in terms of the solution of an appropriate kernel PDE. The pursued approach combines the “backstepping method†and “semigroup theory†.

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  • Abdelhadi Elharfi, 2010. "Feedback Controller Stabilizing Vibrations of a Flexible Cable Related to an Overhead Crane," Mathematical Problems in Engineering, Hindawi, vol. 2010, pages 1-12, October.
    • Handle: RePEc:hin:jnlmpe:984927
    DOI: 10.1155/2010/984927
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