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

Abdelhadi Elharfi

Mathematical Problems in Engineering, 2010, vol. 2010, 1-12

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†.

Date: 2010
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:984927

DOI: 10.1155/2010/984927

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