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Finite-time stabilization of an overhead crane with a flexible cable submitted to an affine tension

Abstract : The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system describing the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is described by the wave equation with a variable coefficient which is an affine function of the curvilinear abscissa along the cable. Using several changes of variables, a backstepping transformation, and a finite-time stable second-order ODE for the dynamics of a conveniently chosen variable, we prove that a global finitetime stabilization occurs for the full system constituted of the platform and the cable. The kernel equations and the finite-time stable ODE are numerically solved in order to compute the nonlinear feedback law, and numerical simulations validating our finite-time stabilization approach are presented.
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https://hal.archives-ouvertes.fr/hal-03141490
Contributor : Marc Wijnand <>
Submitted on : Monday, February 15, 2021 - 12:03:41 PM
Last modification on : Thursday, February 18, 2021 - 3:32:01 AM

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  • HAL Id : hal-03141490, version 1

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Marc Wijnand, Brigitte d'Andréa-Novel, Lionel Rosier. Finite-time stabilization of an overhead crane with a flexible cable submitted to an affine tension. 2021. ⟨hal-03141490⟩

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