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Journal Articles ESAIM: Control, Optimisation and Calculus of Variations Year : 2021

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 coupled 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 finite-time 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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Origin : Publication funded by an institution

Dates and versions

hal-03368719 , version 1 (06-10-2021)

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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. ESAIM: Control, Optimisation and Calculus of Variations, 2021, 27, pp.94. ⟨10.1051/cocv/2021090⟩. ⟨hal-03368719⟩
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