Finite-time stabilization of an overhead crane with a flexible cable

The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system which may serve as a model for the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is assumed to be described by the wave equation with constant coefficients. Using a nonlinear...

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Bibliographic Details
Published in:Mathematics of control, signals, and systems signals, and systems, 2019-06, Vol.31 (2), p.1-19
Main Authors: d’Andréa-Novel, Brigitte, Moyano, Iván, Rosier, Lionel
Format: Article
Language:English
Subjects:
Communications Engineering
Control
Cranes
Hybrid systems
Mathematics
Mathematics and Statistics
Mechatronics
Networks
Nonlinear feedback
Original Article
Robotics
Stabilization
Systems Theory
Wave equations
Well posed problems
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Summary:The paper is concerned with the finite-time stabilization of a hybrid PDE-ODE system which may serve as a model for the motion of an overhead crane with a flexible cable. The dynamics of the flexible cable is assumed to be described by the wave equation with constant coefficients. Using a nonlinear feedback law inspired by those given by Haimo (SIAM J Control Optim 24(4):760–770, 1986 ) for a second-order ODE, we prove that a finite-time stabilization occurs for the full system platform + cable. The global well-posedness of the system is also established by using the theory of nonlinear semigroups.
ISSN:0932-4194
1435-568X
DOI:10.1007/s00498-019-0235-7