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Daniel Thull, Daniel Wild, Andreas Kugi
Infinite-dimensional Control of a Gantry Crane with Heavy Chains
This contribution deals with the application of a flatness-based open-loop tracking controller in combination with a passivity-based closed-loop controller to the infinite-dimensional model of a gantry crane with heavy chains. It turns out that the position of the load serves as a flat output. This enables us to perform the trajectory planning task in a straightforward way. The objective of the stabilizing controller of the error system is on the one hand to provide a good damping of the vibrations of the chains and on the other hand to stabilize the desired position of the cart. Furthermore, the controller has to cope with stick-slip effects which are always present in reality. By means of a suitable passivity-based controller design combined with the classical integrator backstepping approach the demands on the closed-loop system can be fulfilled in a systematic and physically motivated way. The proof of the asymptotic stability is based on the semi-group theory and the invariance principle of LaSalle extended to the infinite-dimensional case. Simulation and measurement results of a laboratory experiment show an excellent performance of the proposed control concept.
at – Automatisierungstechnik, Oldenbourg Wissenschaftsverlag
Print ISSN: 0178-2312
Volume: 53, 08/2005
Pages: 400 - 410