Application of a combined flatness- and passivity-based control concept to a crane with heavy chains and payload

This paper 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 crane with heavy chains and payload. It turns out that the position of the load serves as a flat output. This allows us to perform the trajectory planning task in a straightforward way. The objective of the stabilizing controller 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 in the wheel bearings of the cart which are always present in an experimental setup. 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. Simulation and measurement results of a laboratory experiment show an excellent performance of the proposed control concept.