Time-optimal flatness based control of a gantry crane

This contribution deals with the flatness based control of a gantry crane, where the control objective is to transfer the load from an initial rest position to a final rest position in a minimal transition time. It is well-known that the type of crane model we consider is a differentially flat system, and that the position of the load is a flat output. We exploit this property both for the design of a tracking control as well as for planning time-optimal reference trajectories for the load. We discuss the design of the tracking control in detail, and show in particular how a standard approach which can be found in the literature can be modified systematically such that instead of measurements of certain time derivatives of the flat output we can use measurements of the state of the system. We also present a new approach for the design of time-optimal reference trajectories. In order to solve the resulting nonlinear optimization problem numerically, we use a primal-dual interior point method. Finally, we conclude with measurement results that stem from an implementation on a laboratory model.