Stabilizing Model Predictive Control of a Gantry Crane Based on Flexible Set-Membership Constraints

This paper presents a stabilizing distributed model predictive control of a gantry crane taking into account the variation of cable length. The proposed algorithm is based on the off-line computation of a sequence of 1-step controllable sets and a condition that enables flexible convergence towards a suitably chosen terminal set. The crane is modeled as a two dynamically coupled subsystems where the coupling among them is treated as a variation in the system parameters. In this way the model is converted to a polytopic linear parameter varying model which is used to calculate the terminal set and 1-step controllable sets. The proposed approach is verified through simulation and experimental test on the laboratory model.