Disturbance Estimation Based Robust Control of 2D Overhead Crane

We consider the problem of an underactuated 2D overhead crane control, which includes actuated trolley positioning and unactuated payload swing compensation, in the presence of uncertain disturbances. Firstly, two coordinate transformations are applied successively and some non-restrictive assumptions are adopted to represent the original system in the feedback linearizable form. Then robust controller for the trolley positioning and payload stabilization is designed on the basis of the filtering-based disturbance estimator. The tracking error exponential convergence to an adjustable compact set is proved through rigorous analysis. It is also shown that at the parametrization stage the system parametric uncertainty can be included into the disturbance description, therefore, unlike many known solutions without high gain and sliding mode control techniques, the proposed approach is applicable in case when not only the perturbation, but also the system parameters are unknown. All theoretical results are validated via numerical simulation.