Robust Trajectory Tracking Control of a Differentially Flat Overhead Crane Using Sliding Mode

Abstract

The control of overhead cranes is a benchmark problem, since it is an underactuated mechanism and its mathematical model is nonlinear. During operation the mass of the load is unknown, representing an uncertainty in the inertial parameters, which requires robustness of the controlled system. Our paper proposes a novel robust control method, that combines the differentially flat property of the dynamics with the robustness of the sliding mode control. The sliding surface is constructed to ensure the tracking of the configuration variables whose accelerations is calculated using the flatness property of the dynamic model. This formulation also allows achieving the matching conditions of the parameter uncertainties. Considering a simplified overhead crane model where the load motion is restricted in a vertical plane, two sliding surfaces are defined for the rope angle and rope length, since the cart position can be calculated from the previous two. The suggested control method is successfully validated in simulations as well as using a reduced-size overhead crane. For the real crane, the rope angle was estimated by utilizing the dynamical model, which uses the estimated cart acceleration.