Partially saturated coupling-based control for underactuated overhead cranes with experimental verification

This paper presents a partially saturated coupling-based controller for underactuated overhead cranes. A new storage function characterized with a desired inertia matrix and potential energy function is constructed, which is especially quadratic in a composite state vector, and subsequently, a nonlinear controller is designed by enforcing the coupled-dissipation inequality. Particularly, a composite signal is fabricated to augment the internal coupling between the trolley movement and the payload sway, thus drastically increasing the damping of the control system. The proposed controller is simple and very robust to different/uncertain cable lengths. Besides, the hyperbolic tangent function is adopted so that the proposed controller guarantees a soft trolley motion. In the frame of the Lyapunov theory, LaSalle’s invariance principle is applied to illustrate the asymptotical stability. Simulation and experimental results are presented to verify the effectiveness of the control system.