Partially saturated coupled-dissipation control for underactuated overhead cranes

This paper proposes a partially saturated nonlinear controller for underactuated overhead cranes based on passivity. The main contribution is that the total energy shaping method yields an assignable storage function which is characterized by a desired damping matrix and especially quadratic in a new error vector of the coupling form. Consequently, a partially saturated nonlinear controller enforcing the coupled-dissipation inequality is derived to introduce additional damping terms to the sway angle, thus guaranteeing favorable transit performance. Owing to the elaborate structure of the coupled-dissipation term, the control system can achieve significant oscillation reduction over a wide range of cable lengths and transportation distances without readjusting the control gains. Besides the Lyapunov theory, LaSalle's invariance principle is carried illustrating the corresponding stability. The proposed controller is evaluated through both simulation and experimental results that demonstrate the improved performance and robustness.