Passivity-based coupling control for underactuated three-dimensional overhead cranes

This paper develops a novel Lyapunov function candidate for control of the three-dimensional (3-D) overhead crane, which yields a nonlinear controller to inject active damping. Different from the existing passivity-based controls that employ either the angular displacement or its integral as passive elements, the proposed controller incorporates both of them in a new coupled-dissipation signal, thus significantly enhancing the closed-loop passivity. Owing to the improved passivity, the proposed controller ensures the effective suppression of payload oscillations and robustness. Moreover, the control design is extended with the hyperbolic tangent function to prevent overdriving the trolley. The asymptotic stability is guaranteed by LaSalle's invariance principle. The transit performance of the closed-loop system, including robustness, is validated by numerical simulations.