Modeling and energy-based sway reduction control for tower crane systems with double-pendulum and spherical-pendulum effects

As typical underactuated systems, tower crane systems present complicated nonlinear dynamics. For simplicity, the payload swing is traditionally modeled as a single-pendulum in existing works. Actually, when the hook mass is close to the payload mass, or the size of the payload is large, a tower crane may exhibit double-pendulum effects. In addition, existing control methods assume that the hook and the payload only swing in a plane. To tackle the aforementioned practical problems, we establish the dynamical model of the tower cranes with double-pendulum and spherical-pendulum effects. Then, on this basis, an energy-based controller is designed and analyzed using the established dynamic model. To further obtain rapid hook and payload swing suppression and elimination, the swing part is introduced to the energy-based controller. Lyapunov techniques and LaSalle's invariance theorem are provided to demonstrate the asymptotic stability of the closed-loop system and the convergence of the system states. Simulation results are illustrated to verify the correctness and effectiveness of the designed controller.