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.
The Significant and Profound Impacts of Chou’s Invariance Theorem
