Energy coupled–dissipation control for 3-dimensional overhead cranes

Handling loads with small swings is difficult for a 3-dimensional overhead crane due to its hard nonlinearity. Moreover, the nonlinear dynamics increases the complexity of the required feedback, thus making the closed-loop system sensitive to a variation in the cable length that negatively influences the damping feature. To address these problems, a significant storage function characterized by the desired damping is constructed based on passivity. Consequently, a nonlinear controller is delivered by enforcing the coupled–dissipation inequality, thus drastically increasing the damping of the closed-loop system. In particular, new coupled–dissipation signals are fabricated to augment the coupling between the trolley movement and the payload sway. Due to its very simple structure that excludes the cable length, the proposed controller is robust to unknown cable lengths and easy to implement. In the frame of the Lyapunov theory, LaSalle’s invariance principle is applied to illustrate the corresponding stability. The effectiveness of the proposed control on improving the system performance is verified through simulation results.