Control of the bridge crane by constructing a Lyapunov function: theoretical design and experimental verification

Abstract

For the control problem of bridge cranes, it is challenging to realize fast transportation and efficient swing suppression simultaneously. Motivated by this observation, in this paper, we aim to propose a nonlinear controller achieving these objectives by constructing a desired Lyapunov function. In particular, a constructive Lyapunov function is introduced in a segmented manner. Based on that, a nonlinear control method rendering the dissipation inequality with respect to the constructed Lyapunov function is proposed straightforwardly, which achieves precise trolley positioning along with efficient payload swing elimination. The corresponding stability and convergence analysis is guaranteed by Lyapunov techniques and LaSalle’s invariance principle. Simulation and experimental results are provided to demonstrate the effectiveness and feasibility of the proposed method.