Adaptive control of underactuated crane systems subject to bridge length limitation and parametric uncertainties

In real-world applications, cranes usually suffer from parametric uncertainties, such as unknown friction, cart mass, load mass, and wire length. Moreover, existing crane control methods cannot guarantee the motion scope of the cart, since merely asymptotic results, at best, can be obtained due to the underactuated nature. Due to unexpected overshoots, existing methods, if not well tuned, may drive the cart to go beyond the scope of the bridge. In this paper we consider the control problem for underactuated bridge crane systems by considering the aforementioned two points and present an adaptive nonlinear control law. The control framework is established by total energy shaping, and a novel additional term is introduced into the controller to prevent the cart from running out of the permitted range. Lyapunov-based analysis is utilized to prove asymptotic stability of the closed-loop system´s equilibrium point. Numerical simulation results suggest that the proposed method can achieve superior control performance over existing methods while ensuring the cart motion range limitation, in the presence of uncertain plant parameters.