Adaptive boundary control of an axially moving string system: Application to container cranes

An axially moving system of a string with time - varying length and a mass attached at the lower end is considered to be a fundamental model of a container crane in a dockside. The objective of this paper is to move a load hanging under a very long rope from one place to another and suppressing the transverse vibrations of the load at the end of movement by adaptive control. The Lyapunov function taking the form of the total mechanical energy of the system is adopted to ensure the uniform stability of the closed-loop system. Through experiments, the effectiveness of the proposed control law is demonstrated.