Boundary Control of Container Crane;Two-Stage Control of a Container Crane as Nonflexible and Flexible Cable

In this paper, we proposed a two-stage control of the container crane. The first stage control is time-optimal control for the purpose of fast trolley traveling. With suitable trolley velocity patterns, the sway which is generated during trolley moving is minimized. At the second stage control feedback control law is investigated for the quick suppression of residual vibration after the trolley motion. For more practical system, the container crane system is modeled as a partial differential equation (PDE) system with flexible cable. The dynamics of the cable is derived as a moving system with tension caused by payload using Hamilton's principle for the systems. A control law based upon the Lyapunov's method is derived. It is revealed that a time-varying control force and a suitable passive damping at the actuator can successfully suppress the transverse vibrations.