Passivity Based Control and Time Optimal Trajectory Planning of a Single Mast Stacker Crane

This paper is concerned with feedforward control and active rejection of vibration of a single mast stacker crane used for the automatic storage or retrieval of load carries in high bay racks. Based on an infinite dimensional mathematical model the trajectory planning and tracking problems are discussed. It turns out that the theory of differential flatness in combination with a finite dimensional approximation of the system is a suitable tool to obtain an open loop control law and to derive time optimal trajectories. The application of backstepping to the infinite dimensional model leads to a passivity based controller for the stabilization of the tracking error. Finally, measurement results show the feasibility of this approach.