A Higher Order Adaptive Approach to Tackle the Swinging Problem

In numerous practical applications precise control of a subsystem passively connected to a precisely controllable subsystem by elastic connection is needed. As typical example is a crane carrying its payload swinging on an elastic string can be mentioned. From the point of view of control technology this task is interesting since the connected degree of freedom has little damping and it is apt to keep swinging accordingly. The traditional approaches apply the input shaping technology to assist the human operator responsible for the manipulation task. In the present paper a novel adaptive approach applying fixed point transformations based iterations having local basin of attraction is proposed for simultaneously tackle the problems originating from the imprecisions of the available dynamic model of the system to be controlled and the swinging phenomenon. In the simulation investigations presented a simple model consisting of two connected masspoints is considered: one of them can directly by controlled by control forces, the other one (in the role of the payload) is dragged by the controlled point via an elastic spring. The control considers the 4th time-derivative of the trajectory of the dragged system.N/