Abstract
The efficient transportation by overhead cranes needs fast and accurate positioning, but residual vibration which prevents positioning accuracy generally tends to be induced by fast transportation. In previous paper, we proposed a control method which is based on the characteristic the residual vibration is completely suppressed in a linear undamped system when excited by an external force which does not contain the natural frequency component of the system. To apply this characteristic to nonlinear damped systems, we defined the apparent external force which includes the influence of system nonlinearity and damping. It was confirmed that the residual vibration is suppressed by eliminating natural frequency component from the apparent external force when the rope length is constant. However, if the height of the cargo is different before and after the transportation, it is needed to consider the rope length variation. Therefore, this paper modifies the apparent external force to include the influence of the rope length variation as well as nonlinearity and damping. Numerical simulations demonstrate that this method can suppress the residual vibration when the rope length varies in time. Furthermore, optimization is applied to not only the trolley trajectory but also the rope length variation, and consequently decrease the maximum swing angle of the cargo during transportation.
