Two-step acceleration/deceleration for vibration-damped transfer of a 1DOF overhead traveling crane under open/closed-loop finite-time settling control using solutions of a two-point boundary value problem with half-odd-integer trigonometric functions

This study proposes a finite-time settling function that satisfies a two-point boundary value problem. The function consists of trigonometric functions with a period equal to half-odd integer multiples of the operation time. This function is applied to both open-loop and closed-loop finite-time settling controls. A computational simulation of vibration-damped transfer for an overhead crane was conducted. Without external disturbances, two-step vibration-damping acceleration/deceleration operations were performed. In the open-loop finite-time settling control, residual vibration persisted when the non-linearity of the pendulum was not neglected. On the other hand, residual vibrations were effectively suppressed in the closed-loop finite-time settling control, even during high-speed transfer with a large swing-up angle.