A graphical approach to input-shaping control design for container cranes with hoist

A traditional input-shaping technique is adapted to control transfer maneuvers on quay-side container cranes. The controller is developed using an accurate two-dimensional four-bar-mechanism model of a container crane and accounts for maneuvers that involve large hoisting operations. A graphical representation of the phase plane of the payload oscillations is used to derive mathematical constraints to compute the switching times of a double-step acceleration profile that results in minimal transient and residual oscillations. In contrast with single-step shaped acceleration profiles which are very sensitive to frequency approximations, the proposed double-step profile is less sensitive to small variations in the frequency even for large trolley accelerations.