A Graphical Design of an Input-Shaping Controller for Quay- Side Container Cranes with Large Hoisting: Theory and Experiments

Input-shaping is a practical open-loop strategy for the control of transient and residual oscillations on cranes, especially those having predefined payload transfer paths and repeated maneuvers. In this paper double-step input-shaping control approach is developed to include maneuvers that involve large hoisting distances and speeds. The approach is based on using the graphical representation of the phase plane of the payload oscillations. The phase plane is used to derive mathematical constraints to compute the switching times of a double-step acceleration command profile that will result in minimal transient and residual oscillations. The controller design is based on a two-dimensional four-bar-mechanism model of a container crane. For the purpose of controller design, the model is reduced to a constrained double pendulum with variable length hoisting cable and a kinematic angular constraint. The generated commands were based on both a linear and a nonlinear frequency approximations of the payload oscillation period. Numerical and experimental results demonstrated that in contrast with the single-step input shaping controllers, which are very sensitive to frequency approximations, the proposed doublestep controller is less sensitive to small variations in the frequency even with large commanded accelerations. Using this approach, oscillations during and at the end of transfer maneuvers can be reduced to less than 5 cm on a full size model of a 65 ton quay-side container crane.