Abstract
This work investigates multimode vibration suppression in quay-side container cranes by combining analytical modeling, nonlinear multibody simulation, robust Input Shaping, and experimental implementation. A linearized double-pendulum model preserving the main geometric and inertial properties of the spreader–ISO-container assembly is first derived to characterize its coupled dynamics, comprising a low-frequency global pendular mode and a higher-frequency relative ringing mode. The errors introduced by linearization are assessed against a higher-fidelity Simscape Multibody model over a wide range of operating configurations. The comparison shows that the analytical formulation provides sufficiently accurate estimates of the modal frequency ranges for robust shaper design. Two Unity Magnitude One-Hump shapers are therefore synthesized for the identified low- and high-frequency bands and subsequently convolved into a multimode bang–off–bang command. Sensitivity analysis confirms simultaneous attenuation of both target frequency ranges. Numerical validation on the nonlinear multibody model shows that the reduction in residual vibration remains above 90% over the investigated variations in hoisting length and ISO-container center-of-mass position. Finally, a PLC-based laboratory implementation demonstrates that Unity Magnitude shaping can be executed through timed command toggles without online convolution, supporting its practical implementation using conventional industrial control hardware.