Model-free iterative learning design of arbitrary-time and multi-length zero-vibration shapers

This study presents an iterative learning framework for designing input shapers for crane systems operating under constant cable-length and hoisting conditions. Unlike conventional analytical approaches, the proposed method determines the shaped trolley acceleration directly through repeated input-output learning without requiring an analytical solution or linearization of the system dynamics. Standard, arbitrary maneuver-time, and multi-length zero-vibration shapers are developed using both step and ramp input functions. The proposed approach is evaluated under constant cable-length as well as linear and nonlinear hoisting conditions. The results demonstrate rapid convergence of the learning process and successful suppression of residual payload oscillations while satisfying the prescribed transportation requirements. The arbitrary maneuver-time shaper enables faster payload transportation, whereas the multi-length shaper significantly enhances robustness against cable-length variations. The results also indicate that the shaper performance is largely insensitive to the selected hoisting profile. The proposed framework provides a flexible, robust, and practical methodology for vibration suppression in crane systems and can be readily extended to more complex nonlinear applications.