Designing ZV and ZVD Input Shapers Using the Designed Fixed Output Response Method to Suppress Residual Vibration of Overhead Crane Systems With Trolley Traveling and Payload Hoisting

ABSTRACT Classical Zero Vibration (ZV) and Zero Vibration and Derivative (ZVD) input shapers are designed around a fixed nominal natural frequency and cannot accommodate the time‐varying dynamics introduced when an overhead crane simultaneously travels and hoists a payload. Hoisting continuously changes the effective cable length, producing a time‐varying natural frequency and a Coriolis‐type damping term that standard least‐time‐invariant‐based impulse‐train shapers cannot cancel exactly, leaving residual payload sway that degrades positioning accuracy and safety. This paper extends the Designed Fixed Output Response (DFOR) framework to classical ZV and ZVD input shaper structures to address this fundamental gap. The proposed DFOR‐ZV and DFOR‐ZVD shapers exploit the DFOR method's ability to force, by design, the time‐varying crane system response to follow an equivalent time‐invariant virtual SDOF system, allowing the standard impulse‐train shaper structure to be applied analytically. This yields compact, closed‐form expressions for all shaper impulse amplitudes and timing parameters as explicit functions of the operational natural frequency, cable length, hoisting rate, and maneuver time. The performance of the two new shapers is validated numerically and experimentally on an overhead crane test rig under both no‐hoisting and hoisting scenarios. Systematic comparison against classical ZV and ZVD shapers applied directly to the time‐varying crane model demonstrates that the proposed shapers reduce experimental residual sway by 90% (DFOR‐ZV: 0.1758° vs . 1.7821° for classical ZV and DFOR‐ZVD: 0.0989° vs. 1.0563° for classical ZVD). A robustness analysis with respect to natural frequency uncertainty is also presented. Results confirm that the DFOR‐ZV and DFOR‐ZVD shapers effectively suppress residual sway under hoisting while offering simpler closed‐form parameterization and a well‐defined robustness–maneuver‐time trade‐off relative to classical alternatives.