Abstract This study presents a complete analysis of novel length-mass insensitive shapers designed for nonzero initial conditions, followed by experimental verification of their effectiveness. Input shaping techniques for vibration suppression in overhead cranes, modeled as a double pendulum system, are thoroughly investigated. Modal analysis is employed to characterize system performance and governing equations. The proposed shapers are designed to suppress oscillations arising from nonzero initial conditions, including the system's inherent initial energy, which reflects realistic scenarios such as abrupt stops or external disturbances. With an arbitrarily selected maneuvering time, the proposed shapers effectively eliminate residual vibrations and robustly compensate for variations in system masses and cable lengths. Numerical simulations and experimental results confirm the effectiveness of the proposed shapers in eliminating residual vibrations while maintaining feasible input accelerations. Sensitivity analysis highlights the vulnerability of the zero-vibration shaper and the robustness of the zero-vibration and length-derivative, and zero-vibration and mass-derivative shapers, which effectively mitigate length and mass uncertainties, respectively. Additionally, feasible and infeasible solution regions are identified, emphasizing the importance of proper shaper selection. The results demonstrate that shaped inputs significantly enhance system stability, minimizing oscillations even under parameter variations. Moreover, the findings reveal the influence of system parameters on trolley velocity behavior, including sign alternations, emphasizing the necessity of adaptive shaping strategies. The study highlights the critical role of robust input shaping for real-world crane applications, where variations in payload mass and cable length are inevitable.
Alghanim et al. (Wed,) studied this question.