Robust input shaping for residual vibration suppression in overhead crane systems with suspended beams
摘要
This study investigates the dynamics and control of an undamped suspended Euler–Bernoulli beam suspended from an overhead crane, to eliminate residual vibrations during rest-to-rest maneuvers. The system governing equation is discretized using the finite difference method, and modal analysis is applied to construct the modal model matrix. Modal characteristics derived from this model are used to generate transfer functions, which form the basis for implementing input shaping methods and determining the corresponding input amplitudes. Two multimode input shaping methods, Multimode Zero Vibration and Multimode Zero Vibration and Derivative, are evaluated for their effectiveness in vibration suppression and parameter uncertainty. To streamline practical implementation, fitted functions of the input amplitudes are introduced to generalize the input profiles across various operating conditions. An Effectiveness Index is also proposed to assess input performance in terms of motor stress and maneuver time. Experimental validation is conducted on a scaled overhead crane setup, with beam responses analyzed in the frequency domain. Results demonstrate that both methods effectively reduce vibration, with Multimode Zero Vibration and Derivative showing greater robustness, while Multimode Zero Vibration yields smoother motion. The study highlights the importance of vibration modes in input shaping design and robustness evaluation for controlling flexible crane systems.