Vibration control of flexible dynamic systems using smooth robust input shapers: theory and application
摘要
A new adjustable smooth and robust input shaper for eliminating residual vibration of flexible dynamic systems is proposed. Regardless of the reference input profile provided to the system, the proposed input shaper is capable of generating a smooth-like shaped command by distributing multiple optimized impulses in its sequence. The shaper is characterized by an equidistant time interval between adjacent impulses that can be selected to match the actuator’s sampling time. Smoothness in the shaped command is achieved by minimizing the magnitude differences between adjacent impulses. Additionally, the adjustability of the shaper’s duration and the option to impose zero derivative constraints on residual vibration amplitudes can enhance robustness and suppress vibration amplitudes during transient stages. The magnitudes of the input shaper impulses are determined directly by solving a set of linear equations, thus avoiding the need for nonlinear optimization techniques. The effectiveness of the proposed input shapers is demonstrated through both numerical simulations and experimental validation, showing successful elimination of residual vibrations in an overhead crane system with time-varying nonlinear behavior during hoisting/lowering maneuvers, and numerical suppression of water sloshing in a laterally moving, multi-mode container system.