Minimizing Residual Vibration for Point-to-Point Motion

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Abstract
This paper describes an appropriately shaped forcing function for moving a dynamic system over an incremental distance with minimum residual vibration. The function is constructed by combining harmonics of a “ramped sinusoid” function so that minimum energy is introduced to the system at its resonant frequencies. A test fixture to evaluate this approach is described and experimental results are given. Residual vibration amplitudes for the ramped sinusoid function are compared with those for a square wave input and a bang-bang function. In practice, the ramped sinusoid achieves nearly an order-of-magnitude reduction in residual vibration amplitude as compared to the square wave forcing function.

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