This article describes a continuous function for limiting vibration in flexible systems by convolving the original command to the system. Unlike previous command shaping strategies, a continuous function shapes the original command to suppress vibration. The effectiveness of this method for robustness is explored and quantified. The theoretic analysis shows that this method has more insensitivity at higher frequencies. However, the robust input shaper gets more insensitive at lower frequencies. Experimental results for a planar bridge crane validate the simulated dynamic behavior and the effectiveness of the continuous function.
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