A Negative Specified-duration Shaper to Reduce Residual Vibration Within Arbitrarily Specified Time Shorter Than Half a Period

In input shaping control aimed at reducing residual vibrations, a specified-duration (SD) shaper was proposed as an input shaper with arbitrarily specified shaping time. However, the SD shaper could only be applied when the shaping time was greater than half a period. In this paper, a negative SD shaper is proposed, which can arbitrarily control the shaping time to be shorter than half a period. Unlike conventional SD shapers that use only positive impulses, the proposed negative SD shaper introduces negative impulses. For undamped systems, the method yields a closed-form solution, while for underdamped systems, a numerical solution is provided. Through simulation studies, the residual vibration suppression performance and shaping time of step responses regarding modeling errors of the proposed negative SD shaper are evaluated. The validity of the negative SD shaper is experimentally verified using an experimental setup with a container model.