On a sensitivity function of input shaping control

The performance of input shaping control has been conventionally estimated by a sensitivity function V, but the numerical relationship between the sensitivity function V and maximum residual vibration has not been clear in a quantitative viewpoint. In this paper, we define clearly the sensitivity function in impulse response and step response graphically, and then present the relationship between the sensitivity function and the magnitude of residual vibration responses. The validity of the assertion is demonstrated by means of simulation and experimental studies.