Experimental analysis of natural frequency error to residual vibration in ZV, ZVD, and ZVDD shapers

Input shaping control is an interesting topic in control viewpoint. Recently, input shaping control has many methodologies as ZV, ZVD, ZVDD, EI, UM ... which are developed and published by many researchers on the world. The parameters, which are most important to build an input shaping controller are natural frequency and damping ratio. Actually, these parameters are not easy to determine in actual, in general. The error of natural frequency and damping ratio will be significantly affected to residual vibration in input shaping controller. This paper estimates the effect of natural frequency error to residual vibration of flexible beam in three input shaper ZV, ZVD, and ZVDD. The results will be shown clearly using mathematical form and experiments.