In the literature of input shaping control, two kinds of residual vibration ratio function have been introduced for evaluating the robustness of input shaping control to modeling error. Also, two types of derivative constraints for the residual vibration ratio function have been used for suppressing residual vibration under the condition of having some modeling errors in natural frequency and damping ratio. In this paper, a simplified residual vibration ratio function is presented, which is more convenient to use than the conventional function, and the equivalence of two derivative constraints for the simplified residual vibration ratio function is shown mathematically. The validity of the assertion is demonstrated by means of simulation and experimental studies.
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