Robust motion profiles for the residual vibration reduction of an undamped system

This paper proposes two robust motion profiles to reduce the residual vibration of an undamped system: Trigonometric and trapezoidal acceleration motion profiles. The proposed motion profiles are defined by the total traveling, accelerating, and rising times in acceleration for each profile. Due to their simplicity, implementation of the proposed motion profiles is relatively easier when compared to previous input-shaping motion profiles. Furthermore, the proposed profiles are more robust in terms of system modelling errors than previous s-curve motion profiles. It is found in this paper that the zero vibration and robustness conditions are satisfied if the total traveling, accelerating, and rising times are half-integer multiples of the natural period for the trigonometric profile and integer multiples for the trapezoidal profile.