Design Procedure for Motion Profiles with Sinusoidal Jerk for Vibration Reduction

Abstract

High-speed motions performed by industrial machines can induce severe vibrations that degrade the positioning accuracy and efficiency. To address this issue, this paper proposes a novel motion profile design method utilizing a sinusoidal jerk model to generate fast and smooth motions with low vibrations. The expressions for the acceleration, velocity, and displacement were obtained through successive integrations of the continuous jerk profile. A minimum-time solution with actuator limits was formulated based on an analysis of the critical constraint conditions. Differing from previous studies, the current study introduces an analytical optimization procedure for the profile parameters to minimize both the motion duration and excitation frequency contents corresponding to the system pole. By examining the correlation between the input motion profiles and system responses, the conditions for vibration elimination were identified, highlighting the significance of specific time intervals in controlling the vibration amplitude. Numerical and experimental studies were conducted to validate the effectiveness of the proposed method. The comparative results illustrate that this method outperforms existing baseline techniques in terms of smoothness and vibration attenuation. The residual-vibration level and settling time are significantly reduced with the optimized sinusoidal jerk profile, even in the presence of modeling errors, contributing to higher productivity.