In industrial applications such as numerical control machine tools and robots, high-speed positioning operations are always required to improve productivity. However, high-speed positioning operations cause residual vibration owing to the inertial force of the driven object. To suppress this vibration, researchers have proposed adjusting the time constant and/or applying filters for the positioning command; these are generally applied in the field. However, the acceleration and deceleration time increases when the conventional vibration-suppression methods are applied to suppress lower frequency vibration. The purpose of this study was to establish a design method for positioning commands that minimizes the residual vibration and positioning time. A method to eliminate the natural frequency component was applied. This method is based on the principle that when a specific natural frequency component of an external force is reduced to zero, the natural frequency component of the system will not oscillate. Although the approach can be used to design positioning commands with any positioning time, for actual systems, the torque limitation of motors should be considered because it limits the minimum positioning time. Therefore, in this study, a positioning command that can minimize the positioning time and residual vibration was designed based on the formulated relationships between positioning time and maximum acceleration of positioning command. The effectiveness of this method was verified using an experimental system with torsional beams. We confirmed that the positioning commands designed using the proposed method can minimize residual vibration and positioning time.

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