Time-Suboptimal Vibration-Free Positioning Control of 1-DOF Undamped Linear Oscillatory Systems

Abstract

This paper presents time-suboptimal vibration-free reference trajectories for position control of 1-DOF undamped linear oscillatory systems. By applying the frequency-domain shaping technique to the design of reference acceleration trajectory for a positioning system with an elastically coupled mass, the vibration-free reference trajectory is analytically obtaioned based on its mathematical model. In the frequency-domain shaping, the authors partly solve time-optimal problems with given maximum values of the acceleration and the velocity. As a result, the deterioration of the resulting trajectory in travelling time is minimized and the difference from the so-called time-optimal trajectory is kept small. The traveling time is also comparable to, i.e., sometimes shorter and sometimes longer than, that of UM-ZV (unity-magnitude zero-vibration) shaper. Implementation issues which arise when discrete-time controllers are used to generate the reference trajectory are also investigated. The proposed vibration-free reference trajectories are used in a real linear positioning system and the performance is verified in experiments as well as numerical simulations.