Host: The Japan Society of Mechanical Engineers
Name : Dynamics and Design Conference 2023
Date : August 28, 2023 - August 31, 2023
This paper presents time-suboptimal vibration-free reference trajectories for positioning 1-DOF undamped linear oscillatory systems. The reference trajectory is firstly parameterized in time-domain and then the parameter values are determined to satisfy constraints in both time and frequency domains. One of the frequency domain constraints guarantees the robust-performance of vibration mitigation against variation of natural mode. Time-optimal problems are partly solved under given rated values of the acceleration and the velocity. While analytical solutions are available in the undamped case, the numerical solution is also valuable since it gives another referece trajectory of shorter positioning time. As a result, the deterioration of position time is minimized and the difference from the so-called time-optimal trajectory is kept small. The positioning time is also comparable to the well-known UM-ZV (Unity-Magnitude Zero-Vibration) shaped one and the variant. 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.
