OPTIMAL TRAJECTORY TO MINIMIZE MECHANICAL VIBRATION FOR FAST POSITIONING

摘要

Input shaping techniques have been proposed to reduce the vibration in the positioning of the manipulators. However, a practical application is not simple as the target requirements becomes more precise, because the number of mechanical resonances that need to be taken into account increases, and the robustness against the resonant frequency variations is more critical. The vibrations of the positioning at the final state are easily estimated by the plant transfer function and the jerk waveforms at acceleration, deceleration, and settling. The optimal control input for faster positioning can be obtained by minimizing the width of the jerk and minimizing the mode excitations at the same time. This optimization process can be performed by an adaptive filtering technique. It is based on the least-square algorithm, which generates the jerk waveform that minimizes the least-square sum of the vibration only at the settling. Effectiveness of the method is demostrated by computer simulations and the results for a hard disk drive application are also presented.