The Generation Mechanism of Tracking Error During Acceleration or Deceleration Phase in Ultraprecision Motion Systems

In this paper, the generation mechanism of the tracking error during the acceleration or deceleration phase in ultraprecision motion systems is studied. For the first time, the analytical relationship among the tracking error, a feedforward controller, a feedback controller, and a reference trajectory is presented. Quantitative analysis shows that the tracking error is approximately proportional to a specific derivative of trajectory with given feedback and feedforward controllers. Moreover, the tracking error in ultraprecision motion systems is also greatly influenced by the effect of zero-order hold and time delay, which necessitates jerk feedforward. The analysis not only explains the generation mechanism of the tracking error, but also provides a criterion to judge the accuracy of feedforward coefficients by the shape of a residual tracking error. Based on this criterion, a feedforward tuning algorithm using dichotomy is proposed. The simulation and experiment both well-validate the generation mechanism of the tracking error and the proposed feedforward tuning algorithm.