Position domain PD control: Stability and comparison

In this paper, a position domain PD control for contour tracking is proposed to improve the contour tracking performance. To develop the position domain control, one motion is selected as a master (reference) motion and all other motions are viewed as slave motions. The reference motion is sampled equidistantly in the position domain and used as an independent variable. A dynamic model for the slave motions is developed in the position domain by transforming the original system dynamic equations from the time domain to the position domain. After that, a position domain PD control is proposed, and the stability analysis is conducted based on the Lyapunov function method. The developed position control is applied to linear motion tracking and circular motion tracking, and the comparison study is conducted. Simulation results demonstrate the effectiveness of the position PD control compared with traditional PD control and the crossed-coupled control.