Two-Stage Actuation for Improved Accuracy of Contouring

Two-stage actuation is presented as a method for improved contouring accuracy of biaxial positioning systems. The method applies the concept of dynamic compensation to a two-stage structure where the position error of the the coarse stage serves as the input to the fine stage. The objective of dynamic compensation is to obtain an overall system with the bandwidth of the fine stage and the range of the coarse stage. Based on the widely used second order, Type 1 approximation of the actuator dynamics and proportional position control it is shown that the implementation of the fine stage increases the bandwidth of the entire system and, also, decreases phase lag at lower frequencies. Moreover, higher bandwidth results in smaller comering errors in the response of a single axis. However, the magnitude of the contour error in the neighborhood of the corner is not necessarily reduced by dynamic compensation. Finally, for constant velocity, straight line contours the advantage of two-stage actuation over the conventional single-stage systems lies in its ability to eliminate steady state contour error by eliminating steady state errors in the responses of individual axes.