Two-degree-of-freedom Stage Cooperative Control Based On Cross-coupled Control

To improve precision in precise and ultraprecise machining, a nature way is controlling contour error during machining process. But controlling the tracking error of every single axis do not guarantee the contour error of multi-axis system.Begin with the dual wafer stages, this paper is meant to construct a two-degree-offreedom contour tracking system based on X-axis and Y-axis linear motors manufactured on the stage. In order to synchronize the position of two Y-axis motors, this paper adopted synchronous structure based on coupled deviation. To reduce contour error during contour tracking, this paper adopted cross-coupled control structure over X-axis and Y-axis.Based on the features of linear motors, the paper analyzes force disturbance during movement of linear motor, a set of formulas is given to show the internal accurate model of force disturbance. Actual situation is very complicate when the linear motor moves, so the ideal mathematical formulas could be inaccurate and inappropriate to applying compensation under this ideal model. This paper applied a force disturbance identification process to get the actual approximate model and applied a direct compensation to counteract it.Because the parameter and disturbance is different between two Y-axis linear motors, two motors might shift along their moving direction, which will deteriorate the accuracy of the whole system. The paper applied a synchronous structure to suppress the deviation.This paper introduced a cross-coupled control to eliminate or reduce contour error. It’s an effective solution to control contour error during contour tracking in multi-axis system. Compare not-real-time cross-coupled control structure, real-time cross-coupled control structure include time-varying coupled gain, which is dynamically determined by geometry features of current contour. This feature means real-time cross-coupled control can be more adaptive with complicate contour.The core of a cross-coupled control structure is the contour error estimation. To track arbitrary contour, an appropriate contour error estimation model should be implemented in the structure. This paper introduced several contour error estimation methods of arbitrary contour, analyzed their strengths, weakness and target situation. Some of the methods is simulated in MATLAB with Simulink model, results were included in this paper.At last, this paper proposed a new method to estimate the contour error during arbitrary contour tracking, practicability analyzing was presented to support the method. Also, this paper gave a time and space complexity of the proposed method. The method is easy to implement in the cross-coupled control structure, and it’s more accurate and could lead to smaller contour error comparing to previous methods according to simulation results.Contrast experiments of proposed method and some of previous methods were carried out on specific software and hardware platform to proving the effectiveness of the method.