Fourth-Order Reference Trajectories in Lithography Stages with Weakly-Damped Modes - a Frequency-Domain Perspective

The tracking accuracy in motion control systems like the moving stages in lithography machines, e.g., wafer scanners or metrology inspection tools, is partly determined by how the frequency content of its reference trajectories is transferred to the closed-loop tracking error. In this regard, fourth-order reference trajectories for point-to-point motion will be studied from a frequency-domain perspective. By appropriately pairing the maximum snap and maximum jerk values, weakly-damped modes in the closed-loop response can be robustly dealt with without introducing a penalty on throughput.