Improved noise sensitivity under high-gain feedback in nano-positioning motion systems

To avoid an increased noise response under high-gain feedback in nano-positioning motion systems, a nonlinear (N-PID) control design is proposed. The design is of particular interest in the wafer scanning industry where nano-accuracy should be achieved under high-speed motion. In a variable gain controller setting, the N-PID control design has an observer structure with state-dependent low-pass filter characteristics. Under high-gain feedback and being induced by sufficiently large servo error signals, the nonlinear observer acts as a low-pass filter with a significantly smaller cut-off frequency as compared to the case of low-gain feedback. As a result, the high-frequency noise response that usually increases under high-gain feedback is kept limited. For a validated wafer stage model, the effectiveness of the control approach in dealing with position-dependent behavior is assessed through simulation.