Improving wafer stage performance with multiple hybrid integrator-gain systems

An experimental demonstration is given of a nonlinear feedback controller applied to a short-stroke wafer stage system of an industrial wafer scanner. The controller design adopts a classical linear PID-based configuration in which both the integrator and low-pass filter are replaced with hybrid integrator-gain-based filter elements. The reduced phase lag associated with these filters gives rise to increased design flexibility, and potentially enables a substantial increase in low-frequency disturbance suppression. The nonlinear controller is designed by means of a quasi-linear loop-shaping approach, while stability of the full nonlinear closed-loop system is verified by solving a set of linear matrix inequalities. Performance of the controlled system is discussed on the basis of measurement results obtained from a wafer stage system.