A hybrid integrator-gain based low-pass filter for nonlinear motion control

In this paper a hybrid low-pass filter is developed and subsequently embedded in a PID-based control design. The hybrid element switches between gain and integrator mode, depending on the evaluation of specifically designed switching conditions. Given the properties of the hybrid low-pass filter, which are mainly expressed by reduced phase lag as compared to a linear-equivalent low-pass filter, the bandwidth of the PID-based control design can potentially be increased. Based on describing function analysis, this bandwidth increase is obtained while identical robustness properties of the closed-loop system in terms of bounds imposed on the closed-loop sensitivity function are guaranteed. In this sense, the hybrid control design provides more design freedom compared to the equivalent linear control design, which leads to a factor two improvement in low-frequency disturbance suppression of a state-of-the-art scanning stage of an industrial wafer scanner.