Hybrid integrator design for enhanced tracking in motion control

Abstract

This paper discusses a novel hybrid integrator design that (a) gives improved low-frequency disturbance rejection properties under double-integrator control, but (b) avoids the unwanted occurrence of overshoot and settling effects otherwise resulting from adding an extra linear integrator. The main principle behind this new design is that the resulting hybrid element generates a continuous control output signal based on integrator action when possible, while overall satisfying a sector condition that restricts the input-output behavior to a [0, k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> ]-sector, where k <sub xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">h</sub> is a positive gain derived from a closed-loop stability argument. In fact, closed-loop stability can be guaranteed on the basis of a circle-criterion-like argument and checked through (measured) frequency response data, thereby avoiding the need for parametric models. The strengths of this new hybrid integrator will be demonstrated experimentally on a wafer stage system of an industrial wafer scanner.