Frequency Dependent Nonlinear Iterative Learning Control With Application to a Wafer Stage

Abstract

This paper deals with the control design of a wafer stage setup, catering for the increasing demand for ultra-precision positioning and high throughput devices in line with further miniaturization of the LCD, semiconductor and electronic parts. The developed wafer stage employs a dual stroke principle: a short stroke for fine positioning and a long stroke for coarse positioning. The short stroke is a stage of six-degree-of-freedom with integrated magnetic bearing to counteract the gravity, while the long stroke is a planar motion stage consisting of a integrated three-axis drive motor, which can move along the surface of the Halbach permanent magnet array without generating friction due to being elevated with air bearings. To achieve precision tracking control with zero settling time under high acceleration/velocity motion, iterative learning control has been regarded as an effective means. Linear iterative learning control techniques attenuate the recurring disturbances and amplify the nonrecurring, suffering from a fixed trade-off between convergence rate and noise amplification. In this paper, a frequency dependent amplitude-based nonlinear iterative learning control is proposed. Within a frequency range of interest, the learning gain is continuously updated to improve the control performance of the planar motion stage. Based on the frequency contents of error signal, for error-levels beyond a predefined threshold, additional learning gain will be effectively used to diminish the low-frequency tracking error. Below the threshold, the original low-gain value is maintained to avoid high-frequency noise amplification. Performance assessment on the developed wafer stage setup shows that the proposed nonlinear iterative learning strategy can realize a remarkable performance which includes nanometer positioning and tracking over large travel ranges, and provides a more desirable means to deal with the convergence rate and noise amplification.