Projection-Based Iterative Learning Control for Wafer Scanner Systems

In this paper, an iterative learning controller (ILC) that uses partial but most pertinent information in the error signal from previous cycles is employed for precision control of a wafer stage. Typically, ILC schemes use the error signal from the previous cycle for updating the control input. This error contains both repetitive and nonrepetitive components. The nonrepetitive components of the error cause degradation of performance of the ILC scheme. Based on structural information about the plant and the disturbances, we can determine some basis functions along which the repetitive error is concentrated. This information is extracted by projecting the error signal onto the subspace spanned by these basis functions. The projected error signal is then used in the ILC update law. Stability and convergence conditions are presented for this projection-based ILC update law. The proposed idea is motivated by precision control of a wafer stage. For a constant velocity scan by the wafer stage, the major sources of repetitive error are found to be phase-mismatch and force ripple. These effects are mathematically modeled to obtain the subspace spanned by them. The projection-based ILC scheme using this subspace is then implemented on a prototype one DOF stage and its performance is compared to the standard ILC scheme that uses a frequency-domain filtering to remove nonrepetitive components of the error.