Data-Driven Iterative Feedforward Tuning for a Wafer Stage: A High-Order Approach Based on Instrumental Variables

Abstract

The feedforward controller plays an important role in the achievement of high servo performance of wafer scanning. In this paper, a novel data-driven feedforward tuning method is developed in the presence of noise. Three distinguished features make it different from the existing methods: first, high extrapolation capability to tasks; second, low requirement on the system model; and especially, third, high noise tolerant capability. These superiorities are achieved by a high-order iterative feedforward tuning algorithm based on instrumental variables. It utilizes error data from all past iterations via an integrator in the learning law, yet without the need of the plant model or the sensitivity function. Furthermore, $H_2$ optimization with specified convergence speed constraint is proposed to design the learning gain. Connections and differences between the proposed algorithm and the existing ones are discussed. Experimental results validate the proposed method and confirm its effectiveness and superiority.