Optimal Estimation of Rational Feedforward Control via Instrumental Variables: With Application to a Wafer Stage

Iterative control enables a significant control performance enhancement by learning feedforward command signals from previous tasks in a batch‐to‐batch fashion. The aim of this paper is to develop an approach to estimate the parameters of rational feedforward controllers that provide high performance and extrapolation capabilities towards varying tasks. An instrumental variable‐based algorithm is developed that leads to unbiased parameter estimates and optimal accuracy in terms of variance. Furthermore, a noncausal implementation of rational feedforward controllers is proposed, aiming to improve performance by means of pre‐actuation. Simulation and experimental results are presented to confirm that optimal accuracy is obtained with the proposed approach, and show the advantages of pre‐actuation in terms of performance.