Rational Feedforward Tuning Using Variance-Optimal Instrumental Variables Method Based on Dual-Loop Iterative Learning Control

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The aim of this article is to propose a novel rational feedforward tuning method, by directly mapping the feedforward signal learned by dual-loop iterative learning control (DILC) onto the corresponding reference, that achieves high performance for varying trajectory tracking tasks. The DILC algorithm is first developed by paralleling the standard iterative learning control (ILC) with an additional iterative loop. Different from the standard ILC, DILC can learn an ideal feedforward signal eliminating the reference-induced error even though a robustness filter presents for the robust convergence against model uncertainties. Then, based on the reference and the feedforward signal learned by DILC, an instrumental variable-based algorithm is developed for the parameter tuning of the rational feedforward controller, which leads to unbiased estimates and optimal accuracy in terms of variance. The proposed method combines the performance of DILC with the flexibility of rational feedforward controllers. Comparative simulation and application to an ultraprecision wafer stage illustrate the enhanced performance of the proposed approach compared to the preexisting results.