Stability conditions and robustness analysis of a general MMSE run-to-run controller

Abstract

Run-to-run (R2R) control plays a vital role in monitoring or adjusting the manufacturing process of integrated circuits. In this article we propose a generalized quasi-MMSE controller for a process whose Input-Output (I-O) model follows a general Transfer Function (TF) model with ARIMA disturbance and analytically derive the long-term stability conditions and their limiting distribution. Furthermore, we use a comprehensive simulation study to compare the control performances among several potential controllers when the process I-O model follows a TF model of order (2, 2, 0) with ARIMA disturbance of order (2, 1, 2). The results demonstrate that using improper controllers may seriously affect the control performance in terms of the long-term stability conditions and the short-term total mean squared error. Supplementary materials are available for this article. Go to this article’s online edition of IIE Transactions for Appendices.