Quasi-minimum mean square error run-to-run controller for dynamic models

Abstract

The Exponentially Weighted Moving Average (EWMA) feedback controller is a popular model-based run-to-run feedback controller that primarily uses data from previous process runs to adjust the settings of the next run. The long-term stability conditions and the transient performance of the EWMA controller have received considerable attention in the literature. Most of these studies have assumed that the process Input–Output (I-O) relationship is static and simply considered colored noise models for the process disturbance. However, process dynamics and disturbance dynamics may occur simultaneously. Under this circumstance, using EWMA-based controllers will usually lead to an unsatisfactory performance. To overcome this weakness, this article first proposes a quasi-minimum mean square error controller. The theoretical results of the long-term stability conditions are derived under a first-order transfer function model together with a general disturbance model. Furthermore, comprehensive simulation studies are conducted to compare the proposed controller with existing popular controllers. The results demonstrate that the proposed controller outperforms those popular controllers for most cases, even when the process I-O model is mis-specified or the process parameters are not precisely estimated. Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following supplemental resources: Tables 5 to 7 and Appendix.

Keywords:

• Run-to-run control
• EWMA controller
• dynamic model
• quasi-minimum mean square error controller

Acknowledgments

We are grateful to the Associate Editor and anonymous referees for many insightful suggestions that significantly improve the quality of this article. We would also like to thank Shu-Ling Li for her assistance in running computer programs. The work was partially supported by the National Science Council (Grant no. NSC-100-2221-E-007-060-MY3), MOE 5Y5B project (Contract no. 102N2074E1), and National Center for Theoretical Sciences of Taiwan, Republic of China.