Stability analysis of single EWMA controller under dynamic models

Abstract

The Exponentially Weighted Moving Average (EWMA) feedback controller is a popular model-based run-to-run controller which primarily uses data from previous process runs to adjust settings for the next run. The long-term stability conditions of EWMA controllers for this closed-loop system have received considerable attention in the literature. Most of the reported results are obtained under the assumption that the process I-O (Input-Output) relationship follows a static model. Generally speaking, the effect of the input recipe on the output response can be carried over several periods. In this paper, focusing on a first-order dynamic I-O model and assuming that the process disturbance follows a general ARIMA series, a systematic approach to address this control problem is proposed. First, the long-term stability conditions of a single EWMA controller are investigated. Then, the determination of sample size to allow the design of a single EWMA controller for dynamic models is considered. Under the assumption that the process I-O variables follow a bivariate normal distribution, a formula to calculate sample sizes that allow the stability condition to be met with a minimum probability protection is derived. Finally, the effects of dynamic parameters on the determination of sample size are considered. [Supplementary materials are available for this article. Go to the publisher's online edition of IIE Transactions for the following free supplementary resource: Appendix]