A Study of Variable EWMA Controller

Abstract

The exponentially weighted moving average (EWMA) feedback controller (with a fixed discount factor) is a popular run-by-run control scheme which primarily uses data from past process runs to adjust settings for next production run. Although the EWMA controller with a small discount factor can guarantee a long- term stability (under fairly regular conditions), it usually requires a moderately large number of runs to bring the output of a process to its target. This is impractical for process with small batches. The reason is that the output deviations are usually large at the beginning of the first few production runs and, as a result, the output may be out of process specifications. In order to reduce a possibly high rework rate, we propose a variable discount factor to tackle the problem. We derive the stability conditions and the optimal discount factor of the proposed EWMA controller. An example is given to demonstrate the performance of the proposed controller. Moreover, a heuristic is proposed to simplify the computation of the variable discount factor. It is seen that the proposed method is easy to implement and provides a good approximation to the optimal variable discount factor.