EWMA run-to-run controllers with gain updating: Stability and sensitivity analysis

Exponentially weighted moving average (EWMA) controllers are the most commonly used run-to-run controllers in semiconductor manufacturing. Based on a linear model, an EWMA controller is usually implemented in a way that the process gain is kept as the off-line estimate and the intercept term is updated using an EWMA filter at each run. However, in practice, there are many applications that an EWMA controller is implemented in a way that the process gain is updated in a run-to-run manner while the intercept is kept as the off-line estimate. Although the stability and sensitivity of EWMA controllers with intercept updating has been well known, there is no analysis result on the stability and sensitivity of EWMA controllers with gain updating. In this paper, we analyze the behavior of an EWMA controller with gain updating and compare it to that of an EWMA controller with intercept updating. Both stationary and drifting processes are considered, the expression of the process output are derived and the output variances for stochastic processes are evaluated. In addition, simulation examples are given to illustrate the analysis results.