Long run and transient analysis of a double exponentially weighted moving average feedback controller

The ‘predictor–corrector’ feedback controller is a popular adjustment scheme proposed for the quality control of certain semiconductor manufacturing process steps. This controller is based on a double Exponentially-Weighted Moving Average (EWMA) scheme; thus the performance of the closed-loop system depends on the two weight parameters of the EWMA equations. In this paper, the conditions the weights must satisfy to ensure closed-loop stability are discussed. The optimal determination of the controller weights depends on a trade-off between long-run process variance and transient bias performance. It is shown that small weights, although they can guarantee stability, may result in severe, long transients, an important concern if fabrication is in small batches. An optimization model for finding the controller weights is given and numerically solved. An extension of this type of controllers to the multiple controllable factor case is described. The performance of the controller is illustrated with an application to Chemical Mechanical Polishing, a critical semiconductor manufacturing step.