Stability and performance of a double MEWMA controller for drifted MIMO systems

摘要

Many semiconductor manufacturing processes have, by nature, Multiple-Input and Multiple-Output (MIMO) variables. For a drifted MIMO process, the double Multivariate Exponentially Weighted Moving Average (dMEWMA) controller is a popular run-to-run controller for adjusting the process mean to a desired target. The stability conditions of a dMEWMA controller have received considerable attention in the literature. There are two limitations in the existed literature. First, these approaches only demonstrate that the asymptotic mean will meet a desired target; however, they do not show that mean square error matrix for a process is bounded. Second, they do not have an explicit expression of the process output of the dMEWMA controller for any production run t. Hence, by using a conventional state space formulation, it is impossible to address the process performance (such as process fallout rate of the dMEWMA controller) analytically. Using a different approach, this paper derives an analytical expression for the process output of a dMEWMA controller. The problems of the stability conditions and the performance of the dMEWMA controller can then be addressed successfully.