A multivariate EWMA controller for linear dynamic processes

Most research of run-to-run process control has been based on single-input and single-output processes with static input-output relationships. In practice, many complicated semiconductor manufacturing processes have multiple-input and multiple-output (MIMO) variables. In addition, the effects of previous process input recipes and output responses on the current outputs might be carried over for several process periods. Under these circumstances, using conventional controllers usually results in unsatisfactory performance. To overcome this, a complicated process could be viewed as dynamic MIMO systems with added general process disturbance and this article proposes a dynamic-process multivariate exponentially weighted moving average (MEWMA) controller to adjust those processes. The long-term stability conditions of the proposed controller are derived analytically. Furthermore, by minimizing the total mean square error (TMSE) of the process outputs, the optimal discount matrix of the proposed controller under vector IMA(1, 1) disturbance is derived. Finally, to highlight the contribution of the proposed controller, we also conduct a comprehensive simulation study to compare the control performance of the proposed controller with that of the single MEWMA and self-tuning controllers. On average, the results demonstrate that the proposed controller outperforms the other two controllers with a TMSE reduction about 32% and 43%, respectively.