批次控制為針對半導體製程的特殊生產型態所發展出來的回饋控制工具。實際生產製程I-O模型多為複雜的動態模型。傳統的Single EWMA控制器，在靜態模型參數已知下，為干擾項IMA(1,1)的MMSE控制器，然而，在動態模型下，即使參數已知，並非為MMSE控制器。本文以MMSE控制器的概念為基礎，建構出Exponentially Integral (EI) 回饋控制器來監控常見的動態模型。文中探討此控制器的穩定性條件與最佳折扣因子的決定，並提供穩健的折扣因子選取方法。最後，在兩種 (long-tail 及 short-tail) 常見的動態模型下，分別以 的近似解析解來比較Single EWMA及EI控制器的績效表現，結果顯示EI控制器的績效在不同參數設定下，都比傳統的Single EWMA來的好，尤其是動態參數很明顯時，改善的程度會大幅提升。

Run-to-run (R2R) process control is well developed in semiconductor manufacturing communities. The exponential weighted moving average (EWMA) controller that is a popular model-based R2R controller has received great attention in literature. However, in practical applications, the process I-O model is complex and hybrid, and the effect of the input recipe on the output response can be carried over several periods. The Single EWMA controller is a MMSE controller for the static I-O model with the process disturbance following IMA(1,1) and the process parameters being known. It does not eliminate the effects on the dynamic parameters and cause a highly initial bias for the first few batches. In this paper we propose the Exponentially Integral (EI) controller to adjust the dynamic models. First, we derive the stability condition of EI controller and the optimal discount factor, and provide a robust discount factor selection. Finally, comparing with a Single EWMA controller, the performance of EI controller is better than Single EMWA controller under various combinations of parameter, especially in the dynamic parameter large.

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