EI控制器在動態模型下之績效及穩定性分析

Performance and Stability Analysis of EI Controller under Dynamic Models

詹昱宏(Yu-Hung Jan)

指導教授 ： 曾勝滄

國立清華大學/理學院/統計學研究所/碩士(2008年)

摘要

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。

關鍵字

批次控制 ； 動態模型 ； 折扣因子 ； 穩定條件 ； PI控制器 ； EWMA回饋控制器 ； EI控制器

並列摘要

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.

並列關鍵字

R2R ProcessControl ； Stability Condition ； Dynamic Model ； HASH(0x1cd4af70) ； HASH(0x1cd4b010) ； HASH(0x1cd4b0b0) ； HASH(0x1cd4b150)

參考文獻

[13] 林建華 (2006) “多變量EWMA控制器之績效及其穩定性研究”， 國立清華大學統計學研究所博士論文。

[1] Del Castillo, E. (1999), “Long Run and Transient Analysis of a Double EWMA Feedback Controller,” IIE Transactions, 31, 1157-1169.

[2] Fan, S., Jiang, B. C., Jen, C. H. and Wang, C. C. (2002), “SISO run-to-run feedback controller using triple EWMA smoothing for semiconductor manufacturing processes”, International Journal of Production Research, 40(13), 3093-3120.

[3] Ingolfsson, A. and Sachs, E. (1993), “Stability and Sensitivity of an EWMA Controller,” Journal of Quality Technology, 25, 271-287.

[4] Jen, C. H. and Jiang, B. C. (2007), “Combining on-line experiment and process control methods for changes in a dynamic model”, International Journal of Production Research, 46(13), 3665-3682.