簡易檢索 / 詳目顯示

研究生: 張玉琪
Yu-Chi Chang
論文名稱: 提升 Double EWMA 控制器績效之研究
A Study on the Enhancement of Double EWMA Control Scheme
指導教授: 桑慧敏
Wheyming Song
曾勝滄
Sheng-Tsaing Tseng
口試委員:
學位類別: 博士
Doctor
系所名稱: 工學院 - 工業工程與工程管理學系
Department of Industrial Engineering and Engineering Management
論文出版年: 2007
畢業學年度: 95
語文別: 中文
論文頁數: 65
中文關鍵詞: 批次控制遞迴最小平方法起始截距項估計值控制器最佳折扣因子區域最小值
外文關鍵詞: Run to run control, Double EWMA controller, Recursive least squares, Initial intercept iteratively adjusted (IIIA) controller, optimal discount factors, local optimal, dEWMA controller, IIIA controller
相關次數: 點閱:4下載:0
分享至:
查詢本校圖書館目錄 查詢臺灣博碩士論文知識加值系統 勘誤回報
  • 本論文之研究目標為提高單投入單產出 (SISO) 的批次控制的績效,本研究以降低double EWMA (dEWMA) 控制器所造成的產出偏差 (bias) 為研究的切入點,本研究提出一個以 dEWMA 為基礎的控制器,並將此控制器命名為起始截距項估計值控制器(initial intercept iteratively adjusted (IIIA) scheme,簡稱IIIA控制器),利用逐次調整起始截距項的技巧來消除 dEWMA 控制器所造成的產出偏差(bias)。

    為了驗證IIIA 控制器的績效表現,本研究進行了IIIA 控制器、dEWMA與遞迴最小平方法(recursive least squares, RLS)控制器的績效比較,績效之比較標準為產出之均方差(MSE),結果發現在參數未提示的情形下, IIIA 控制器略勝一籌。

    為了增進對折扣因子的瞭解,本研究也提出了兩個 dEWMA 與 IIIA 之折扣因子與均方差間關係的性質,藉由這兩個性質可以很快找出 dEWMA 與 IIIA 的最佳折扣因子,從不同參數的 IIIA 最佳折扣因子的值,我們歸納出當製程模型之干擾項為白干擾時,第三批次後 IIIA 最佳折扣因子為(0.001, -0.001)。


    The research objective of this thesis is improving the performance of single-input-single-output (SISO) feedback control. The strategy of our approach begins from eliminating the bias of double Exponential Weighted Moving Average (dEWMA) controller. We propose an initial intercept iteratively adjusted (IIIA) control scheme, which is based on the dEWMA controller. The methodology of the IIIA controller is adjusting the initial intercept estimate run by run.

    An analytic expression of the process output and its MSE of the IIIA controller are revealed in this study. Furthermore, the performance of IIIA controller is compared with dEWMA and recursive least squares (RLS) controller in this research, and we found that IIIA controller is better than the other two controllers in most of our studied cases when the parameters of the process are assumed unknown.

    We also reveal two important properties on the discount factors of the dEWMA and IIIA controllers for a linear process. These two properties are helpful for the efficiency of selecting the optimal discount factors.

    1 緒論....................................................1 1.1 研究背景............................................1 1.2 研究動機與研究範圍..................................4 1.3 研究程序............................................5 1.4 研究目標............................................6 2文獻探討.................................................8 2.1 批次回饋控制的緣起..................................8 2.2 整合模組的研究......................................8 2.3 回饋控制模組的研究..................................9 2.3.1 製程無漂移之控制器研究..........................9 2.3.2 製程含漂移之控制器研究.........................11 2.3.3 其他泛用型之控制器研究.........................15 3 IIIA 控制器及其績效之研究..............................17 3.1 Double EWMA控制器之偏差(off-target)分析..........17 3.2 構建 IIIA 控制器的理論基礎.........................18 3.3 IIIA 控制器的控制程序..............................21 3.4 xi 已知下的研究成果與績效表現......................22 3.5 xi 未知下的績效表現................................27 3.6 本章結論...........................................34 4 dEWMA 及 IIIA控制器折扣因子之研究......................35 4.1 折扣因子與控制績效 MSE 的關係研究..................35 4.1.1 對稱性質.......................................35 4.1.2 「區域最小值等於全域最小值」性質...............36 4.2 修訂版的最陡斜率演算法.............................38 4.3 最佳折扣因子及其搜尋效率之分析.....................42 4.4 本章結論...........................................46 5 結論與後續研究.........................................47 5.1 結論...............................................47 5.2 後續研究...........................................48 參考文獻.................................................51 附錄.....................................................54 附錄1、引理 1 的證明...................................54 附錄2、引理 2 的證明...................................54 附錄3、結果 1 的證明...................................54 附錄4、性質 1-2 的證明.................................56 附錄5、各種不同製程參數之dEWMA和IIIA控制器的等高線圖...63

    [1] 李水彬 (2001),多變量 EWMA 控制器設計之研究,清華大學統計學研究所之博士論文,2001。
    [2] Alt, F.B. (1985). “Multivariate Quality Control.” Encyclopedia of the Statistical Sciences, Johnson, N.L., Kotz, S. and Read, C.R. (eds), John Wiley, New York, pp. 111-122.
    [3] Arfken, G. (1985). "The Method of Steepest Descents." §7.4 in Mathematical Methods for Physicists, 3rd ed. Orlando, FL: Academic Press, pp. 428-436.
    [4] Box, G. E. P., Jenkins, G. M., and Reinsel, G. C. (1994). Time Series Analysis: Forecasting and Control. Third Edition, Prentice Hall.
    [5] Butler, S. W. and Stefani, J. A. (1994). Supervisory run-to-run control of a polysilicon gate etch using in situ ellipsometry. IEEE Transactions on Semiconductor Manufacturing, 7(2), 193-201.
    [6] Chang, Y.C. (2007) The Efficiency Improvement on Searching the Optimal Discount Factors of the double EWMA and IIIA Controllers. Quality Technology & Quantitative Management, to appear 4(4).
    [7] Chen, A. and Guo, R. S. (2001) Age-based double EWMA controller and its application to CMP processes, IEEE Transactions on Semiconductor Manufacturing, 14(1), 11-19.
    [8] Del Castillo, E. and Hurwitz, A. (1997). Run to run process control: A literature review and some extensions. Journal of Quality Technology, 29(2), 184-196.
    [9] Del Castillo, E. (1999). Long run and transient analysis of a double EWMA feedback controller. IIE Transactions, 31(12), 1157-1169.
    [10] Del Castillo, E. (2001). Some properties of EWMA feedback quality adjustment schemes for drifting disturbance. Journal of Quality Technology, 33(2), 153-166.
    [11] Del Castillo, E. (2002). Statistical Process Adjustment for Quality Control. John Willy & Sons.
    [12] Fan, S.K 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.
    [13] Hankinson M., Vincent T., Irani K.B., and Khargonekar P.P. (1997), Integrated real-time and run-to-run control of etch depth in reactive ion etching. IEEE Transactions on Semiconductor Manufacturing, 10(1), 121-130.
    [14] Ingolfsson, A. and Sachs, E. (1993). Stability and sensitivity of an EWMA controller. Journal of Quality Technology, 25(4), 271-287.
    [15] Ljung, Lennart. and Soderstrom, Torsten. (1983). Theory and Practice of Recursive Identification. MIT Press.
    [16] Montgomery, D. C. and Keats, J. B. (1994). Integrating statistical process control and engineering process control. Journal of Quality Technology, 26(2), 79-87.
    [17] Patel, N. S. and Jenkins, S. T. (2000). Adaptive optimization of run-to-run controllers: the EWMA example. IEEE Transactions on semiconductor engineering, 13(1), 97-107.
    [18] Pollock, D.S.G. (1999). A Handbook of Time-Series Analysis, Signal Processing and Dynamics. Academic Press.
    [19] Sachs, E. and Ingolfsson, A. (1990). Tuning a process while performing SPC: an approach based on the sequential design of experiments. Proceedings of the Advanced Semiconductor Manufacturing Conference and Workshop, Danvers, MA, Sept. 10-12, 1990.
    [20] Sachs, E., Guo, R., Ha, S., and Hu, A. (1991). Process control system for VLSI fabrication. IEEE Transactions on Semiconductor Manufacturing, 4(2), 134-144.
    [21] Su, C.T. and Hsu, C.C. (2004). A time-varying weights tuning method of the double EWMA controller. Omega-International Journal of Management Science, 32(6), 473-480.
    [22] Tseng, S.T., Chou, R.J., and Lee, S.P. (2002a). Statistical design of a double EWMA controller. Applied Stochastic Models in Business and Industry, 18(3), 313-322.
    [23] Tseng, S.T., Chou, R.J., and Lee, S.P. (2002b). A study of multivariate EWMA controller. IIE Transactions, 34(6), 541-549.
    [24] Tseng, S.T., Yeh, A. B., Tsung, F., and Chan, Y.Y. (2003). A study of variable EWMA controller. IEEE Transactions on Semiconductor Manufacturing, 16(4), 633-643.
    [25] Tseng, S.T., Song, W., and Chang, Y.C. (2005). An Initial Intercept Iteratively Adjusted (IIIA) Controller: An Enhanced Double EWMA Feedback Control Scheme. IEEE Transactions on Semiconductor Manufacturing, 18(3), 448-457.
    [26] Tsung, F. and Shi, J. (1999). Integrated design of run-to-run PID controller and SPC monitoring for process disturbance rejection. IIE Transactions, 31(6), 517-527.

    無法下載圖示 全文公開日期 本全文未授權公開 (校內網路)
    全文公開日期 本全文未授權公開 (校外網路)

    QR CODE