以SVM-PLS模式為基礎的控制策略應用於
多產品多機台之製程

本研究首先於單變數系統中以SVM模式與KSVM模式設計少量數據時多產品多機台製程的控制策略，其中SVM模式為基礎的控制策略，主要是考慮所有產品與機台之特性下針對線性系統迴歸模式，而KSVM為基礎的控制策略則同樣地在考慮所有產品與機台之特性下，針對非線性系統迴歸模式，模式迴歸後，以每ㄧ個機台為單位去做控制設計，所以當機台操作完一批後，我們可利用其所得資訊代入dEWMA控制器修正模式，並設計下一批的操作作動。之後，對於多變數系統中變數間具有關聯性以及SVM無法處理多個輸出變數(Multiple Output)的問題，本研究利用PLS模式從原始空間多變數投射至子空間後，將Score值以SVM模式與KSVM模式迴歸出內部模式，迴歸模式後，同樣地，以每個機台為單位去做控制設計，當機台操作完ㄧ批後，利用其所得資訊投射至子空間得到Score值，利用dEWMA控制器修正模式，並設計下一批的子空間操作作動後，最後再投射回原始空間中得到實際之操作作動。最後，本研究於單變數系統與多變數系統分別以淺層溝渠隔離製程及化學機械研磨製程為測試範例，並針對製程的衰退干擾與設定點改變的狀況做測試，驗證本研究所提出的迴歸模式於少量數據下的控制效能，說明本研究所提出控制策略的優勢。

關鍵字

批次控制；多機台多產品；支持向量機

並列摘要

The objectives of this thesis is to develop modeling and control algorithm for multi-tools and multi-products(MTMP) process of SISO and MIMO system. Initially, support vector machine(SVM) is demonstrated to be very effective in process modeling of limited data. Then the proposed methodology utilizes kernel support vector machine(KSVM) to perform nonlinear modeling wherein the original variables are mapped using a kernel function into a feature space where linear regression is done. To eliminate the effects of unknown disturbances and drifts, the KSVM expression for the KSVM controller is modified to include constants that are updated in a manner similar to the constants used in double exponential weighting moving average (dEWMA) method and the control law for KSVM controller is derived. For linear modeling of MIMO process, SVM-PLS method first applies the PLS outer relation to transform the original variables to latent variables. Then the same SVM used in SISO case is employed in the PLS inner relation. For nonlinear modeling of MIMO process, KSVM-PLS method first applies the PLS outer relation to transform the original variables to latent variables. Then the same KSVM used in SISO case is employed in the PLS inner relation. Illustrative examples are presented to demonstrate the effectiveness of SVM, KSVM, SVM-PLS and KSVM-PLS method in process modeling and control of SISO and MIMO processes respectively. Even if there is a limited data in process modeling, KSVM still has a good capability of characterizing the nonlinear behavior. The performance of the proposed KSVM control algorithm is highly satisfactory and is superior to other MTMP control algorithms in controlling MTMP processes with either aging tools or setpoint changes.

並列關鍵字

run-to-run control ； multi-tools ； multi-product ； SVM

參考文獻

S. Shellamn, J. Taylor, “Run by Run Control of Chemical-Mechanical Polishing,” IEEE Trans. CPMT(C), 19, 307 (1996)

3. S. W. Butler, J. A. Stefani, “Supervisory Run-to-Run Control of a Polysilicon Gate Etch Using in Situ Ellipsometry,” IEEE Trans. Semicond. Manuf., 7, 193 (1994)

4. E. Del Castillo, R. Rajagopal, “A Multivariable Double EWMA Process Adjustment Scheme for Drifting Processes,” IIE Trans., 34, 1055 (2002)

5. E. Del Castillo, R. Rajagopal, “An Analysis and MIMO Extension of a Double EWMA Run-to-Run Controller for Non-squared Systems,” Int. J. Reliability, Quality Safety Eng., 10, 417 (2003)

6. C. Cortes, V. N. Vapnik, “Support-vector network,” Machine Learning, 20, 273-297 (1995)

國際替代計量

以SVM-PLS模式為基礎的控制策略應用於多產品多機台之製程

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