批次間程序常見於半導體製造業，可表示為一線性迴歸式，其中截距項與斜率項分別代表輸出擾動與時變程序增益。本論文針對這兩種擾動的排除，提出分別以內模與類內模控制架構為依據之強健控制器設計，在滿足H無窮範數和時延邊限的指定強健性條件下，獲得最佳的批次間操作性能。
半導體製程中常發生確定性斜坡漂移擾動和IMA(1,1)形式之隨機性擾動，兩者會分別造成程序輸出的暫態偏差和持續隨機變化。為了評估其對控制性能的影響，本論文推導出暫態性能指標及長期性能指標之閉合公式，並以兩指標乘以加權值產生之複合性能指標，作為控制器參數選擇的標準。加權值的選擇是用來權衡確定性和隨機性擾動對輸出的不同影響。
批次間程序之量測時延具有不確定性與隨機性，因此含固定時延之控制器難以獲得良好的控制效果。本論文發展出混合式批次間控制器設計，藉由指定適當強健性和交替使用含不同時延的兩種濾波器，可在隨機時延發生時達到極佳的控制性能。

Run-to-run processes are often seen in semiconductor manufacturing. They can be expressed by a linear regression equation, where the intercept and slope terms represent the output disturbance and time-varying process gain respectively. To reject these two kinds of disturbances, the thesis proposes robust controller designs based on the internal model and quasi internal model control structures, respectively. Under the designated robustness constraints on the H-infinity norm and delay margin, the optimal performance can be obtained for run-to-run operation.

Deterministic ramp drifts and stochastic IMA(1,1) disturbances usually occur in semiconductor processes, which result in transient deviations and persistent random variations in the process output, respectively. To evaluate their effects on control performance, the thesis derives closed-form formulae for a transient performance index and a long-run performance index. A composite performance index, obtained by multiplying the transient and long-run indices by their respective weighting factors, then serves as the criterion for the selection of controller parameters. The selection of the weighting factors is a trade-off between the different output effects from the deterministic and stochastic disturbances.

Metrology delays in run-to-run processes are uncertain and stochastic. Therefore, a controller with a fixed delay could hardly yield good performance. The thesis develops a hybrid run-to-run controller design by virtue of specifying appropriate robustness and alternating between two filters with different delays. The hybrid design can achieve much better performance in the presence of stochastic delays.

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王銘賢，含未知時變增益批次間程序之類內模控制設計，國立成功大學
化學工程系碩士論文，2011。

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