批次控制在半導體生產製程中扮演極重要的監控角色。既有文獻之批次回饋控制方法大多建構在SISO系統且製程之I-O模型為靜態模型下，然而，生產線實際上卻為MIMO系統且製程同時具有遷移效應較為常見；文獻上有qMMSE控制器被提出來監控此類動態生產製程，由於此控制器僅限於當製程I-O模型為 TF (1,1,1) + VIMA (1,1) 下被建構出來；因此當模型為一般化的 TF (r,s,1) + VARIMA (p,d,q) 模型時，其製程的TMSE之表現並不理想。針對此缺點，本論文提出修正的一般化動態qMMSE回饋控制器，並分別推導出此控制器底下的製程產出公式、製程穩定條件，並同時針對既有的文獻進行理論修正。最後，本文亦探討當實際製程I-O模型為 TF (2,2,1) + VARIMA (1,1,1) 時，此真實模型底下的控制器與模型誤判後的控制器之績效表現；結果顯示，本文提出的控制器之優點為不僅能將製程產出值更快速地調整到目標值，同時亦可使製程的TMSE大幅降低，也能夠發現製程干擾項的誤判對於控制器將會產生嚴重的影響。

Run-to-run control plays a critical role in monitoring or adjusting the IC manufacturing process. Traditionally, in literature, most of the process I-O model deals with single-input single-output (SISO) static model. However, it’s more common to see that the process I-O model follows the multiple-input multiple-output (MIMO) with a dynamic carry-over effect model. Recently, a qMMSE controller has been proposed to monitor such a dynamic MIMO process. The controller, however, is restricted to the case that the process I-O model follows TF (1,1,1) with VIMA (1,1) disturbance. This qMMSE controller, in general, does not perform well when the I-O model follows TF (r,s,1) with VARIMA (p,d,q) disturbance. To overcome this difficulty, this study first constructs a generalized MIMO dynamic qMMSE controller. Then, the process output formula and the stability conditions of the proposed controller are derived, respectively. We use a CMP example to illustrate the proposed method. The results demonstrate that the proposed controller not only adjusts the process output value more quickly to the target value, but also reduces the TMSE of the process significantly. Finally, when the actual I-O model follows TF (2,2,1) + VARIMA (1,1,1), this study uses a simulation study to address the misspecification effects of using wrong controllers. The simulation result shows that using a wrong controller will have serious impacts on the process stability conditions and performance of process TMSE.

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