半導體製程中，EWMA與double EWMA批次間控制器對於固定的量測時延具有良好的控制效果，但由於量測設備的昂貴和量測耗時，量測時延容易產生不確定性與隨機性，因而使得控制效果變差。本論文針對具馬可夫性質之隨機量測時延，提出兩種切換式批次間控制器和三種含單一濾波器之傳統批次間控制器，並相互比較以找出最佳控制器設計。
批次間控制器常需處理漂移式確定性擾動及ARMA(1,1)模型所描述之隨機性擾動，前者會使程序輸出偏離設定之目標值，而後者會使其發生持續性隨機變動。為了分析各種批次間控制系統之隨機穩定性與擾動消除性能，本研究先假設控制器包含一或多個二階內模控制濾波器，然後利用給定轉移機率之隨機變數來代表量測時延，最後建立狀態空間系統模型，其中狀態變數被擴增來引入隨機量測時延和擾動的影響。此系統模型配合李亞普諾夫函數，可獲得判斷控制系統隨機穩定性的分析方法。另外，透過穩定系統模型的模擬，推導出暫態性能指標的閉合公式來評估確定性擾動的影響，亦可快速計算出長期性能指標來評估隨機性擾動的影響。作為整體控制性能評估標準的權衡性能指標，即由兩種指標加權組合而成。在轉移機率未知的情況下，本研究提出切換式批次間控制器的簡易最佳設計，可達成權衡性能指標的最小化，且控制效果遠遠優於傳統批次間控制器。

In semiconductor processes, run-to-run (RtR) controllers such as EWMA (exponentially weighted moving average) and double EWMA controllers work well for fixed metrology delay. However, expensive metrology devices and time-consuming measurement may render metrology delay uncertain and stochastic, thus deteriorating the control performance. To deal with stochastic metrology delay with the Markov property, this thesis presents two switched RtR controllers and three conventional RtR controllers involving single filters, and compares them with each other to find the optimal controller design.
RtR controllers are often faced with deterministic disturbances of drift type and stochastic disturbances described by an ARMA(1,1) (autoregressive moving average) model. The former may cause the process output to deviate from the desired target, while the latter may cause it to fluctuate randomly and persistently. To analyze the stochastic stability and disturbance-rejection performance of various RtR control systems, this research first assumes that the controller consists of one or more second-order filters in the internal model control structure, then utilizes a random variable with specified transition probabilities to represent the measurement delay, and finally establishes a state-space system model with state variables augmented to incorporate the effects of stochastic measurement delay and disturbances. The system model in conjunction with the Lyapunov function can yield an analysis method to determine the stochastic stability of the control system. In addition, via the simulation of the stable system model, a transient performance index in closed form is derived to assess the effect of deterministic disturbances, and a long-run performance index can be computed rapidly to assess the effect of stochastic disturbances. The weighted combination of the two indices is employed to form a tradeoff performance index serving as an overall performance criterion. When the transition probabilities are unknown, a simple optimal design of the switched controller is proposed to minimize the tradeoff performance index. Its control performance is far superior to that of the conventional RtR controllers.

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