在半導體批次製程中，批次間控制常被用來調整每個批次的輸入配方，以降低擾動所造成的產品品質變化。然而許多批次間控制器並未在最佳條件下操作，可能原因包括不適當的控制器結構、較差的強健性、以及缺乏適當的性能標準來決定控制參數的配置。本論文針對量測時延和複雜擾動動態的存在及穩定強健性的要求，發展出符合最佳控制器結構之性能指標與簡易穩定性分析方法，以獲得批次間控制器之強健最佳設計。
批次間控制常面對多種形式的確定性與隨機性擾動，兩者分別會使得製程輸出偏離目標值與發生持續性隨機變異。本論文以暫態性能指標來評估確定性擾動的影響，以長期性能指標來評估隨機性擾動的影響，最後結合兩指標來形成權衡性能指標，做為評估整體性能的標準。在內模控制架構下，批次間控制器的設計可簡化為濾波器的設計，根據擾動動態和強健性限制，選擇最佳的濾波器階次和參數配置。具體而言，二階濾波器最適合處理確定性偏移和ARMA(1,1)隨機性擾動，而三階濾波器最適合處理確定性漂移和IMA(1,1)隨機性擾動。為了完成強健最佳設計，可將權衡性能指標最小化，推導出濾波器參數配置的最佳解，並利用所提簡易方法來分析相應之穩定強健性。當此未受限最佳設計無法滿足穩定強健性要求時，本論文另外提出受限最佳濾波器的設計流程，並為此建立數個基於增益邊限之強健性圖形。藉由這些圖形，此設計流程可以快速且有效地獲得滿足穩定強健性限制的全域最佳濾波器參數。

In semiconductor manufacturing, run-to-run (RtR) control is commonly used to reduce the variability in the product quality induced by disturbances. In this thesis, a tradeoff performance index and a simple stability analysis method are developed to yield the robust optimal design of an RtR controller with metrology delays. A transient performance index is employed to assess the effects of a deterministic disturbance, whereas a long-run performance index is employed to assess the effects of a stochastic disturbance. The two indices are combined to form a tradeoff performance index to serve as an overall performance criterion. In the internal model control framework, the design of an RtR controller can be implemented by the design of a filter with a suitable order. Specifically, a second-order filter is best suited to a deterministic shift and an ARMA(1,1) stochastic disturbance, while a third-order filter is best suited to a deterministic drift and an IMA(1,1) stochastic disturbance. To achieve the robust optimal design, the tradeoff performance index is minimized to derive the optimal solution of filter parameters and the associated stability robustness is analyzed. If the unconstrained optimal design does not satisfy the requirements on stability robustness, a design procedure is provided to find the constrained optimal filter. To this end, several robustness diagrams are established based on user-specified gain margins. With the aid of these diagrams, the design procedure can identify rapidly the globally optimal filter parameters that meet the constraints on stability robustness.

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