本研究主要針對饋料批次生化反應器及管式流動反應器進行最佳化控制問題的探討，首先引用Pontryagin最小化原理來定義最佳化問題，並運用極限控制概念，以階段性方式控制系統，再藉由奇異值控制理論避開複雜的兩端點邊界值問題。
依上述最佳化架構下，分別對饋料批次生化反應器及管式流動反應器進行最佳化的設計，最後對系統進行韌性測試，運用非線性模式預測控制進行干擾消除，將系統維持在最佳狀態。

This research mainly aims at probing into the optimal control problem (abbreviated as OCP) of fed-batch bio-reactor and tubular flow reactor. First of all, the minimum principle of Pontryagin are introduced to define the optimal control problem. Moreover, the concept of Extremal control is utilized in the performance. With the control of bang-bang type, the system would be manipulated. In addition, Singular control theory is applied to avoid the complex problem of the two point boundary value problem.
According to the optimal construction indicated above, the optimal design of fed-batch bio-reactor and tubular flow reactor would be operated individually. Finally, the study proceeds the robust test in order to maintain the best condition of this system by using nonlinear model predictive control which can remove the disturbance, and to maintain the system at the optimal condition.

目錄
摘要 I
ABSTRACT II
誌謝 III
目錄 IV
表目錄 VII
圖目錄 VIII
符號說明 IX
第一章 緒論 1
1.1研究動機 1
1.2研究方法 1
1.3研究目的 2
第二章 最佳化理論 3
2.1前言 3
2.2最佳化問題規劃 3
2.2.1數學模型 3
2.2.2物理限制 4
2.2.3特性指標 4
2.2.4最佳控制問題 5
2.3 PONTRYAGIN最小化理論 6
2.4兩端點邊界值的問題 8
2.5奇異控制法 8
2.5.1奇異控制理論 9
2.5.2極限控制(Extremal controls) 11
第三章 最佳化控制應用於生化反應器 12
3.1前言 12
3.2饋料批次生化系統 12
3.2.1數學模式 12
3.2.2系統條件 13
3.2.3系統限制 14
3.3最佳化控制 16
3.3.1最佳化問題分析 16
3.3.2 Pontryagin理論 17
3.3.3奇異值控制法 18
3.3.4極限控制 18
3.4最佳控制軌跡 19
3.4.1盤尼西林 19
3.4.2菌體生長期 19
3.4.3產物生成期 20
3.4.4最佳軌跡 20
3.5模式預測控制 25
3.5.1前言 25
3.5.2模式預測控制策略 25
3.5.3非線性模式預測控制 28
3.6 韌性測試 30
3.6.1加入干擾源 30
3.6.2 非線性模式預測控制 30
3.7結果與討論 35
第四章 最佳化控制應用於 管式流動反應器 36
4.1前言 36
4.2管式流動反應系統 36
4.2.1數學模式 38
4.2.2系統條件 38
4.2.3系統限制 39
4.3流動反應系統之穩態模式 40
4.3.1系統穩態模式 40
4.3.2系統穩態定管壁溫度分析 40
4.4管式流動反應器之穩態模式的最佳化控制 43
4.4.1穩態模式之最佳化問題設計 43
4.4.2 Pontryagin理論 43
4.4.3奇異值控制法 44
4.4.4極限控制法 44
4.5穩態模式之最佳化控制軌跡 45
4.5.1控制階段 45
4.5.2最佳化軌跡 45
4.5.3權重值設計 45
4.6流動反應系統最佳化控制分析 51
4.6.1最佳化控制軌跡 51
4.6.2最佳化控制的操作變數設定 51
4.6.3有限差分法在管式反應系統之應用 51
4.7 韌性測試 55
4.7.1加入干擾源 55
4.7.2 非線性模式預測控制 55
4.8結果與討論 63
第五章 結論與展望 64
5.1最佳化問題設計 64
5.2生化反應器 64
5.3管式流動反應器 65
參考文獻 66
附錄 69
作者簡介 72

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