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研究生:李明育
研究生(外文):Ming-Yu Lee
論文名稱:動態最適化方法之探討─以反應系統為例
論文名稱(外文):An Investigation on Dynamic Optimization with Case StudiesAn Investigation on Dynamic Optimization with Case StudiesAn Investigation on Dynamic Optimization with Case Studies
指導教授:程學恆
指導教授(外文):Shueh-Hen Cheng
學位類別:碩士
校院名稱:東海大學
系所名稱:化學工程學系
學門:工程學門
學類:化學工程學類
論文種類:學術論文
論文出版年:2006
畢業學年度:94
語文別:中文
論文頁數:106
中文關鍵詞:動態最適化正交配置法極大值原理
外文關鍵詞:dynamic optimizationOCFEmaximum principle
相關次數:
  • 被引用被引用:1
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動態最適化在化工領域中應用相當廣泛,如最適化控制、批式饋料醱酵程序等,其重要性也日漸受到重視。本研究應用三種不同最佳化方法-逐步式最佳化方法、極大值原理,以及有限元素正交配置法,探討兩個不同反應器之最佳化問題,一是非恆溫的二氯乙烷裂解反應器最適化,尋求最佳之熱通量分佈,能使得在固定總熱通量下,得到最大氯乙烯產率,以及固定氯乙烯產率之下,最低總吸熱量;另一個案則是探討恆溫的串級催化反應系統之最適化問題,找出最佳之觸媒混合分佈。
除了尋找最佳控制分佈外,本研究詳加探討了此些動態最適化方法之執行面,藉由個案進一步的比較最佳化方法之建構、最佳化之精確性、猜值之敏感性、配位點個數之影響、計算效率、以及具有限制條件的問題等。由結果發現其中以逐步式最佳化方法在建構方面最為直接,且收斂速度最快,而有限元素配置法雖然計算時間最長,但較有彈性,可處理各種複雜限制條件之問題,此外最適化結果亦會受配位點影響。
Dynamic optimization problems can be found in various areas of chemical engineering such as optimal control and fed-batch fermentation and are increasingly gaining importance. This study deals primarily with the application of three optimization methods, namely sequential method, Pontraygin’s maximum principle, and orthogonal collocation on finite element (OCFE) method. Two case studies involving the optimization of chemical reactor systems are presented. One is concerned with the optimization of a non-isothermal ethylene dichloride pyrolysis reactor. The objective is to find the optimal heat flux profile under which maximum vinyl chloride monomer yield can be achieved. It is also posed as a heat minimization problem with the product yield being specified. The other is concerned with the optimization of an isothermal packed-bed reactor with two consecutive reactions, one reversible and one irreversible.
The case studies are analyzed in the context of theoretical framework, implementation, accuracy, sensitivity to initial control profiles, computational accuracy, effect of collocation points, and application limitations. Optimization results are presented. Sequential method has shown to be the most direct method for implementation and has the fastest convergence speed. On the other hand, OCFE, with lower computation efficiency, is more flexible to deal with especially when problems have complex constraints.
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中文摘要…………………………………………………………...….....I
英文摘要………………………………………………………………...II
誌謝..........................................................................................................III
目錄……………………………………………………………………..VI
表目錄………………………………………………………………...VIII
圖目錄…………………………………………………………………...X

第一章 緒論……………………………………………………………1
1-1前言……………………………………………………………..1
1-2 研究動機……………………………………………………….2
1-3論文結構與組織………………………………………………..4
第二章 動態最佳化……………………………………………………5
2-1簡介與回顧…………………………..…………………………5
2-1.1最適化問題分析………………...………………………7
2-1.2最佳化問題分類………………….……………………..9
2-1.3 數學模式建立…………………………………………11
2-1.3.1 微分方程式模式……………………….………12
2-1.3.2微分代數方程式模式…………………………..13
2-2微分代數方程式最適化問題…………………………………17
2-3 最佳化策略…………………………………………………...19
2-3.1逐步式最適化方法…………………………………….19
2-3.2同步式最適化方法…………………………………….20
2-4最佳化求解方法………………………………………………21
2-4.1古典變分法…………………………………………….21
2-4.2極大值理論…………………………………………….22
2-4.3動態規劃法…………………………………………….23
2-4.4控制參數法…………………………………………….24
2-4.5配置法………………………………………………….25
第三章 最佳化策略…………………………………………………..26
3-1連續式最佳化方法……………………………………………26
3-2極大值原理……………………………………………………29
3-3配置法…………………………………………………………33
3-3.1全域配置法…………………………………………….33
3-3.2 有限元素正交配置法…………………………………37
第四章 個案研究及結果討論………………………………………...41
4-1 Case I:EDC裂解反應器…………………………………….41
4-1.1 Case I 模擬……………………………….……………47
4-1.2 Case I最佳化-(A)最大出口VCM產率……………....52
4-2.2.1 Case IA-1 逐步式最佳化方法………………....53
4-1.2.2 Case IA-2 極大值策略………………………....57
4-1.2.3 Case IA-3 有限元素正交配置法…………....…59
4-1.2.3 Case IA-4連續性控制分佈…………………….61
4-1.3 Case I最佳化-(B)反應器最低熱供給…………………63
4-1.3.1 Case IB-1 逐步式最佳化方法…………………65
4-1.3.2 Case IB-2 極大值策略…………………………66
4-1.3.3 Case IB-3 有限元素正交配置…………………68
4-1.3.3 Case IB-4 連續性控制分佈……………………69
4-2 Case II 混合觸媒問題………………………………….……..71
4-2.1 Case II-1 逐步式最佳化方法…………………………75
4-2.2 Case II-2 極大值策略…………………………………78
4-2.3 Case II-3 有限元素正交配置法………………………82
4-2.4 Case II-4 連續性控制分佈……………………………84
4-3 結果討論…………………………………………………….86
4-3.1 Case I最佳化結果討論……………………………….86
4-3.2 Case II最佳化結果討論……………………………….87
4-3.3 動態最適化方法建構之比較…………………………87
4-3.4 最佳化之精確性………………………………………89
4-3.5 起始猜值之敏感性……………………………………89
4-3.6 計算效率………………………………………………93
4-3.7 具有限制條件的問題…………………………………95
第五章 結論與建議…………………………………………………..96
5-1 結論..................................…………………………………….96
5-2 建議……………………..................................……………….97
符號說明………………………………………………………………..98
參考文獻………………………………………………………………100
附錄A EDC pyrolysis model.................................................................104
簡歷........................................................................................................106
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