臺灣博碩士論文加值系統

本研究探討了非理想混合對連續攪拌槽反應器（CSTR）的反應軌跡和輸入多重穩態的影響。在傳統的理想混合假設下，CSTR被認為具有均勻的溶液混合和相同的組成分佈。然而，實際工廠CSTR操作中，反應器存在著不完全混合，這可能導致反應物和產物在反應器中的分佈不均勻。
我們首先研究了非理想混合對CSTR不同的複雜化學反應軌跡的影響，論文中的複雜化學反應，包含連續競爭複雜反應與Van de Vusse 複雜反應，我們研究的結果發現非理想混合會影響到CSTR 穩態濃度曲線與槽中反應軌跡，這些結果對於複雜化學反應的CSTR設計有很大的助益。
針對上述成果，我們將複雜化學反應延伸到自身催化反應，並以預先混合的單一進料與未預先混合的雙進料兩種不同進料狀況，探討非理想混合對CSTR 穩態濃度曲線與槽中反應軌跡。研究結果顯示非理想混合不只會影響到單一穩態與多重穩態的產生，更進一步影響到槽中反應軌跡，這些成果還沒有學者探討，對於自身催化反應的CSTR設計有很大的參考價值。
論文也探討非理想混合對CSTR控制操作的影響，由於非理想混合會使CSTR在有非線性化學反應產生輸出多重穩態，進一步也會產生輸入多重穩態，這也引起一般的反應器控制策略無法達成好的控制結果，尤其在有同時出現輸出多重穩態與輸入多重穩態的CSTR控制操作時，會使得一般的反應器控制策略發揮更是困難重重。
本文針對非線性化學反應為 (k_1 C_A^')/(1+k_2 C_A^' )^2 的非理想混合CSTR進行轉移函數推導，掌握所有的動態特性，首先探討學者已發表的線性控制策略與非線性控制策略分別對三種狀況，一、無輸出多重穩態，二、只有輸出多重穩態三、同時具有輸出多重穩態與輸入多重穩態影響，我們的研究結果顯示線性控制策略只能應付前面兩種狀況，無法應付同時具有輸出多重穩態與輸入多重穩態狀況，上述的研究成果對於CSTR控指策略有很大的參考價值。
最後， 本論文嘗試結合模式誤差補償與控制器合成法之CSTR控指策略探討上述三種狀況，我們的研究結果顯示我們所提出的控制策略優於學者已發表的線性控制策略與非線性控制策略，上述的研究成果對於CSTR控指策略有很大的參考價值。未來，我們也將新控制策略延伸到其他具有同時具有輸出多重穩態與輸入多重穩態的化學反應系統。

This study investigates the impact of non-ideal mixing on the reaction trajectory and input multiplicity of a Continuous Stirred Tank Reactor (CSTR). Under the traditional assumption of ideal mixing, the CSTR is believed to have uniform solution mixing and the same composition distribute tion. However, in practical CSTR operations, the reactor exhibits incomplete mixing, which can lead to non-uniform distribution of reactants and products within the reactor.
We first examine the influence of non-ideal mixing on the reaction trajectory of CSTR for different complex chemical reactions, including the consecutive competitive complex reaction and Van de Vuuse complex reaction. The results of our study reveal that non-ideal mixing affects the steady- state concentration curve and reaction trajectory within the tank. These findings are highly beneficial for the design of CSTRs in complex chemical reactions.
Building upon the aforementioned results, we extend the investigation of complex chemical reactions to self-catalytic reactions. We explore the effects of non-ideal mixing on the steady-state concentration curve and reaction trajectory of CSTR for two different feeding conditions: pre-mixed single feed and non-premixed dual feed. The research findings demonstrate that non-ideal mixing not only impacts the generation of single and multiple steady states but also influences the reaction trajectory within the tank. These insights, which have not been explored by previ ous researchers , provide valuable references for the design of CSTRs in self-catalytic reactions.
Lastly, the paper investigates the influence of non-ideal mixing on the control operation of CSTR. Due to non-ideal mixing, the CSTR exhibits output multiplicity resulting from nonlinear chemical reactions, which further leads to input multiplicity. This renders conventional re actor control strategies ineffective, particularly when dealing with the simultaneous occurrence of output and input multiplicity in CSTR control operations. For a non-linear chemical reaction represented by (k_1 C_A^')/(1+k_2 C_A^' )^2 in non-ideal mixing CSTR, we derive the transfer function and capture all dynamic characteristics. We first examine the linear control strategies and nonlinear control strategies previously published by scholars separately for three scenarios: 1) no output multiplicity, 2) only output multiplicity, and 3) simultaneous presence of output and input multiplicity. Our research results indicate that linear control strategies can only handle the first two scenarios and fail to address the situation involving both output and input multiplicity. These research findings provide significant references for CSTR control strategies.
Finally, this study attempts to integrate model error compensation and controller synthesis methods to explore the control strategies for the CSTR system under the aforementioned three conditions. Our research results demonstrate that the proposed control strategy outperforms The linear and nonlinear control strategies were previously published by scholars. These findings hold significant reference value for CSTR control strategies. In the future, we will also extend the novel control strategy to other chemical reaction systems that exhibit both multiple output steady states and multiple input steady states.

摘要 i
Abstract iv
致謝 vii
目錄 viii
表目錄 xiii
圖目錄 xv
第一章 緒論 1
1.1前言 1
1.2文獻回顧 2
1.3 研究動機 5
第二章 非理想混合對Cholette模型下實際CSTR複雜反應軌跡的動態行為的影響 6
2.1 模式 6
2.2 解析解 7
2.3 極值的定性行為和分析 9
2.4穩定狀態曲線 10
2.5 結果與討論 14
2.5.1情況 1 (a_11<a_22) 14
2.5.2情況 2 (a_11>a_22) 15
2.5.3情況 3 (a_11=a_22) 15
2.6 結論 24
2.7 符號說明 25
第三章 非理想混合對Cholette模型下實際CSTR Van de Vusse反應軌跡的動態行為的影響 27
3.1 模式 27
3.2 解析解 28
3.3 極值的定性行為和分析 31
3.4 穩定狀態曲線 32
3.5 結果與討論 36
3.5.1情況 1 (c_11<c_22) 36
3.5.2情況 2 (c_11>c_22) 37
3.5.3情況 3 (c_11=c_22=c) 37
3.6結論 45
3.7 符號說明 46
第四章 預先混合與未預先混合對自身催化反應多重穩態之影響 48
4.1研究方法與內容 48
4.1.1反應系統與數學模式 48
4.1.2產生多重穩態之必要充分條件 51
4.2數值模擬與驗證 52
4.2.1相圖建立 52
4.2.2模擬結果 53
4.3結果與討論 55
4.3.1預先混合 55
4.3.2未預先混合 56
4.3.3 穩定性分析 56
4.3.4 特徵分解與操作條件 57
4.4結論 82
4.5符號說明 83
第五章 非理想攪拌對基於Cholette模型的CSTR的超前-滯後反應的影響-輸入多重穩態和控制器性能的模擬研究 84
5.1 系統說明 85
5.1.1 模式 85
5.1.2 輸入多重穩態與輸出多重穩態 86
5.1.3 轉移函數 87
5.1.4 穩定/不穩定極點和零點 89
5.1.5 積分控制器 92
5.2 結果與討論 94
5.2.1 轉移函數和系統穩定性 95
5.2.2 控制器性能 104
5.3 結論 112
5.4 符號說明 114
第六章 結合模式誤差補償與控制器合成法之CSTR控制策略探討同時具有輸出多重穩態與輸入多重穩態影響 115
6.1 傳統上直接合成法控制器 116
6.2 加入一階過濾器之直接合成法控制器 121
6.3 模式誤差補償器的控制策略 126
6.4 結合模式誤差補償與控制器合成法之CSTR控制策略 130
6.5結論 136
6.6 符號說明 137
第七章 結論與未來展望 139
參考文獻 142
附錄A 150

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