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研究生:范景翔
研究生(外文):Chiang-Hsiang Fan
論文名稱:非線性系統動態行為之預測與分析
論文名稱(外文):Prediction and Analyis of the Dynamic Behavior of Nonlinear Systems
指導教授:黃世宏
指導教授(外文):Shyh-Hong Hwang
學位類別:碩士
校院名稱:國立成功大學
系所名稱:化學工程學系碩博士班
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:2002
畢業學年度:90
語文別:中文
論文頁數:122
中文關鍵詞:非線性動態分歧
外文關鍵詞:NonlinearDynamicBifurcation
相關次數:
  • 被引用被引用:2
  • 點閱點閱:714
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  • 下載下載:199
  • 收藏至我的研究室書目清單書目收藏:0
化工程序由於存在高度非線性,導致其經常出現複雜的動態行為,包括多重恆態、週期震盪、週期倍增、圓環面或甚至達到混沌狀態。
本論文以化工程序中常見的連續攪拌反應器系統作為研究對象,針對該系統的一般性分歧點,應用分歧理論裡的Center Manifold 映射及標準模型(Normal Form)來預測分歧點附近的動態變化。我們首先分析該系統在不同開環操作範圍中的線性穩定性變化情形。接著,分別加入比例與比例積分控制器,藉著調整控制器參數來觀察控制器所衍生分歧點附近的非線性動態變化。在比例控制下, 標準模型可預測出週期震盪的振幅與穩定性,其結果與系統與安全操作範圍密切相關。而在比例積分控制下,藉由調整比例與積分增益來觀察系統經由週期倍增發展至混沌的路徑。最後,藉著費根堡數的計算,可以更準確地找出系統週期倍增的對應參數值。
High nonlinearity existing in most chemical processes could result in complicated dynamic behavior, including multiple steady states, limit cycles, period doubling, torus and chaos.
This thesis analyzes a continuous stirred tank reactor system often encountered in the process industry. Generic bifurcation points of the system are explored and the dynamics in the vicinity of each bifurcation point are predicted based on center manifold projection and normal form provided by bifurcation theory. First, we analyze the linearized stability of the CSTR system under various open-loop operating ranges. Subsequently, a proportional and a proportional-integral controller are introduced, and the resulting nonlinear dynamic behavior near the controller-induced bifurcation points are observed by adjusting the controller gains. Under proportional control, the normal form model gives immediately the amplitude and stability of the limit cycle, which are consistent with the simulation results. Under proportional-integral control, we can identify the route from period doubling to chaos with changes in the controller gains. Finally, parameter values at which period doubling occurs is further confirmed by the Feigenbaum number.
第一章 緒論 1
1.1 研究動機 1
1.2 文獻回顧 4
1.3 章節與組織 8

第二章 研究方法及理論 9
2.1 Center Manifold 理論 13
2.2 Normal Form 理論 21
2.3 Unfolding 分析 28

第三章 實例應用:系統描述及系統穩定性分析 33
3.1 系統描述 34
3.2 線性穩定分析 38
3.3 閉環穩定性分析 42

第四章 比例控制器下之動態行為模式分析 53
4.1 比例控制系統之Normal Form分析 54
4.2 Hopf Bifurcation 與 Limit Cycles 60

第五章 比例積分控制器下之動態行為模式分析 69
5.1比例控制系統之Normal Form分析 70
5.2 Hopf Bifurcation 73
5.3 Double-Zero Bifurcation 87
5.4 費根堡數 FeigenbaumδNimber 92

第六章 結論與未來展望 96
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