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.

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