摘 要
本文分析了化學工程中各個反應罐的物質濃度在平衡狀態下和非平衡狀態下隨時間變化而變化的趨勢，運用數學模型將化工問題轉化為數學問題，列出數學表示式，利用控制論的知識對模型進行穩定性分析，並通過舉例來計算，本文根據常微分方程的基本理論，採用解析法和常數變易法兩種方法進行了計算，結合MATLAB計算出結果，並用圖的形式反映出來。不僅對化學工程學的研究有重要意義，而且因為它與微分方程定性理論有著密切的聯絡，因此，這也是數學在現實生活中的.應用。
關鍵詞: 解析法； 穩定性分析；平衡狀態；非平衡狀態；物料平衡原理；
Abstract
In this paper, I have made an analysis of the trend that the material density in each react pot is varied with time under Equilibrium state and non-equilibrium state in chemical engineering, utilizing the mathematical model to turn the chemical question into the mathematics question, I list the expression formula of mathematics, and utilize knowledge of cybernetics to carry on stable analysis to the model. Through calculating with an example and according to the basis theory of the ordinary differential equation, this article uses two methods including the analytic method and the constant change method to carry on the computation, following it, I combine MATLAB to calculate the result and utilize MATLAB to draw the figure to reflect the result of the calculation. Not only the theory will significant for research of chemical engineering, but also there are some close connections with stable analysis which is in differential equation. so, this is application of mathematics in actual life.
Key words: Analytic method ; Stability analysis ;Equilibrium state ;Non-equilibrium state ;Balanced principle of the supplies;
1 問題的提出及模型的假設
1.1 問題的提出
在化學工程中要研究彼此關聯的幾個反應罐中物質濃度的變化(見圖1)，其中，各個反應罐的濃
