摘 要
本文分析了化学工程中各个反应罐的物质浓度在平衡状态下和非平衡状态下随时间变化而变化的趋势，运用数学模型将化工问题转化为数学问题，列出数学表达式，利用控制论的知识对模型进行稳定性分析，并通过举例来计算，本文根据常微分方程的基本理论，采用解析法和常数变易法两种方法进行了计算，结合MATLAB计算出结果，并用图的形式反映出来。不仅对化学工程学的研究有重要意义，而且因为它与微分方程定性理论有着密切的联系，因此，这也是数学在现实生活中的应用。
关键词: 解析法； 稳定性分析；平衡状态；非平衡状态；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 问题的提出及模型的假设
1.1 问题的提出
在化学工程中要研究彼此关联的几个反应罐中物质浓度的变化(见图
1)，其中，各个反应罐的浓