控制系统的数学模型

　　一、线性定常连续系统微分方程的一般形式:
　　控制系统的 数学模型是描述 系统内部物理量 (或变量)之间关系的数学表达式 。在静态条 件下 (即变量各阶导数为零)，描述变量之间关系的代数方程叫静态数学模 型；而描述变量各阶导数之间关系的微分方程叫数学模型。
　　二、控制系统的数学建模过程 确定系统(元件)的输入量、输出量. 按照系统中元件 遵循的科学规律 (物理, 化学等),围绕输入量和输出量以及中间变量, 列解方程式. 消去中间变量 , 得到只有输出量和输入量及其各阶导数的微分方程.
　　建立控制系统的数学模型，并在此基础上对控制系统进行分析、综合，是机电控制工程的基本方法。如果将物理系统在信号传递过程中的动态特性用数学表达式描述出来，就得到了组成物理系统的数学模型。
　　经典控制理论采用的数学模型主要以传递函数为基础。而现代控制理论采用的数学模型主要以状态空间方程为基础。而以物理定律及实验规律为依据的微分方程又是最基本的数学模型，是列写传递函数和状态空间方程的基础。
　　翻译成英文：
　　Mathematical model of control system
　　1. The general form of the differential equation of linear time-invariant continuous system:
　　The mathematical model of the control system is a mathematical expression that describes the relationship between the physical quantities (or variables) within the system.
　　Under static conditions (that is, the derivative of each order of the variable is zero), the algebraic equation describing the relationship between the variables is called the static mathematical model.
　　And the differential equation describing the relationship between the derivatives of the variable is called the mathematical model.
　　Second, the mathematical modeling process of the control system
　　Determine the input and output of the system (component).
　　According to the scientific laws (physics, chemistry, etc.) that the components in the system follow, formulate equations around the input and output and intermediate variables.
　　Eliminate the intermediate variables, and obtain a differential equation with only the output and input and their derivatives.
　　Establishing the mathematical model of the control system, and analyzing and synthesizing the control system on this basis, is the basic method of electromechanical control engineering.
　　If the dynamic characteristics of the physical system in the signal transmission process are described by mathematical expressions, the mathematical model that constitutes the physical system is obtained.
　　参考资料：百度
　　英文翻译：Google翻译
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