There are two methods to establish the mathematical model of control system: analytical method and experimental method. Analytical method is to analyze the motion mechanism of each part of the system and write the corresponding motion equation according to their physical or chemical laws. For example, there are Kirchhoff's law in electricity, Newton's law in mechanics, thermodynamic law in thermodynamics and so on. The experimental method is to artificially apply some test signals to the system, record its output response, and approximate it with an appropriate mathematical model. This method is called system identification. In recent years, system identification has developed into an independent discipline. This chapter focuses on the method of establishing the mathematical model of the system by analytical method.
In automatic control theory, there are many kinds of mathematical models, such as differential equation, difference equation and state equation. Complex number field has transfer function and structure diagram; Frequency domain has frequency characteristics.