What is Mathematical Model

       To study and examine a control system, it is necessary to have some type of equivalent representation of the system. Such a representation can be obtained from the mathematical equations, governing behavior of the system. Most of such mathematical equations are differential equations whether the system may be electrical, mechanical, thermal, hydraulic etc.

Note: The set of mathematical equations, describing the dynamic characteristics of a system is called mathematical model of the system.Obtaining the mathematical model is the first step in analyzing a given system. In the mathematical model, the various operations in the system are represented by the mathematical equations.

       Most of the control systems contain mechanical or electrical or both types of elements and components. To analyze such systems, it is necessary to convert such systems into mathematical models based on transfer function approach. From mathematical angle of view, models of mechanical and electrical components are exactly analogous to each other. Not only this, but we can show that for given mechanical system there is always an analogous electrical network exists and vice versa. The mathematical equations describing both the systems are exactly same in nature.

       As we are well familiar with the behavior of electrical networks and methods of writing equations for it, it will be better if we can draw equivalent electrical networks for given mechanical systems. This will help us in writing system equations in simplified manner and with more detailed understanding.