Here, we show a second order electrical system with a block having the transfer function inside it. The order of the differential equation is the number of the highest derivative. The transfer function model of this system is shown below. Many dynamic systems models are described by high-order differential equations. The above equation is a transfer function of the second order electrical system.

$v_o(s)$ is the Laplace transform of the output voltage $v_o$ $v_i(s)$ is the Laplace transform of the input voltage $v_i$ The input voltage applied to this circuit is $v_i$ and the voltage across the capacitor is the output voltage $v_o$. All these electrical elements are connected in series. This circuit consists of resistor, inductor and capacitor. Get the differential equation in terms of input and output by eliminating the intermediate variable(s).Д¬onsider the following electrical system as shown in the following figure. Follow these steps for differential equation model.ДЄpply basic laws to the given control system. Differential Equation ModelДifferential equation model is a time domain mathematical model of control systems. Let us discuss the first two models in this chapter.

The following mathematical models are mostly used. Design of control system means finding the mathematical model when we know the input and the output. Analysis of control system means finding the output when we know the input and mathematical model. These models are useful for analysis and design of control systems. The control systems can be represented with a set of mathematical equations known as mathematical model.

Electrical Analogies of Mechanical Systems.

Modeling differential equation systems