Mathematical Modelling of Electrical Systems

In this post we will discuss on mathematical modelling of electrical systems which is very essential for further study of control systems. In my early post I discuss on What is an automatic control systems? And Classification of Control Systems, you may read those.

The system may be considered to be consisting of an inter connection of smaller components or elements, whose behaviour can be described by means of mathematical equations or relationships.

Most of the electrical systems can be modelled by three basic elements: Resistor, inductor, and capacitor. Circuits consisting of these three elements are analysed by using Kirchhoff’s Voltage law and Current law.

Resistor: In bellow the circuit model of resistor is shown in Fig.

Mathematical Modelling of Electrical Systems

The mathematical model is given by the Ohm’s law relationship,

Mathematical Modelling of Electrical Systems

Inductor: In bellow the the circuit representation is shown in Fig

Mathematical Modelling of Electrical Systems

The input output relations are given by Faraday’s law,

Mathematical Modelling of Electrical Systems

If only a single coil is considered, the inductance is known as self-inductance. If a voltage is induced in a as second coil due to a current in the first coil, the voltage is said to be due to mutual inductance, as shown in Fig

Mathematical Modelling of Electrical Systems Mathematical Modelling of Electrical Systems

Capacitor: In bellow the circuit symbol of a capacitor is given in Fig.

Mathematical Modelling of Electrical Systems lapcap1

If we integration of v(t) is known as the charge on the capacitor and is denoted by ‘q’. Thus

 Mathematical Modelling of Electrical Systems

 

In above discussion we can see the Mathematical Modelling of Electrical Systems which has come to act when we go for Laplace transform. It will come to act when we will go for calculate transient response of an electrical systems in time domain.

Hope this above discussion on Mathematical Modelling of Electrical Systems will be helpful to you.

Please follow our website for further discussion on various topic related control systems. In future we will discussion on

1 Time Response Analysis of Control Systems

2 Stability of Systems

3 Root Locus Analysis

4 Frequency Response of Control Systems

 

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