The control system can be classified as electrical, mechanical, hydraulic, thermal and so on. All systems can be described by integrodifferential equations of various orders. While the output of such systems for any input can be obtained by solving such integrodiferential equations. Mathematically, it is very difficult to solve equations in time domain. The Laplace transform of such integrodifferential equations converts them into simple algebraic equations. All the complicated computations then can be easily performed in s domain as the equations to be handled are algebraic in nature. Such transformed equations are known as equations in frequency domain.
Then by eliminating unwanted variable, the required variable in s domain can be obtained. Then by using technique variable, the required variable in s domain can be obtained. Then by using technique of Laplace inverse, time domain function for the required variable can be obtained. Hence making the computations easy by converting the integrodifferential equations into algebraic is the main essence of the Laplace transform.
