What is Laplace transform? How it is used in control system?

Can any one tell me why Laplace transform is taken in modelling a control system?What is Laplace transform? How it is used in control system?
Laplace transform is one of the mathematical tools useful to solve some of the integrals in the interval from 0 to infinity %26amp; also for designing and analysing the analog signals.


Control system mainly deals with the analog systems. So, many times it is required to take the integral in the interval from 0 to infinity if the initial conditions are absent. In addition to this, Laplace transform converts the function into frequency domain which is easy to evaluate. By taking the inverse laplace transform of the transfer function ( ratio of laplace of output to the laplace of input ), we can obtain the time response of the given system. Hence, Laplace transform is used in control system.What is Laplace transform? How it is used in control system?
Hey this is a pretty fundamental question, and since you're asking you must be in 1st or 2nd year right?





Well buddy, why do you take log? i mean logarithm? you can just use a calculator right? but u still take it. why? simple, cos each machine has a limit to its processing capacity. So log helps you convert a large number to a smaller one, manipulate it and then utilize the result using an inverse function, either 10^x or e^x in case of ln|x|.





Now consider WHEN you use log. when ur multiplying. certainly not when you're adding or subtracting right? Why? because add sub, both are easier operations which occur on a bit by bit basis, or rather in layman's terms which occur one digit pair at a time. Multiplying and dividing (which is inverse multiplication) is a more cumbersome process so u use log, right?





Now come to Laplace transform. When you want to solve a set of differential equations, do you want to use those huge rubbish techniques you learnt in 1st year math or do you want to do it in an easier way using a transformation technique?? Naturally, the latter right?





So Laplace transform (hey im writin LT ok?) is a technique mainly utilized in engineering purposes for system modeling in which a large differential equation must be solved. Taking LT converts this integrodifferential equation into an algebraic simple equation. (integro-differential means it has integrals of dx as well as df/dx terms.. )





After converting to algebraic form, they can be partially fractioned into standard forms, and Laplace Inverse can be taken to get the solution of the equation.





Mainly Laplace Transform converts a quantity from time domain to an s-domain, where s is a complex variable which is written as @+jW where @ = sigma or the neper frequency and W is the radian freq which ur familiar with. Check out Van Valkenburg for more details about the s-plane and s-domain.





Your second question is a bit immature buddy. Its like asking wat is the use of integration in physics.. I mean, you'll need LT for ur BTech or BE course throughout if ur in the Electrical Engg department, and gradually u'll get the reason why we use it. As i said, ask urself how is integration used in physics and ull realize why this question is very difficult to answer. LT is INTEGRAL in control systems. trust me. Learn it well.