Why use transfer functions than differential equations?

1. Why do we use transfer functions?
2. Which approach is better amongst the differential equation and transfer function Why?
3. Is a transfer function a differential equation?
4. Why transfer function based analysis is widely used in control system?

Why do we use transfer functions?

The key advantage of transfer functions is that they allow engineers to use simple algebraic equations instead of complex differential equations for analyzing and designing systems.

Which approach is better amongst the differential equation and transfer function Why?

Because differential equations are unwieldy and hard to deal with, and you can't see the behaviour on different frequencies from these, whereas transfer functions just give you the behaviour of an LTI system given an excitation of given property. Much easier to work with! Save this answer.

Is a transfer function a differential equation?

The transfer function can be obtained by inspection or by by simple algebraic manipulations of the differential equations that describe the systems. Transfer functions can describe systems of very high order, even infinite dimensional systems gov- erned by partial differential equations.

Why transfer function based analysis is widely used in control system?

It helps determine important system parameters such as poles, zeros, etc. The system stability can be easily analyzed using the transfer function. It helps to relate output with input.