## Final value theorem

The final value theorem is used to trace out the final signal value using the signal spectrum.

## Laplace final value theorem

If you know F(s), and if you don’t know F (t) related to that F(s), you can trace the final value of that F (t).

The F (t) and its 1st derivate are replacing transformable, then the find value of F (t) is

F (∞) = Limit. sf. (s)

s→0

## Final value theorem steady-state error

It is a deviation of the steady state is known as steady state error. We can find the steady state error using the final value theorem, it is represented with ess.

ess=limt→∞e(t)=lims→0sE(s)ess=limt→∞e(t)=lims→0sE(s)

Where,

E(s) is the Laplace transform of the error signal, e(t)e(t)

## Initial and final value theorem

The initial theorem is used to trace initial value using known spectrum and unknown it is,

F (0) = Limit sf (s)/ s→∞

The final theorem is used to trace the final value using spectrum and signal it is like using,

F (∞) = Limit. Sf. (s)/ s→0

Using both the theorems such as initial and final theorems, you can easily trace the overall range of the signal.