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.

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