# Transfer function and laplace

1. Jan 5, 2013

### Pavoo

1. The problem statement, all variables and given/known data

Consider this control system below:

R = set point
E = remaining error
V = interference

My question is, if both R and V are unit step $\frac{a}{s}$, what will the value of U be when time t$\rightarrow$$\infty$ ?

2. Relevant equations

This question is based on the final value theorem of Laplace transform such as:

Other relevant transfer functions:

$\frac{U}{V}=\frac{-GR*GP}{1+GR*GP}$

$\frac{U}{R}=\frac{GR}{1+GR*GP}$

3. The attempt at a solution

$\lim_{s\rightarrow0}\frac{U}{V}+\lim_{s\rightarrow0}\frac{U}{V}=s*\frac{a}{s}*\frac{-GR*GP}{1+GR*GP}+s*\frac{a}{s}*\frac{GR}{1+GR*GP}$

Is that an ok solution?
The question is how do I use the final value theorem if BOTH signals are step? I know how to do it with one signal, that's easy, but how do I calculate when two signals are step?
I have no answer to this question, but rather asking how I should approach these kind of problems.