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Transfer function and laplace

  1. Jan 5, 2013 #1
    1. The problem statement, all variables and given/known data

    Consider this control system below:

    Regl_Q.png

    R = set point
    E = remaining error
    V = interference

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

    2. Relevant equations

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

    375a07a4fc83085fc0a5d36529507eaa.png

    Other relevant transfer functions:

    [itex]\frac{U}{V}=\frac{-GR*GP}{1+GR*GP}[/itex]

    [itex]\frac{U}{R}=\frac{GR}{1+GR*GP}[/itex]

    3. The attempt at a solution

    [itex]\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}[/itex]

    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.
     
  2. jcsd
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