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Transfer function with Disturbance

  1. May 13, 2015 #1
    1. The problem statement, all variables and given/known data
    Find the steady-state error due to a disturbance Td(s) = 1/s.

    Set R(s) = 0.

    if given a system:


    Snapshot.jpg

    2. Relevant equations
    n/a

    3. The attempt at a solution

    I need Y(s)/Td(s). To do this I must find Y(s) in terms of the transfer function Y(s)/R(s) which I have obtained. This gives me an expression for Y(s) in terms of G(s), Gc(s), and R(s).

    3D%20R%28s%29%20%5Cfrac%7BG%28s%29G_%7Bc%7D%28s%29%7D%7B1%20+%20G%28s%29G_%7Bc%7D%28s%29%7D.gif



    Now I must solve for Y(s)/Td(s).

    If Td(s) = 1/s, then I should just multiply Y(s) by s and be done with it. However, the book gets a totally different answer.

    specifically, I am not sure how R(s) disappears along with the rest of the numerator in the result.

    Thanks for your time.
     
  2. jcsd
  3. May 13, 2015 #2

    rude man

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    Homework Helper
    Gold Member

    Why? R(s) = 0!
     
  4. May 14, 2015 #3

    LvW

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    Your transfer function is valid for the R(s) input only.
    The function referred to the Td(s) input looks different!
     
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