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Block diagrams to transfer functions

  1. Mar 30, 2014 #1
    1. The problem statement, all variables and given/known data
    I am trying to write a block diagram as a transfer function.

    hINLD1J.png

    2. Relevant equations



    3. The attempt at a solution
    Let ##G = \frac{1}{s}##, ##H = \frac{K}{Js + a}##, and ##L= K_f##. Then wouldn't the closed loop transfer function be written as
    $$
    \frac{\frac{HLG}{1+HL}}{1 + \frac{HLG}{1+HL}} = \frac{KK_f}{s^2J + (KK_f + a)s + KK_f}
    $$
    I only ask because the book has it as
    $$
    \frac{K}{s^2J + (KK_f + a)s + K}
    $$
    and I don't see how that was obtained.
     
    Last edited: Mar 30, 2014
  2. jcsd
  3. Mar 30, 2014 #2
    The transfer function for your inner feedback loop is [itex]\frac{H(s)}{1 + H(s) L(s)}[/itex], not [itex]\frac{H(s) L(s)}{1 + H(s) L(s)}[/itex].

    I think that should sort it out.
     
  4. Mar 30, 2014 #3
    Can you explain why that is?
     
  5. Mar 30, 2014 #4
    It's an easy mistake to make. The transfer function in the forward path appears in both the numerator and denominator of the closed-loop transfer function but the transfer function in the feedback path does not:
    http://en.wikipedia.org/wiki/Closed-loop_transfer_function
     
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