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Block diagram reduction

  1. May 14, 2015 #1
    • Note -- you must show your work on schoolwork problems before we can offer tutorial help
    1. The problem statement, all variables and given/known data
    I have got 2 questions like this and I'm struggling any help would be much appreciated please. Thanks

    2. Relevant equations


    3. The attempt at a solution
     

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  2. jcsd
  3. May 14, 2015 #2

    Hesch

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    Just reduce loop by loop, inside out.

    Use Masons rule. Rightmost inner "loop" is just an addition: G3 + G4.
     
  4. May 14, 2015 #3
    Thanks for the quick response, I will try and understand what you've written and look at masons rule.
     
  5. May 14, 2015 #4

    Hesch

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    Masons rule says, that if you have a loop with a forward feeding block, G, and a negative back-feeding block, H, the transfer function of the reduced block will be:

    G / ( 1 + G * H )

    Now the leftmost inner block has positive feed back, so the transfer function for this loop will be:

    ( G1 * G2 ) / ( 1 - G1 * G2 * H1 )
     
  6. May 14, 2015 #5
    Thanks very much for explaining this, now I've got to draw this out step by step. Much appreciated.

    Thanks

    John
     
  7. May 18, 2015 #6
    Hi

    So will the inner right loop be (G3 + G4) ?

    Thanks
     
  8. May 18, 2015 #7

    Hesch

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    Yes: input*G3 + input*G4 = input*(G3+G4) = output.

    Transfer function = output/input = (G3+G4).
     
  9. May 18, 2015 #8
    Hi

    So this is how it should look with the two transformations ?

    Thanks for help
     

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  10. May 19, 2015 #9

    Hesch

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    It's not a transformation, it's a reduction of the Laplace transformed.

    The reduced transfer function (leftmost inner loop) must be drawn as one block wherein there is a fraction: Numerator = (G1*G2), denominator = (1 - G1*G2*H1).

    Otherwise your drawn transfer function will be read as: ( G1*G2 ) * ( 1 - G1*G2*H1 ).
     
  11. May 19, 2015 #10
    Hi

    Ok thanks very much for your help now the next question looks more involved.
     
  12. May 19, 2015 #11
    Hi which I'm put would I start with as there are 3 ? Please thanks for your help
     

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  13. May 19, 2015 #12

    Hesch

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    Did you reduce the outer loop in the first question?

    I don't quite understand your question ( maybe because I'm not american or english ): 3 of what? Inputs? Please reword your question.

    Furthermore I don't understand what is meant by the question in 2): Describe the relationship . . . ?

    You can "move" θd1 and θd2 backwards in the loop, dividing them with the transfer function they are passing by this movement. Doing this you will have one (parallel) input:

    θi + ( θd1/G1 ) + ( θd2/(H2*G2*G1) ).

    Having removed the inputs from the loop, you can reduce the loop, and multiply its transfer function by its 3 inputs in parallel.

    ( My best guess ).
     
    Last edited: May 19, 2015
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