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Block Diagram Reduction - Control Systems Engineering

  1. Dec 18, 2015 #1
    1. The problem statement, all variables and given/known data
    Determine the closed loop transfer functions of the systems shown below:

    Screenshot (41).png

    2. Relevant equations
    Standard block diagram algebra.

    3. The attempt at a solution

    I've moved the take off point such that the diagram now looks like:

    Screenshot (40).png

    I am having difficulty determining G1(s). The solution given is

    G1(s) = 4(s + 2) + 1 = 4s + 9

    But it is not obvious to me where this is coming from. Taking G1(s) as given, I am able to solve the rest of the question without issue.

    Any help appreciated.
  2. jcsd
  3. Dec 18, 2015 #2


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    2017 Award

    The question is a little confusing. The combination of the (s+2) and the gain 4 is clearly 4(s+2). Is that what you mean by G1? If you want to consolidate that loop (second diagram) including the summation block, it would be 4(s+2)+1.
  4. Dec 18, 2015 #3


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    You have nothing to do than to write down the output of the summing block as a function of the input:
    Vout=Vin + Vin*4*(s+2)=Vin(1+4(s+2)).
    From this it follows Vout/Vin=4s+9
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