Block diagram reduction feedforward loop.

Discussion in 'Homework Help' started by Electromech man, Feb 2, 2011.

  1. Electromech man

    Thread Starter New Member

    May 2, 2009
    8
    0
    I have come across a block diagram that has me stumped. What has me stumped is the loop with no block on it.

    Obviously if it had a block it would simply be G/(1+-GH). I am referring to the simplification of the first block of course...

    Please see attachment.

    Can anyone offer me any assistance?


    Regards.
     
  2. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    The diagram doesn't have a loop and even if it had a block, you couldn't use the feedback formula.

    When there's a simple line, you can always make one with H=1.

    Notice that in this example, you don't have feedback, the signal keeps going forward and never returns.

    Thus you have two systems in parallel. One that is H1=2/(s+1) and one that is H2=1.

    Is that clear?
     
  3. Electromech man

    Thread Starter New Member

    May 2, 2009
    8
    0
    Yes I believe so.

    So does that make the parallel loop H1 + H2 = 2/(s +1) + 1?

    Then I go on to find the transfer function with G(s) = 2/(s + 1) + 1 and Gc(s) = K/s(s + 2)?


    Regards.
     
  4. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    Yes... almost.

    The H2=1 is subtracted, so it it H=2/(s+1)-1.
    The final system will be H*Gc.

    And just remember that a parallel path is different than a loop. The loop refers to feedback.
     
  5. Electromech man

    Thread Starter New Member

    May 2, 2009
    8
    0
    T(s) = Y(s)/R(s) = G(s)Gc(s)/[1 + G(s)Gc(s)] is it not?

    G(s) = 2/(s+1)-1.

    I have Gc(s) = K/[s(s + 2)

    With your information I get a Transfer Function of

    K - sK/[s^3 + 3s^2 + s(2 - K) + K]

    Can these be done on Matlab?


    Regards.
     
  6. Georacer

    Moderator

    Nov 25, 2009
    5,142
    1,266
    The formula T(s)=\frac{G(s)}{1 \pm G(s)H(s)} is valid only for a feedback loop, where signal goes backwards. This isn't the case as the signal goes only forwards.

    Thus the TF is simply T(s)=\left( \frac{2}{s+1}+1\right) \cdot \left( \frac{K}{s(s+2)} \right).

    In Matlab that would be
    Code ( (Unknown Language)):
    1.  
    2. K=10 %you need to define a value for K, in order to use it
    3. G1=tf(2,[1 1]);
    4. G2=tf(1,1);
    5. G=parallel(G1,G2);
    6. Gc=tf(K,[1 2 0]);
    7. T=series(G1,Gc)
    8.  
    I 'm not currently able to test the code I provided as Matlab isn't installed in this computer yet.
     
Loading...