Transfer function of a controller

Discussion in 'Homework Help' started by wtrow, Dec 3, 2010.

  1. wtrow

    Thread Starter New Member

    Oct 21, 2009
    18
    0
    Attached I have a picture of a 2 degree of freedom controller I have to come up with a transfer function for. Problem is, I'm not sure if I made the equations correctly (we were given only one very simple example).

    I have:

    Y(s)=E(s)*C1(s)+P(s)
    E(s)=X(s)-C2(s)-P(s)*Y(s)-Y(s)

    if those are even correct then I need to solve for Y(s)/X(s), which I am also having trouble with.

    I'm stuck at:

    Y(s)/X(s)=(1-C2(s)/X(s)+P(s)/(C1(s)*X(s)))/(1/C1(s)+P(s)+1)

    with no way to eliminate the extra X(s)'s.

    Any help would be appreciated.
     
    • 331.png
      331.png
      File size:
      15.8 KB
      Views:
      18
  2. t_n_k

    AAC Fanatic!

    Mar 6, 2009
    5,448
    782
    E=X-Y

    Positive input to second SJ is C1*E=C1*(X-Y)
    Negative input to second SJ is C2*Y
    Output of second SJ is C1*(X-Y)-C2*Y

    But Y=P*(output of second SJ )

    So Y=P*[C1*(X-Y)-C2*Y]

    Simplify from there by collecting terms in Y on one side of equation.
     
    wtrow likes this.
Loading...