# Transfer function of a controller

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

1. ### wtrow Thread Starter New Member

Oct 21, 2009
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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.

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2. ### t_n_k AAC Fanatic!

Mar 6, 2009
5,448
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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.

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