# Getting transfer function from block diagram

I am having trouble figuring out this step in an example question I've been given. I'm supposed to be finding the 'transfer function in the forward path'. This image shows the block diagram (top) and what I have been told is the correct forward path transfer function (circled with red).

But based off of my understanding of that a forward path transfer function is, I would have said Gfp = 5 * s+4/(s+5)(s+8)

Where am I going wrong?

You have missed the feedback path.
(R(s) - 2*C(S))*5(s+4)/ ((s+5)(s+8)) = C(s), and so on

Also, the closed loop transfer function vs open in case the feedback is 1

H(s) = F(s) / (1+F(s)); in your case the feedback is 2 so, you have to move it in the loop.

Your forward path transfer function Gfp is correct. The circled expression is the transfer function of the whole system with feedback. However, the denominator should be D(s)=[1+2(Gfp)] because the loop gain is LG=-2(Gfp).

I can't understand why it's (2-1). For negative feedback it would be just 1+10(s+4)/[(s+5)(s+8)] in denominator. Thus, you get 5(s+4)/(s^2+23s+80).or didnt I understand you right?

Thank you everyone for your answers. In the end I got so confused I had to go and hunt down my lecturer in his office and ask. He said that because there is a component in the feedback loop (so it's not unity gain) I had to use this formula to convert the transfer function into the 'equivalent unity gain transfer function':

Ge(s) = G(s) / (1 + H(s)G(s) - G(s))

where G(s) is the top part of the block diagram and H(s) is the feedback loop.

btw the e in Ge(s) stands for 'equivalent'.

This gave me the right answer :)

• The equation Ge(s)=.... is false. According to the well-known formula from H. Black for feedback systems we have Ge(s)=G(s)/(1+G(s)H(s)). It is very easy to proof this function. Instead of asking again your lecturer you should consult a good textbook.
– LvW
Oct 5 '15 at 8:02