# Homework Help: Block diagrams to transfer functions

1. Mar 30, 2014

### Dustinsfl

1. The problem statement, all variables and given/known data
I am trying to write a block diagram as a transfer function.

2. Relevant equations

3. The attempt at a solution
Let $G = \frac{1}{s}$, $H = \frac{K}{Js + a}$, and $L= K_f$. Then wouldn't the closed loop transfer function be written as
$$\frac{\frac{HLG}{1+HL}}{1 + \frac{HLG}{1+HL}} = \frac{KK_f}{s^2J + (KK_f + a)s + KK_f}$$
I only ask because the book has it as
$$\frac{K}{s^2J + (KK_f + a)s + K}$$
and I don't see how that was obtained.

Last edited: Mar 30, 2014
2. Mar 30, 2014

### milesyoung

The transfer function for your inner feedback loop is $\frac{H(s)}{1 + H(s) L(s)}$, not $\frac{H(s) L(s)}{1 + H(s) L(s)}$.

I think that should sort it out.

3. Mar 30, 2014

### Dustinsfl

Can you explain why that is?

4. Mar 30, 2014

### milesyoung

It's an easy mistake to make. The transfer function in the forward path appears in both the numerator and denominator of the closed-loop transfer function but the transfer function in the feedback path does not:
http://en.wikipedia.org/wiki/Closed-loop_transfer_function