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For the system shown below I am trying to get the system function.

I tried putting it into the equation:

$$T(s) = \frac{C_G(s)}{1+C_G(s)\cdot H(s)}$$

where $$ C_G(s) = \frac{K}{s(s+3)(s+4)}$$ and $$H(s) = \frac{8}{(s+7)}$$.

But this didn't give me the correct answer which is apparently: $$T(s) = \frac{K}{s^3 + 8s^2 + 15s + K}$$

Any help with this will be greatly appreciated!

enter image description here

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Just put some formula onto the various nodes: -

enter image description here

Can you see how this works and how E(s) becomes: -

$$R(s) - Y(s)$$

Therefore: -

$$Y(s) = (R(s) - Y(s)) \cdot \left( \dfrac{K}{(s+3)(s+5)}\cdot\dfrac{1}{s}\right)$$

Just rearrange to group Y(s) terms and solve. Can you take it from here (it should be fairly straightforward)?

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