GATE 2024 EE – Question 20

Control Systems · Mathematical modelling and representation of systems, Feedback principle, Transfer function, Block diagrams and Signal flow graphs · 1 mark · Multiple choice

For the block-diagram shown in the figure, the transfer function $\dfrac{C(s)}{R(s)}$ is

$\dfrac{G(s)}{1+2G(s)}$
$-\dfrac{G(s)}{1+2G(s)}$
$\dfrac{G(s)}{1-2G(s)}$
$-\dfrac{G(s)}{1-2G(s)}$

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Correct answer: (D) $-\dfrac{G(s)}{1-2G(s)}$

Explanation

The first summer gives $e_1=R-C$ (outer negative feedback). The second summer takes $-e_1$ and $+C$ (inner positive feedback): $e_2=-(R-C)+C=-R+2C$. Then $C=G\,e_2=G(-R+2C)$, so $C(1-2G)=-GR$ and $\dfrac CR=-\dfrac{G}{1-2G}$.