A Bode magnitude plot for the transfer function G(s) of a plant is shown in the figure. Which one of the following transfer functions best describes the plant?

\frac{1000 (s + 10)}{s + 100}

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\frac{10 (s + 10)}{s (s + 1000)}

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\frac{s + 1000}{10 s (s + 10)}

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\frac{s + 1000}{10 (s + 10)}

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Solution

The correct option is D $\frac{s + 1000}{10 (s + 10)}$
From initial line equation,
$d B = 20 l o g_{10} K . . . (1)$

as we know,
$20 d B = 20 l o g_{10} K$
$i . e ., K = 10$

Now, form the given plot we know type of system in one.

Hence,
$G (s) = \frac{K (1 + s T_{1})}{(1 + s T_{2})}$

$T_{2} = \frac{1}{10}; T_{1} = \frac{1}{1000}$

$= \frac{10 (1 + 0.001 s)}{(1 + 0.1 s)} = \frac{1}{10} \frac{(1000 + s)}{(s + 10)}$

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