Question

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?

• A. $\frac{1000(s+10)}{s+100}$
• B. $\frac{10(s+10)}{s(s+1000)}$
• C. $\frac{s+1000}{10s(s+10)}$
• D. $\frac{s+1000}{10(s+10)}$

Answer 1

The correct option is D $\frac{s+1000}{10(s+10)}$

From initial line equation,
$dB=20lo{g}_{10}K...\left(1\right)$

as we know,
$20dB=20lo{g}_{10}K$
$i.e.,K=10$

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

Hence,
$G\left(s\right)=\frac{K(1+s{T}_1)}{(1+s{T}_2)}$

$T_2=\frac{1}{10};T_1=\frac{1}{1000}$

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