Question

The system having the Bode magnitude plot show in figure below has the transfer fucntion(s).

• A. $\frac{60(s+0.01)(s+0.1)}{s^2(s+0.05{)}^2}$
  
• B. $\frac{10(1+10s)}{s(1+20s)}$
• C. $\frac{3(s+0.05)}{s(s+0.2)(s+1)}$
• D. $\frac{5(s+0.1)}{s(s+0.05)}$

Answer 1

Answer: (B), (D)

$\frac{5(s+0.1)}{s(s+0.05)}$

Type=1
$Polesat\Rightarrow \omega =0,0.05$
$Zeroat\Rightarrow \omega =0.1$
using initial line equation
$dB=20logK-20log\left(\omega \right)$
at $\omega =0.01$
$dB=60$
$\because 60=-20$$log\left(0.01\right)+20logK$
On solving, $K=10$
Therefore,
$Transferfunction=\frac{10(1+10s)}{s(1+20s)}=\frac{5(s+0.1)}{s(s+0.05)}$