Question

The open-loop transfer function of a feedback control system is $\frac{1}{(s+1{)}^3}$

The gain margin of the system is

• A. 16
• B. 8
• C. 4
• D. 2

Answer 1

The correct option is B 8

$-3ta{n}^{-1}\omega =-{180}^o$
$\therefore ta{n}^{-1}\omega ={60}^o$
$\therefore \omega =\sqrt{3}$(Phase crossover freq.)
$a=\frac{1}{(\sqrt{1+{\omega }^2}{)}^3}=\frac{1}{(\sqrt{1+3}{)}^3}$

$=\frac{1}{2^3}=\frac{1}{8}$
Gain margin $=\frac{1}{a}=8$