Question

The gain margin and the phase margin of a feedback system with $G\left(s\right)H\left(s\right)=\frac{s}{(s+100{)}^3}$ are

• A. $0dB,0^{\circ }$
• B. $\infty ,\infty$
• C. $\infty ,0^{\circ }$
• D. $88.5dB,\infty$

Answer 1

The correct option is B $\infty ,\infty$

$G\left(s\right)H\left(s\right)=\frac{s}{(s+100{)}^3}$
Calculating ${\omega }_{pc},$
$-{180}^{\circ }=+90-3{\tan }^{-1}\frac{{\omega }_{pc}}{100}$
$-{270}^{\circ }=-3{\tan }^{-1}\frac{{\omega }_{pc}}{100}$
$or,{\omega }_{pc}=\infty$
$\therefore G.M=\infty$
Hence cannot be determined.
Calcuating ${\omega }_{pc}$
$From|G\left(s\right)H\left(s\right)|=1$
${\omega }_{pc}=negativevalue$
G.M and P.M . of the system cannot be determined