Question

Two unity feedback systems A and B with open - loop transfer functions are.

$G_A\left(s\right)=\frac{9}{s(s+1)}$ and $G_B\left(s\right)=\frac{16}{s(s+2)}$

Which of the following statement is correct?

• A. System A has higher overshoot than system B.
• B. System A has lower overshoot than B
• C. System A has lower setting time than B
• D. Both have equal settling times

Answer 1

The correct option is A System A has higher overshoot than system B.

(a)
$H_1\left(s\right)=\frac{9}{s^2+s+9}$ $H_1\left(s\right)=\frac{16}{s^2+2s+16}$
${\omega }_n^2=9$ ${\omega }_n^2=16$
${\omega }_n=3$ ${\omega }_n=4$
$2{\xi }_A{\omega }_n=1$ $2{\xi }_B{\omega }_n=2$
${\xi }_A\left(6\right)=1$ ${\xi }_A\left(4\right)=1$

${\xi }_A=\frac{1}{6}$ ${\xi }_A=\frac{1}{4}$

As, ${\xi }_A<{\xi }_B$

$M_{P_A}>M_{P_B}$

$\therefore$ Statement A is correct.