Question

For a second-order system with the closed-loop transfer function $T\left(s\right)=\frac{9}{s^2+4s+9}.$ The settling time for 2 % band, in seconds, is

• A. $1.5$
• B. $2.0$
• C. $3.0$
• D. $4.0$

Answer 1

The correct option is B $2.0$

$t_s=\frac{4}{\xi {\omega }_n}$

$2\xi {\omega }_n=4$

$\Rightarrow \xi {\omega }_n=2$

$\therefore t_s=\frac{4}{2}=2$