Consider the unity$-$feedback system above with

$\backslash [$

G$($s$)=\backslash$frac$\{$K$\}\{$s$($s$+20)($s$+40)\}$

$\backslash ]$

The system is operating at $\backslash (20\backslash \%\backslash )$ overshoot. Design a compensator to decrease the settling time by a factor of $2$ without affecting the percent overshoot and do the following: $[$Section: $9\mathrm{.}3]$

$($a$)$ Evaluate the uncompensated system's dominant poles, gain, and settling time.

$($b$)$ Evaluate the compensated system's dominant poles and settling time.

$($c$)$ Evaluate the compensator's pole and zero. Find the required gain.

$($d$)$ Use MATLAB or any other computer program to simulate the compensated and uncompensated systems' step response.