Problem $1$ Review the Extra notes for $2$nd order approximation

For the given unity feedback system with

$()=1$

$(+5)3$

$($a$)$ Find the location of the dominant poles to yield a $1\mathrm{.}2$ second settling time and overshoot of $15\%$

$($b$)$ If a compensator $()=+$

$+$

with a zero at $=1$ is used to achieve the conditions of Part

a$,$ what must be the angular contribution and location of the compensator pole be$?$

$($c$)$ Find the gain $$ required to meet the requirements stated in Part a$.$

$($d$)$ Find the location of the other closed$-$loop poles for the compensated system and discuss the

validity of your seco