Q$5$ Given the following open$-$loop plant, $[$Section: $12\mathrm{.}2]$

$G(s)=\frac{20}{(s+2)(s+4)(s+8)}$

design a controller to yield a $15\%$ overshoot and a settling time of $0\mathrm{.}75$ second. Place the third pole $10$ times as far from the imaginary axis as the dominant pole pair. Use the phase variables for state$-$variable feedback.