Consider the closed$-$loop system below, where R$($s$)$ is a unit$-$step

input and the process to be controlled is described by the following transfer function:

G$($s$)=4$

s$2+$ s$.$

$1.$ Assume that Gc$($s$)=1$ and find the percentage overshoot Mp$.$

$2.$ Design Gc$($s$)$ as a PD controller in order to reduce the percentage overshoot of

the closed$-$loop system response to $10\%($e$.$g$.$ Mp $=0\mathrm{.}1)$ with peak taking place

at time tp $=3\mathrm{.}927$ s$.$