E$12\mathrm{.}5$ A system has a process function Gs K s s s $()()()=++47$ with K$=50$ and unity feedback with a PD compensator $.$ G s K K s c p D $()=+$ The objective is to design $()$ G s c so that the percent overshoot to a step is $$ PO $..10\%,$ and the settling time $($with a $2\%$ criterion$)$ is $$ Ts $3$s$.$ Find a suitable $()$ G s c $.$ What is the effect of decreasing process gain from K K $50$to $25==$ on the percent overshoot and settling time?