Use frequency response approach to design a lag-lead compensator for a unity feedback system where the loop transmittance is

\[
\mathrm{G}(s)=\frac{\mathrm{K}(s+8)}{s(s+4)(s+20)}
\]

The design goals are

(i) peak overshoot \(=15 \%\)

(ii) settling time \(=0.1 \mathrm{sec}\)

(iii) velocity error coefficient \(\mathrm{K}_{v}=1000\).