Use frequency response methods to design a cascade, single, passive lag-lead compensator for a unity feedback system with open loop transmittance

\[
\mathrm{G}(s)=\frac{\mathrm{K}}{s(s+1)(s+2)}
\]

to meet the following design goals:

(i) the ramp error coefficient \(\mathrm{K}_{v}=10 \mathrm{sec}^{-1}\)

(ii) phase margin \(\phi_{m s}=50^{\circ}\)

(iii) gain margin \(\geq 10 \mathrm{~dB}\)