A system in unity feedback configuration has the loop transmittance

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

Using frequency response techniques, do the following:

(a) Find \(\mathrm{K}\) to meet the specification on steady state error to a unit ramp input \(\leq 0.5\).

(b) Sketch Bode plots using the gain \(\mathrm{K}\) found in part (a) and read the phase margin there from.

(c) Design a cascade lead compensator so as to improve the phase margin found in part (b) to a value \(\geq 45^{\circ}\).