A unity feedback system has the loop transmittance [ mathrm{G}(s)=frac{1000 mathrm{~K}}{s(s+40)(s+100)} ] Design a lead compensator so

Question:

A unity feedback system has the loop transmittance

\[
\mathrm{G}(s)=\frac{1000 \mathrm{~K}}{s(s+40)(s+100)}
\]

Design a lead compensator so as to achieve the following specifications:

(i) Peak overshoot $=15 \%$

(ii) Error coefficient $\mathrm{K}_{v}=40$

(iii) Peak time $=0.1$ second.

Use frequency response approach.