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

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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.

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