The open loop transfer function of a system in unity feedback configuration, is

\[
\mathrm{G}(s)=\frac{\mathrm{K}}{(s+1)(s+2)(s+10)}
\]

Use the root locus approach to do the following:

(a) Determine the value of \(\mathrm{K}\) such that system exhibits peak overshoot of \(57.2 \%\).

(b) Find the steady state error when system is forced to track a step input.

(c) Insert a PI compensator in series with system \(\mathrm{G}(s)\) in the forward path with transmittance

\[
\mathrm{G}_{\mathrm{PI}}(s)=\frac{s+0.15}{s}
\]

and show that steady state error improves while almost preserving the transient response adjusted in part (a)