The open loop transfer function of a closed loop system is [ mathrm{G}(s) mathrm{H}(s)=frac{mathrm{K}}{s(s+1)(2 s+1)} ] Determine

Question:

The open loop transfer function of a closed loop system is

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

Determine phase cross over frequency $\omega_{p c}$ and gain margin in terms of $\mathrm{K}$. Is the closed loop system stable for $\mathrm{K}=2$ ? What is critical value of $\mathrm{K}$ for stability ?

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