Question: The open loop transfer function of a unity feedback control system is given by [ mathrm{G}(s) mathrm{H}(s)=frac{mathrm{K}}{s(s+1)(1+2 s)(1+3 s)} ] Determine the value of (mathrm{K})

The open loop transfer function of a unity feedback control system is given by

\[
\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}}{s(s+1)(1+2 s)(1+3 s)}
\]

Determine the value of $\mathrm{K}$

(i) for which the system is stable.

(ii) which will cause sustained oscillations in the closed-loop system.

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