A feedback system has loop function (mathrm{G}(s) mathrm{H}(s)=frac{mathrm{K}}{s(1+0.5 s)(1+s)}), determine analytically (a) the value of (K) so

Question:

A feedback system has loop function $\mathrm{G}(s) \mathrm{H}(s)=\frac{\mathrm{K}}{s(1+0.5 s)(1+s)}$, determine analytically

(a) the value of $K$ so that system exhibits GM of $+6 \mathrm{~dB}$.

(b) The value of $\mathrm{K}$ so that system exhibits PM of $+30^{\circ}$.

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