Question: The open-loop transfer function of a feedback control system is [ mathrm{G}(s) mathrm{H}(s)=frac{1}{(s+1)^{3}} ] The gain margin of the system is (a) 2 (b) 4

The open-loop transfer function of a feedback control system is

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

The gain margin of the system is
(a) 2
(b) 4
(c) 8
(d) 16

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The gain margin of a system is found from its openloop frequency response Its the gain at which the phase shift first reaches 180 degrees also referred as phase crossover frequency or it can be viewed as how much you can increase the gain before the system goes unstable Given that the openloop transfer function of the feedback control system is GsHs 1 s1 We convert s to jw where j sqrt1 because we need to figure out the frequency response of the system So it becomes GjwHjw 1 jw1 The magnitude and phase of this frequency response are Magnitude GjwHjw 1 jw1 Phase 3tan1w The gain margin is the frequency where the phase reaches 180 degrees In this case this is when 3 tan1w 180 Consequently we find that w tan1803 1 The gain at w ... View full answer

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