Discussion
The open loop transfer function of a unity feedback control system has open loop transfer function as: \(G(s) = 10 / (s(1 + 0.02s)(1 + 0.2s))\).
The phase at the gain crossover frequency is \(-150^\circ\). The gain at phase crossover frequency is \(+15\) dB.
What is the value of phase margin and gain margin?
Answer: A
The phase margin is 180 degrees plus the phase at the gain crossover frequency.
\[ PM = 180^\circ + (-150^\circ) = 30^\circ \]
The gain margin is defined from the gain at the phase crossover frequency. The item states a value of 15 dB and the key gives it as +15 dB, so the pair is \(30^\circ\) and 15 dB, option A. Strictly, a positive 15 dB gain at the phase crossover frequency would mean a gain margin of \(-15\) dB (an unstable loop); the item is loosely worded and the key takes the 15 dB as the magnitude of the margin.
The other options give a phase margin of \(-150^\circ\), \(-180^\circ\) or \(0^\circ\), which do not follow from \(-150^\circ\) at crossover. The answer is option A.
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