What does the phase margin tell you about a system's stability?

What does the phase margin tell you about a system's stability?

• A. Phase margin indicates the magnitude of the open-loop gain.
• B. Phase margin indicates how far the phase is from -180 degrees at the gain crossover; larger phase margin implies greater robustness to model uncertainty.
• C. Phase margin measures time delay.
• D. Phase margin has no relation to stability.

Answer: (B)

Phase margin tells you how close the system is to instability in a feedback loop. It’s the amount of extra phase lag, beyond what the current loop already has, that would push the system to the brink of instability. Practically, you look at the frequency where the open-loop gain crosses unity (1 or 0 dB); the phase there is some value. If that phase is, say, -120 degrees, the phase margin is 60 degrees (since -180 + 60 = -120). A larger phase margin means the system can tolerate more model uncertainty, unmodeled dynamics, or small time delays without becoming unstable, so it’s a measure of robustness. The magnitude of the open-loop gain at that frequency isn’t what phase margin represents, and phase margin is not a direct measure of time delay, though delays can affect it. And yes, phase margin is related to stability—the statement that it isn’t is incorrect.

Phase margin tells you how close the system is to instability in a feedback loop. It’s the amount of extra phase lag, beyond what the current loop already has, that would push the system to the brink of instability. Practically, you look at the frequency where the open-loop gain crosses unity (1 or 0 dB); the phase there is some value. If that phase is, say, -120 degrees, the phase margin is 60 degrees (since -180 + 60 = -120). A larger phase margin means the system can tolerate more model uncertainty, unmodeled dynamics, or small time delays without becoming unstable, so it’s a measure of robustness. The magnitude of the open-loop gain at that frequency isn’t what phase margin represents, and phase margin is not a direct measure of time delay, though delays can affect it. And yes, phase margin is related to stability—the statement that it isn’t is incorrect.