Control Engineering Basics
Which of the following correctly describes the gain margin and phase margin read from the Bode plot of the loop transfer function?
- AThe gain margin is the difference of the phase from −180° at the frequency where the gain is 0 dB, and the phase margin is the difference of the gain from 0 dB at the frequency where the phase is −180°
- BThe gain margin is the difference of the gain from 0 dB at the frequency where the phase is −180°, and the phase margin is the difference of the phase from −180° at the frequency where the gain is 0 dB
- CBoth the gain margin and the phase margin are read on the closed-loop Bode plot at the frequency where the gain is −3 dB
Show answer and explanation
Answer: B. The gain margin is the difference of the gain from 0 dB at the frequency where the phase is −180°, and the phase margin is the difference of the phase from −180° at the frequency where the gain is 0 dB
The gain margin is how many decibels the gain is below 0 dB at the phase crossover frequency, where the phase reaches −180°. The phase margin is how many degrees the phase still is from −180° at the gain crossover frequency, where the gain is 0 dB. Both measure how close the loop transfer function comes to the point −1 (gain 0 dB, phase −180°), and they are read from the loop transfer function, not the closed loop. For servo systems, a gain margin of about 10 to 20 dB and a phase margin of about 40 to 60° are common guidelines.
- A. The two definitions are swapped.
- B. Correct. Each is read at the frequency where the other quantity reaches its limit.
- C. Stability margins are read from the loop transfer function, not from the closed loop.