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Mechanical Engineering QUESTION #2394
Question 1
The gain margin (GM) of a control system is defined as:
  • \(GM = 1/|Y_1(j\omega_{pc})|\) where \(\omega_{pc}\) is the phase crossover frequency (where phase \(= -180°\))✔️
  • \(GM = |Y_1(j\omega_{gc})|\) where \(\omega_{gc}\) is the gain crossover frequency
  • \(GM = \angle Y_1(j\omega_{gc})\)
  • The maximum gain before the system becomes underdamped
Correct Answer Explanation
Gain margin: \(GM=1/|Y_1(j\omega_{pc})|\) where \(\omega_{pc}\) is the phase crossover frequency (\(\angle Y_1=-180°\)). In dB: \(GM(dB)=-20\log|Y_1(j\omega_{pc})|\). GM indicates how much the gain can be increased before instability. Typically \(GM\geq6\) dB is desired.