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Mechanical Engineering QUESTION #2390
Question 1
The phase margin (PM) of a control system is defined as:
  • The gain at the phase crossover frequency
  • \(PM = 180° + \angle Y_1(j\omega_{gc})\) where \(\omega_{gc}\) is the gain crossover frequency (where \(|Y_1(j\omega)|=1\))✔️
  • \(PM = |Y_1(j\omega_{pc})|\) where \(\omega_{pc}\) is the phase crossover frequency
  • The bandwidth of the closed-loop system
Correct Answer Explanation
Phase margin: \(PM=180°+\phi_{gc}\) where \(\phi_{gc}=\angle Y_1(j\omega_{gc})\) at the gain crossover frequency. PM indicates how much additional phase lag would bring the system to the verge of instability. Typically \(PM\geq45°\) is desired.