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Mechanical Engineering QUESTION #2393
Question 1
The bandwidth \(\omega_b\) of a closed-loop control system is defined as the frequency at which the closed-loop magnitude \(M(\omega)\) drops to:
  • \(M(\omega_b) = M(0)/2\)
  • \(M(\omega_b) = M(0)/\sqrt{2}\) (i.e., \(-3\) dB below \(M(0)\))✔️
  • \(M(\omega_b) = 0\)
  • \(M(\omega_b) = M(0) \cdot \sqrt{2}\)
Correct Answer Explanation
Bandwidth: \(M(\omega_b)=M(0)/\sqrt{2}\), i.e., the response is \(-3\) dB below its low-frequency value. In dB: \(20\log M(\omega_b)=20\log M(0)-3\) dB. Larger bandwidth means faster system response.