Question

Which of the following best describes the phase and sinusoidal components in the given control system plot?

• A. \( \sin \omega_c \), \( \theta \) is \( \omega_p \)
• B. \( R \text{ is } \omega_p \), \( \theta \text{ is } \omega_c \)
• C. \( \theta \text{ is } \omega_c \), \( \sin \text{ is } \omega_p \)
• D. \( R \text{ is } \omega_c \), \( \sin \omega_p \)

Hint:

In control systems, the gain crossover frequency (\( \omega_c \)) and phase crossover frequency (\( \omega_p \)) help analyze stability margins using Bode and Nyquist plots.

Answer 1

The Correct Option is A

Understanding Frequency Domain Parameters.
The given diagram represents a frequency response plot, likely from Nyquist Stability Criterion or Bode Plot Analysis. 1. Sinusoidal Component \( \sin \omega_c \):
- Indicates the system's response at critical frequency \( \omega_c \).
- This often corresponds to the gain crossover frequency in a Bode plot.
2. Phase Angle \( \theta \) at \( \omega_p \):
- \( \omega_p \) is the phase crossover frequency, where phase margin is measured.
- It is a key factor in stability determination.
Thus, the correct answer is: \[ \sin \omega_c, \quad \theta \text{ is } \omega_p \]