The GATE Grind

GATE 2025 EC – Question 16

Control Systems · Routh-Hurwitz and Nyquist Stability Criteria · 1 mark · Multiple choice

The Nyquist plot of a system is given in the figure below. Let $\omega_P$, $\omega_Q$, $\omega_R$, and $\omega_S$ be the positive frequencies at the points $P$, $Q$, $R$, and $S$, respectively.

Which one of the following statements is TRUE?

Diagram for GATE 2025 EC question 16
  1. $\omega_S$ is the gain crossover frequency and $\omega_P$ is the phase crossover frequency
  2. $\omega_Q$ is the gain crossover frequency and $\omega_R$ is the phase crossover frequency
  3. $\omega_Q$ is the gain crossover frequency and $\omega_S$ is the phase crossover frequency
  4. $\omega_S$ is the gain crossover frequency and $\omega_Q$ is the phase crossover frequency

Practise this question in The GATE Grind →

Show answer and explanation

Correct answer: (D) $\omega_S$ is the gain crossover frequency and $\omega_Q$ is the phase crossover frequency

Explanation

The gain crossover frequency is where $|G(j\omega)|=1$, i.e. where the plot meets the unit circle: that is point $S$ (P and R lie inside the unit circle). The phase crossover frequency is where the plot crosses the negative real axis: that is point $Q$. So $\omega_S$ is the gain crossover and $\omega_Q$ is the phase crossover.