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GATE 2019 EE – Question 39

Control Systems · Stability analysis using Routh-Hurwitz and Nyquist criteria, Bode plots, Root loci · 2 marks · Multiple choice

The asymptotic Bode magnitude plot of a minimum phase transfer function $G(s)$ is shown below.

Consider the following two statements.

Statement I: Transfer function $G(s)$ has three poles and one zero.

Statement II: At very high frequency ($\omega\to\infty$), the phase angle $\angle G(j\omega)=-\frac{3\pi}{2}$.

Which one of the following options is correct?

Diagram for GATE 2019 EE question 39
  1. Statement I is true and statement II is false.
  2. Statement I is false and statement II is true.
  3. Both the statements are true.
  4. Both the statements are false.

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Show answer and explanation

Correct answer: (B) Statement I is false and statement II is true.

Explanation

The plot starts at $-20$ dB/decade, steepens by $-20$ at $\omega=1$ (to $-40$) and by another $-20$ at $\omega=20$ (to $-60$). That is one integrator plus two more poles, three poles and no zero, so Statement I is false. The relative degree is 3, so the phase tends to $-3\times90^\circ=-\frac{3\pi}2$ and Statement II is true.