3. Frequency Analysis

Nyquist Criterion — Quiz

Test your understanding of nyquist criterion with 5 practice questions.

Practice Questions

Question 1

Given an open-loop transfer function $G(s)H(s) = \frac{K}{s(s+1)(s+2)}$, determine the range of $K$ for which the closed-loop system is stable using the Nyquist criterion.

Question 2

Consider an open-loop transfer function $G(s)H(s)$ with one pole in the right-half plane ($P=1$). If the Nyquist plot encircles the critical point $-1 + j0$ once in the counter-clockwise direction ($N=1$), what is the number of zeros ($Z$) of the characteristic equation in the right-half plane?

Question 3

For a system with an open-loop transfer function $G(s)H(s) = \frac{1}{s(s+1)}$, what is the gain margin if the Nyquist plot intersects the negative real axis at $-0.5$?

Question 4

An open-loop transfer function has a pole at $s=j\omega_0$. How is the Nyquist contour modified to handle this pole, and what is the implication for stability analysis?

Question 5

Consider a system with an open-loop transfer function $G(s)H(s) = \frac{10}{(s+1)(s+2)}$. Determine the number of encirclements ($N$) of the critical point $-1 + j0$ required for closed-loop stability.