3. Frequency Analysis

Closed-loop Frequency — Quiz

Test your understanding of closed-loop frequency with 5 practice questions.

Practice Questions

Question 1

Given a closed-loop system with a unity feedback and an open-loop transfer function $L(s)$, which of the following statements is true regarding the relationship between the sensitivity function $S(s)$ and the complementary sensitivity function $T(s)$?

Question 2

Consider a closed-loop system. If the gain margin is found to be $20 \text{ dB}$ and the phase margin is $45^{\circ}$, what can be inferred about the system's stability and robustness?

Question 3

For a closed-loop control system, if the magnitude of the sensitivity function $|S(j\omega)|$ exhibits a peak greater than 1 at a specific frequency $ \omega_p $, what is the most significant implication for the system's performance?

Question 4

In the context of closed-loop frequency response, what is the primary implication of a resonant peak in the magnitude response of the complementary sensitivity function $|T(j\omega)|$?

Question 5

When designing a closed-loop system, what is the primary trade-off involved in simultaneously trying to reduce the sensitivity function $S(s)$ at low frequencies and the complementary sensitivity function $T(s)$ at high frequencies?