Question:

A unity feedback system that uses proportional-integral (PI) control is shown in the figure. 

Show Hint

For a PI controller, the system stability can be checked using the Routh-Hurwitz criterion or Nyquist plot, and adjusting \( K_p \) and \( K_i \).
Updated On: Dec 26, 2025
Hide Solution
collegedunia
Verified By Collegedunia

Correct Answer: 3.125

Solution and Explanation

The transfer function for the system is given as: \[ G(s) = \frac{2}{s^3 + 4s^2 + 5s + 2}. \] The characteristic equation for the closed-loop system is: \[ 1 + K_p + \frac{K_i}{s} G(s) = 0. \] The stability of the system is controlled by the values of \( K_p \) and \( K_i \). To ensure marginal stability, we use the Nyquist criterion or Routh-Hurwitz criterion. The maximum value of \( K_i \) that can be chosen to keep the system stable is given by: \[ K_i = 3.125. \] Thus, the maximum value of \( K_i \) for marginal stability is \( \boxed{3.125} \).
Was this answer helpful?
0
0

Questions Asked in GATE EC exam

View More Questions