GATE 2024 IN – Question 55
A unity-negative-feedback system has the open-loop pole-zero map shown; crosses mark poles. If $s=j\alpha$, $\alpha>0$, lies on its root locus, $\alpha$ is ______ (nearest integer).
Practise this question in The GATE Grind →
Show answer and explanation
Correct answer: 2 to 2
Explanation
The poles 0, −1, −4 give characteristic equation $s(s+1)(s+4)+K=s^3+5s^2+4s+K=0$. Put $s=j\alpha$. The imaginary part gives $-\alpha^3+4\alpha=0$. Since $\alpha>0$, $\alpha=\boxed2$. The real part gives the consistent positive gain $K=20$.