Question

The root locus diagram has loop transfer function G(s)H(s) = K/ s(s+4)(s^2+4s+5) has

(a) No breakaway points

(b) Three real breakaway points

(c) Only one breakaway points

(d) One real and two complex breakaway points

I had been asked this question in an interview for internship.

This question is from Stability Analysis by Describing Functions in division Nonlinear Systems of Control Systems

Answer 1

Right choice is (b) Three real breakaway points

The explanation is: The breakaway points are the points where the root locus branches break and it is not necessary that this point must lie on the root locus calculated by differentiating the value of K with respect to s and equating it with zero.