Question

The open loop transfer function of the feedback control system is given by G(s) =K(s+3)/s(s+4)^2(s+5)(s+6). The number of asymptotes and the centroid of asymptotes of the root loci of closed loop system is

(a) 4 and (-4,0)

(b) 3 and (-12,0)

(c) -4 and (-4,0)

(d) -3 and (-12,0)

I got this question during an interview.

This interesting question is from Construction of Root Loci topic in division The Root Locus Technique of Control Systems

Answer 1

The correct choice is (a) 4 and (-4,0)

For explanation: Number of Poles = 5

Zeroes =1

Asymptotes =P-Z =4

Centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z

Centroid = -4-4-5-6+3/4 =-4.