Question

Determine the centroid of the root locus for the system having G(s)H(s) = K/(s+1)(s^2+4s+5)

(a) -2.1

(b) -1.78

(c) -1.66

(d) -1.06

Answer 1

Correct option is (c) -1.66

To explain I would say: Roots of the open loop transfer function are -1,-2+j, -2-j then centroid =Σreal part of open loop pole-Σreal part of open loop zeroes/P-Z

Centroid =(-1-2-2)-0/3 =-5/3 =-1.66.