Question

A unity feedback system has an open loop transfer function of the form

$KG\left(s\right)=\frac{K(s+a)}{s^2(s+b)};b>a$

Which of the loci shown in figure can be valid rootloci for the system?

• A.
• B.
• C.
• D.

Answer 1

The correct option is A

P = 3, Z = 1

and two repeating poles at origin

$Centroid=\frac{0-b-(-a)}{3-1}$

$=\frac{-(b-a)}{2}<0$

$Angleofasymptotes=\frac{(2q+1){180}^0}{3-1}$

$={90}^0(forq=0)$

$={270}^0(forq=1)$

$\therefore$ Option (a) is correct.