Question

Figure shows the root locus plot (location of poles not given) of a third order system whose open loop transfer function is

• A. $\frac{K}{s^3}$
• B. $\frac{K}{s^2(s+1)}$
• C. $\frac{K}{s(s^2+1)}$
• D. $\frac{K}{s(s^2-1)}$

Answer 1

The correct option is B $\frac{K}{s^2(s+1)}$



These are three asympototes with angle ${60}^0,{180}^{0}and{300}^0.$

Angle of asympotoes

$=\frac{(2k+1){180}^0}{P-Z}$

Where, k = 0, 1, 2 upto (P - Z) -1

as angles are ${60}^0,{180}^{0}and{300}^0$

it means P - Z = 3

Intersection of asympototes on real axis

$x=\frac{\sum poles-\sum zeros}{P-Z}$

Since, system does not have zeros

$x=\frac{\sum poles}{P}$

As asympototes intersect at origin, it means all the three poles are at origin.

Hence, option (a) is correct.