GATE Electrical Engineering (EE) Test: The Root Locus Technique - 1 Free

The root locus is defined as location of closed loop poles when system gain k is varied from zero to infinity.

Centroid is the intersection point of asymptotes of the complete root loci which lie on the real axis.

Number of open loop poies = P = 3
and number of open loop zeros = Z = 1
Poles are at: s = -1 ± j, 0 and zero is at s = -2


= 0
Here, P - Z = 2
So, angle of asymptotes are given by

Centroid = Sum of real part of open loop pole-sum of real part of open loop zeros / P - Z.

Addition of real pole to an open loop T.F. decreases the stability because root locus shifts towards right of s-plane. Hence, assertion is a false statement.

Number of branches terminating at infinity = 3 = P - Z.
Number of branches terminating at zero = Z= 0.
Poles are at s = 0 and s = -3 ± j1.

Since, three number of poles have to terminate at infinity, therefore the two complex poles will terminate at infinity due to which there will be intersection of root locus branches with jω-axis. Now, characteristic equation is

Given, s(s - 1) + K(s + 1) = 0 

Branches of root locus either terminate at infinity or zero. Here, one branch is terminating at s = -2, therefore there is a zero at s -2. Since two branches are meeting between s = -3 and s = -4, therefore there is a breakaway point between s = -3 and -4, Hence, there must be poles at s = (-1 ± j).
Therefore, open loop T.F. is

Here, P = 2 and Z = 1.
Thus, one branch terminates at s = -2 (zero) and one branch terminate sat infinity ( P - Z = 1).

∴  Number of branches terminating at infinity = P - Z = 2.
Number of branches terminating at zero = Z = 1.

Here, (-1.65 ± j0.936) is not a part of root locus. Thus, it has only one breakaway point s = 0.