Correct Answer : -3
Explaination : We will first calculate the number of branches approaching infinity and then the asymptotes. With the help of asymptotes, we will calculate the value of centroid.
The given transfer function of the system is G(s) = K / [(s + 1) (s + 4 + 4j) (s + 4 - 4j)].
The number of asymptotes is equal to the number of branches approaching infinity. There are no zeroes but three poles.
So, P - Z = 3
Let's calculate the value of the poles by equating the denominator equal to zero. We get:
Poles located at: -1,
The angle of asymptotes is calculated by:
Θ = (2q + 1) 180 / (P - Z)
Here, q = 0, 1, 2…
The number of asymptotes is equal to the number of branches approaching infinity.
So, we will calculate the asymptotes at value 0, 1, and 2.
For q = 0,
Θ=180⁄3=60degrees
For q = 1,
Θ=(2+1) 180⁄3=180degrees
For q = 2,
Θ=(4+1) 180⁄3=300degrees
Centroid is defined as a common point where all the asymptotes intersect on the real axis.
σ= / (P - Z)
σ= (- 1 - 4 - 4 - 0) / 3
σ=(-9)⁄3
σ=-3