I can't figure out how to find the root locus centroid for the poles of this simple equation in a positive feedback system.
$$
H(s)=\frac{s}{s^2+3s+1}
$$
I have read in many places that the centroid is found by this formula:
$$
c=\frac{sum(P)-sum(Z)}{p-z}
$$
The transfer function poles are:
$$
p1=-1.5+\frac{\sqrt{5}}{2} \\
p2=-1.5-\frac{\sqrt{5}}{2}
$$
So the centroid should be:
$$
c=\frac{-1.5+\frac{\sqrt{5}}{2}-1.5-\frac{\sqrt{5}}{2}-0}{2-1}=-3
$$
However, in this video
https://youtu.be/eyb_RzOnfGY?t=559 , and also Matlab says that the right answer for the centroid is c=-1.
What I am doing wrong in the calculation?
Please!
Best Answer
Wouldn't the centroid be at -3? Ill put it in MATLAB and see what I get (dont have enough rep to add comments) EDIT: This seems right to me, I noticed you only have H(s), do you know if there was any G(s)? I tried to click the link to the video and it wouldn't load, best of luck.
$$ c = \frac{-1.5 + \frac{\sqrt5}{2} -1.5 - \frac{\sqrt5}{2} - 0}{1}$$
$$ c = \frac{-3}{1} = -3$$