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 , and also Matlab says that the right answer for the centroid is c=-1.What I am doing wrong in the calculation? Please!
$\endgroup$ 12 Answers
$\begingroup$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.
$$ c = \frac{-1.5 + \frac{\sqrt5}{2} -1.5 - \frac{\sqrt5}{2} - 0}{1}$$
$$ c = \frac{-3}{1} = -3$$
Centroid is -3. However, since the relative degree of this system is 1 you don't need to compute the centroid, for we know there is only one branch that goes to infinity, and it goes to whether $+\infty$ or $-\infty$ in the real line. What has made you confused about -1 is that this point is one of the breakpoints but not the centroid.
$\endgroup$
