Difference between centroid and break away/in point

[spoonyluv]

Hi, I am studying control engineering and we are covering root locus concept right now. My knowledge of this concept is varied..I get some things and others I don't. One thing I don't understand is the difference between centroid and breakaway/in point. So for example for this function: 1/((s)(s+2)(s+3)), we have 3 poles at s=0,-2, -3. The website that has the example calculates the centroid at -1.67 (which I agree with). And the breakaway points are -2.5 and -.78.

-2.5 won't be counted because it isn't part of the root locus. However, what's the role of -.78?. In the picture above the author seems to put the square that represents the breakaway point in the same point as the centroid. I'm not sure why...which tells me that I do not have a good understanding of the role played by the centroid versus breakaway point. if someone can explain in layman terms the difference, i would appreciate it. Thanks!

 

[sanjayx1x1]

dear u have calculated wrong value for break point. seconed break away point occurs between 0 and 2.
and breakaway points are the point from where two branches meet and tend to either zero or infinity while centroide is just intersection point of asymptote.