Say that we have a root locus diagram with n poles and m zeroes. And we determine that the root locus on the real axis lies between two of these poles and breaks away from the real axis and tends to infinity somewhere in between these points.
There are formulae to determine what angle the asymptote makes with the real axis as well as what point the root locus "breaks away" from the real axis.
I have noticed from some examples that the point at which the root locus breaks is often half-way in between the two poles I was talking about. But sometimes its not. Is there a rule of thumb to determine when this is the case? This would make drawing root locus diagrams much quicker and give me more intuition on the topic.
This might sound a bit confusing, http://www.facstaff.bucknell.edu/mastascu/econtrolhtml/RootLocus/RLocus1ARCADE.html has some examples on root locus diagrams. The "Three Real Poles" and "Three Poles, One Zero" examples show what I meant about the "breakaway point" being exactly halfway between two poles whilst my textbook uses long formulae to determine a "breaksway point" which is not halfway between the two poles.