Root Locus - 5
Rule 2 - Drawing Asymptotes for Infinite Zeros
It is a normal occurrence to have less finite zeros than finite poles, so often a system will have infinite zeros. For each infinite zero, the root locus will have a branch that travels to the infinite zero along an asymptote. So there will be one asymptote for each infinite zero. But where are the infinite zeros? This rule answers that question.
Each asymptote is oriented at an angle from the positive real axis. The asymptote angles are designated qa.
If we look at this equation more closely, notice that the asymptote angles are odd multiples of p/(#poles-#zeros). So if there is one infinite zero, there is one asymptote and its asymptote angle is 180°. If there are two infinite zeros, there will be two asymptotes with angles p/2 and 3p/2. With three asymptotes, the angles are 60°, 180°, and 300° (-60°).
Once you know the asymptote angles, you need to know where to have them intersect the real axis. They all intersect at a single point, sa. The location of sa is given by
Example
Draw the approximate root locus for
