9. A breakaway point sB is a point on the real axis where two or more branches arrive or depart. This point is calculated by solving the equation dB(i)/di = 0 and calculating its roots.

As an example of the above rules, we construct the root locus diagram shown in Fig. 18-7 of a feedback system whose open-loop transfer function is given by

We first determine the poles and zeros of GH. For this function, there is no zero and there are three poles on the real axis at j = - 2, - 3. and - 4. marked by crosses in the figure. Because there are no zeros, the branches are asymptotic to straight lines at infinity. The center of these asymptotes is at p

The asymptotes make an angle 0 with the real axis where

0 0

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