F-12  Appendix F Properties and Co

F-12  Appendix F Properties and Construction of the Root Loci
this case, the breakaway point represents a double root of the equation when the value of
K is assigned the value corresponding to the point. Figure F-9(b) shows another common
situation when two complex-conjugate root loci approach the real axis, meet at the breakaway
point, and then depart in opposite directions along the real axis. In general, a breakaway
point may involve more than two root loci. Figure F-9(c) illustrates a situation when
the breakaway point represents a fourth-order root.
A root-locus diagram can have, of course, more than one breakaway point. Moreover,
the breakaway points need not always be on the real axis. Because of the conjugate symmetry
of the root loci, the breakaway points not on the real axis must be in complexconjugate
pairs. Refer to Fig. F-12 for an example of root loci with complex breakaway
points. The properties of the breakaway points of root loci are given as follows:
The breakaway points on the root loci of 1  KG1(s)H1(s)  0 must satisfy