Root Locus for 2 Complex Conjugate Poles

Cuthbert Nyack
Applet shows root locus of a system with 2 pairs of complex conjugate poles. There are 4 asymptotes at ±45° and ±135°.


Parameters (0.0, 1.0, 0.05, 1.0, 0.0, 2.0) show a system with 2 cc poles at -1 ± j0.05 and at -1 ± j0.0 which is stable for K < 4. This is almost equivalent to system with 4 real poles at -1.


Parameters (0.0, 1.0, 3.0, 1.0, 0.3, 1.0) show a system with 2 cc poles at -1 ± j3 and at -1 ± j0.3 which is stable for K < 42.


Parameters (0.0, 1.0, 1.0, 1.0, 1.0, 2.0) show a system with 2 cc poles at -1 ± j1 and at -1 ± j1 which is stable for K < 8.


Parameters (0.0, 1.0, 2.0, 1.0, 0.0, 2.0) show a system with 2 cc poles at -1 ± j2 and at -1 ± j0 which is stable for K < 16. From these parameters the appearance of the locus changes when the real part of either pair is increased or decreased.





Gif image illustrating how applet should appear is shown below.

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COPYRIGHT 2006 Cuthbert Nyack.