Root Locus for 3 Real Poles 2 Complex Conjugate Poles and 2 Complex Conjugate Zeros

Cuthbert Nyack
Applet shows the locus of a system with 3 real poles, 2 cc poles and 2 cc zeros. This system has 5 loci and 3 asymptotes at ±60° and -180°.

Parameters (0.0, 2.3, 0.8, 0.7, 0.1, 0.6, 0.4, 1.3) show a system with 3 real poles at -0.7, -0.6, -0.1, 2 cc poles at -2.3 ± j0.8 and 2 cc zeros at -0.4 ± j1.3. Increasing K show that the system is stable for K < 2.3, unstable for 22.03 > K > 2.3, stable for 22.03 > K > 46.14 and unstable for K > 46.14. There are 2 ranges of K for stability and 2 ranges for instability.


Parameters (0.0, 2.7, 2.0, 0.4, 0.4, 0.4, 0.75, 1.4) show a system with 3 real poles at -0.4, 2 ccpoles at -2.7 ± j2.0 and 2 cc zeros at -0.75 ± j1.4. Increasing K show that the system is stable for K < 3.71, unstable for 25.19 > K > 3.71, stable for 49.69 > K > 25.19 and unstable for K > 49.69. There are 2 ranges of K for stability and 2 ranges for instability.


Parameters (0.0, 2.0, 1.5, 1.7, 0.2, 1.0, 1.5, 0.8) show a system with 3 real poles at -1.7, -0.2, -1.0, 2 cc poles at -2.0 ± j1.5 and 2 cc zeros at -1.5 ± j0.8. Increasing K show that the system is stable for K < 21.1 and unstable for K > 21.01.
Parameters (0.0, 1.5, 0.3, 1.5, 1.5, 1.5, 3.5, 3.0) show a system with 3 real poles at -1.5, 2 cc poles at -1.5 ± j0.3 and 2 cc zeros at -3.5 ± j3.0. Increasing K show that the system is stable for K < 1.48 and unstable for K > 1.48.

Moving the zeros to -1.0 ± j1.4 keeps the system stable for K up to 46.96.



Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.