Root Locus for 1 Real Pole, 4 Complex Conjugate Poles and 2 Complex Conjugate Zeros

Cuthbert Nyack

Applet shows the locus of a system with 1 real poles, 4 cc poles and 2 cc zeros. This system has 5 loci and 3 asymptotes at ±60° and -180°.

For the parameters (K, 2.4, 0.6, 1.25, 0.8, 0.05, 0.7, 1.8), the system has 1 real pole at -0.05 and 2 pairs of cc poles at -2.4 ± j0.6, 1.25 ± j0.8 and 2 cc zeros at 0.7 ± j1.8. Increasing K shows the system is stable for K < 10.8, unstable for 37.9 > K > 10.8, stable for 63.4 > K > 37.9, and unstable for K > 63.4.

Moving the zeros to 0.8 ± j1.1 results in the system being stable for K < 57.6 and unstable for K > 57.6.

Moving the zeros to 0.8 ± j1.85 results in the system being stable for K < 9.3 and unstable for K > 9.3.

Moving the zeros to 3.5 ± j3.0 results in the system being stable for K < 1.0 and unstable for K > 1.0.

Gif image below shows how applet should appear.

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