Root Locus for 3 Real Poles and 2 Complex Conjugate Zeros

Cuthbert Nyack

Applet shows the root locus of a system with 3 real poles and 2 complex conjugate zeros. The system has 3 loci, 2 ending at the open loop zeros and one ending up along the only asymptote at -180°.

Parameters (0.0, 1.0, 0.5, 0.1, 1.6, 3.0) has poles at -0.1, -0.5, -1.0 and ccz zeros at -1.6 ± j3.0. It is stable for K < 0.2 and K > 1.67 and unstable for other K's.

Parameters (0.0, 1.0, 0.5, 0.1, 1.7, 0.35) has poles at -0.1, -0.5, -1.0 and ccz zeros at -1.7 ± j0.35. It is always stable because the locus never crosses the imaginary axis. As K increases the CL poles move to the left and damp out the transient oscillations.

Gif image below shows how applet should appear.

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