Root Locus for 2 Real Poles, 2 Complex Conjugate Poles and 1 Real Zero

Cuthbert Nyack
Applet shows the root locus of a system with 2 real poles, 2 cc poles and 1 zero. It has the asymptotic characteristics of a third order system with asymptotes at ±60° and -180°.


Parameters (0.0, 1.0, 0.5, 2.5, 1.5, 3.0, 2.0) has 2 real poles at -0.5, -1.0, 2 cc poles at -1.5 ± j3.0 and 1 real zero at -2.5 and is stable for K < 23.8(obtained by increasing K to 23.8).


Parameters (0.0, 0.7, 0.3, 2.0, 2.0, 2.5, 2.0) has 2 real poles at -0.3, -0.7, 2 cc poles at -2.0 ± j2.5 and 1 real zero at -2.0 and is stable for K > 25.2(obtained by increasing K to 25.2).


Parameters (0.0, -0.5, 1.0, 2.0, 1.5, 3.0, 2.0) has 2 real poles at +0.5, -1.0, 2 cc poles at -1.5 ± j3.0 and 1 real zero at -2.0 and is stable for K > 2.8 and K < 21.2(obtained by increasing K to 21.2).





Gif image illustrating how applet should appear is shown below.

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COPYRIGHT 2006 Cuthbert Nyack.