Root Locus for 5 Real Poles, 2 Real Zeros.

Cuthbert Nyack
Applet shows the locus of a system with 5 open loop poles. This system has 3 asymptotes at ±60° and -180°. Since 2 of the asymptotes cross the imaginary axis, then the system will always become unstable if K is made large enough.

Eg parameters (K, 2.5, 2.0, 1.5, 1.0, 0.5, 3.0, 1.25) has 5 OL poles at -2.5, -2.0, -1.5, -1.0, -0.5 and is unstable if K > 10.63. At this value of K the CL poles are -1.2523, -3.1239 ± j 0.3951 and 0.0 ± j 1.874.

Eg parameters (K, 1.5, 1.5, 1.5, 1.5, 1.5, 2.0, 1.0) becomes unstable if K > 27.71. At this value of K the CL poles are -4.4977, -1.001, -2.001 and 0.0 ± j 2.6444.

Eg parameters (K, 1.0, 1.0, 1.0, 1.0, 1.0, 1.5, 0.5) becomes unstable if K > 8.43.





Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.