Root Locus for 5 Real Poles

Cuthbert Nyack
Applet shows the locus of a system with 5 open loop poles. This system has 5 asymptotes at ±36°, ±108° 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) has 5 poles at -2.5, -2.0, -1.5, -1.0, -0.5 and is unstable if K > 14.56.

Eg parameters (K, 1.5, 1.5, 1.5, 1.5, 1.5) becomes unstable if K > 21.96.

Eg parameters (K, 1.0, 1.0, 1.0, 1.0, 1.0) becomes unstable if K > 2.88.

The Closed loop poles for 5th order systems are obtained by numerical aproximation and are subject to small errors.




Gif image below shows how applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.