Root Locus for 4 Real Poles

Cuthbert Nyack
Applet shows root locus of system with 4 real poles. This system has 4 asymptotes at ±45° and at ±135° which appears to originate at the center of gravity of the pole configuration.


Parameters (0.0, 1.0, 1.0, 1.0, 1.0) show the locus with 4 poles at -1 consisting of 4 straight lines starting from -1 and going to ±∞ at angles ±45° and ±135°.
Parameters (4.0, 1.0, 1.0, 1.0, 1.0) show one pair of complex conjugate poles are on the imaginary axis ±j1.0 and the system is oscillatory with w = 1.0. The system is unstable for K > 4.0.


Parameters (0.0, 2.0, 2.0, 2.0, 2.0) show the locus with 4 poles at -2. System is unstable for K > 64 with w = 2.0 when the poles reach the imaginary axis.


Parameters (0.0, 2.0, 1.5, 1.0, 0.5) show the locus with 4 poles evenly spaced along the real axis. The loci move along the real axis for small K then tends towards the asymptote. System is unstable for K > 7.9.





Gif image illustrating how applet should appear is shown below.

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COPYRIGHT 2006 Cuthbert Nyack.