Root Locus for 2 Real Poles

Cuthbert Nyack

The root locus for a system with open loop poles at -a, -b are shown below.
For small K, the poles are on the real axis. For larger K the poles are complex conjugate along a vertical line at -(a+b)/2.
For (0.2, 2.0, 1.0, 1.0) the poles are real at -1.723 and -1.276 as shown on applet.

For (6.0, 0.1, 0.5, 1.0) the poles are complex conjugate at -0.3 ±j 2.441 as shown on applet. The step response is shown in white and the frequency response (magnitude along the H axis) for w from 0 to 4 is shown as the light purple line.

For (6.0, 0.1, 0.0, 1.0) the poles are complex conjugate at -0.05 ±j 2.448 as shown on applet. In this case the poles are close to the imaginary axis, the step response is lightly damped and the frequency response shows a sharp peak at w = 2.448.

Gif image illustrating how applet should appear is shown below.

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