LagLead Compensator Root Locus.

Cuthbert Nyack
This applet shows the root locus of a 2 pole system with a Lag Compensator. The screen shows a rectangular portion of the s plane of width xwk, height yhk and centered at (xck, yck). Some cases are mentioned below.

Parameters (0.0, 0.5, 1.5, 10.0, 3.0, 1.0, 0.0, 0.0, 18.0, 14.0) show P control of a 2 pole system.

Parameters (0.0, 0.5, 1.5, 10.0, 3.0, 10.0, 0.0, 0.0, 18.0, 14.0) show LagLead compensation of a 2 pole system.

Starting from the origin the LagLead compensator has a pole and zero of the Lag part, then a zero and pole of the Lead part. The details of the root locus depends on the location of the system pole with respect to the compensator ones.
Parameters (0.0, 0.5, 2.0, 10.0, 3.0, 10.0, -2.0, 0.0, 7.0, 1.0) show poles at 0.0, -0.01(1/bTG), Zeros at -0.1(1/TG), -0.5(1/TL), Poles at -2.0(1/T1) and -5.0(b/TL).
The locus near the origin can be seen by the parameters (0.0, 0.5, 2.0, 10.0, 3.0, 10.0, -0.1, 0.0, 0.25, 0.2).

Parameters (0.0, 1.5, 1.4, 10.0, 3.0, 8.0, -2.0, 0.0, 11.0, 10.0) show the case where system pole lies to the right of the Lead Zero. Parameters (0.0, 1.5, 1.4, 10.0, 3.0, 8.0, -0.5, 0.0, 1.0, 0.5) show an expanded view of the locus near the origin in this case.
Parameters (0.0, 2.1, 1.7, 10.0, 3.0, 10.0, -0.5, 0.0, 1.0, 0.8) show an expanded view of a similar case.



Gif images below show how the applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.