Lag 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, 1.0, 10.0, 3.0, 1.0, 0.0, 0.0, 7.5, 8.0) show P control of a 2 pole system.

Parameters (0.0, 0.5, 1.0, 10.0, 3.0, 10.0, 0.0, 0.0, 7.5, 8.0) show Lag compensation of a 2 pole system.

Parameters (0.0, 0.5, 1.0, 10.0, 3.0, 10.0, -0.1, 0.0, 0.25, 0.21) show Lag compensation with an expanded view of the area close to the origin. 2 Loci start at the 2 poles 0 and -0.01, they meet, break away into the complex plane, meet at ~-0.205, one ends at the zero at -0.1 while the moves to the left to meet the loci which started at the pole at -2.0. (0.0, 0.5, 1.0, 10.0, 3.0, 10.0, -0.9, 0.0, 2.4, 1.0)

Parameters (0.0, 0.5, 1.0, 10.0, 3.0, 0.6, 0.0, 0.0, 7.5, 8.0) show Lead compensation of a 2 pole system. The behaviour near the origin is now different because the zero of the compensator is closer to the pole at the origin unlike the lag compensator where the pole is closer.





Gif image below show how the applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.