Sampled PID Root locus

Cuthbert Nyack
This applet shows the root locus of a sampled 2 pole system with a PID Controller. 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 (0.1, 1.0, 2.001, 0.2, 0.04, 1.0, -1.0, 0.0, 4.0, 4.0) show the locus with pole at 0.0 and zero at -0.98 clearly visible.

Parameters (0.1, 1.0, 2.001, 0.2, 0.04, 1.0, 0.85, 0.0, 0.3, 0.3) show the locus with poles at 1.0 and 0.9802, zero at 0.9737, pole at 0.9607 and zero at 0.8541 clearly visible.

Parameters (0.1, 1.0, 2.001, 0.2, 0.04, 1.74, 0.85, 0.0, 0.3, 0.3) show the locus with poles at 1.0, 0.9802 and 0.9607 and zeros at 0.9452 and 0.8786 clearly visible.

Parameters (0.1, 1.0, 2.001, 0.2, 0.04, 0.75, 0.85, 0.0, 0.3, 0.3) show the case where Ti < 4Td so the OL zeros are now complex conjugate at 0.9103 ± j 0.0286.

The zeros remain the same as K changes, the poles move with K and can be located by the parameters (xck, yck, xwk, yhk) eg for parameters (10.0, 1.0, 2.001, 0.2, 0.1, 1.2, -1.0, 0.0, 4.0, 4.0)
(0.06, 0.0, 0.01, 0.01) show OL pole at 0 has moved to 0.058.
(0.9, 0.0, 0.01, 0.01) show OL pole at 0.9048 has moved to 0.8991.
(0.91, 0.18, 0.01, 0.01) show poles at 1.0 and 0.9512 has moved to 0.913 ± j 0.1808.



Gif image below show how the applet should appear.

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COPYRIGHT 2006 Cuthbert Nyack.