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.