PID Controller Root Locus.
Cuthbert Nyack
This applet shows the root locus of a 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, 0.6, 1.5, 0.0, 3.0, 50.0, -2.0, 0.0, 7.5, 8.0) Td = 0
and Ti very large effectively P control of 2 pole system.
Parameters (0.1, 0.6, 1.5, 0.3, 3.0, 50.0, -2.0, 0.0, 7.5, 8.0) PD with
small I contribution. One part of the locus goes from the
pole at 0 to the zero at -0.02. The second part consists of 2 loci starting at the 2
poles -0.666 and -1.666 and ending at the zero at -3.313 and at
infinity.
Parameters (0.1, 0.6, 1.5, 0.3, 3.0, 1.85, -1.0, 0.0, 2.0, 1.0) The zero
at -0.678 is to the left of the pole at -0.5 and a change in the shape
of the locus occurs.
Parameters (0.1, 0.6, 1.5, 0.3, 3.0, 1.83, -1.0, 0.0, 1.5, 0.8) Another
change occurs.
Parameters (0.1, 0.6, 1.5, 0.4, 3.0, 1.86, -1.2, 0.0, 2.0, 1.0) Another
change.
Parameters (0.1, 0.6, 1.6, 0.4, 3.0, 1.87, -1.2, 0.0, 2.0, 1.0) Another
change.
Parameters (0.1, 0.6, 1.6, 0.39, 3.0, 1.87, -1.4, 0.0, 2.0, 1.2) Another
change.
Parameters (0.1, 0.6, 1.5, 0.3, 3.0, 1.33, -1.0, 0.0, 3.0, 1.0) Zero continues to move to left.
Parameters (0.1, 1.0, 1.5, 0.3, 3.0, 1.21, -1.2, 0.0, 3.0, 1.0) Zero now to the left of pole at -1.0.
Parameters (0.1, 1.0, 1.5, 0.3, 3.0, 1.1, -1.2, 0.0, 3.0, 2.0) Controller now has complex conjugate zeros.
Parameters (0.1, 1.0, 1.5, 0.3, 3.0, 1.0, -1.2, 0.0, 3.0, 4.0) Another change has occured.
Gif images below show how the applet should appear.
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COPYRIGHT © 2006 Cuthbert Nyack.