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.