P, PD, PI, PID Control 2P T1T2 Nyquist Plot

Cuthbert Nyack

Applet shows frequency response(Nyquist plot) of a second order type 0 system with P, PI, PD and PID controllers.

The parameter values (10.0, 1.0, 1.0, 8.0, 0.3, 0.2, 1.0, 0.3) give a overview of how P, PD, PI and PID controlled systems are related on Nyquist plots.
P control is orange curve, phase going from 0 to -180° as frequency increases.
PD control is yellow curve, compared with the P controller this shows a phase advance at higher frequencies.
PI control is cyan curve showing an increased phase lag compared with P control. The phase change is -90° at low frequencies.
PID control is green curve. Compared with P control it has an increased phase lag at low frequencies and a reduced phase lag at high frequencies.

This system can be unstable and one possible set of parameter values which is unstable is (10.0, 4.0, 5.0, 1.5, 0.31, 1.0, 6.0, x). With these parameters the green(PID) curve passes over the -1 point marked by the white x, indicating an oscillation shown by the red curve.

Gif image below show how the applet should appear.

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