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

Cuthbert Nyack

Applet shows the frequency response(Bode plot) of a type 0 system with P, PI, PD and PID control.

P control:- magnitude response follows yellow-green at low frequencies and dark red at high frequencies, just the yellow line shifted upwards by 20*Log(K). The phase is equal to that of the system ie blue plot.

PD control:- Magnitude is yellow-green line, follows P control at low frequencies and PID control at high frequencies. Phase is shown by light green line.

PI control:- Magnitude is the dark red line, follows PID at low frequencies and P at high frequencies. Phase is shown by brown line.

PID control:- Magnitude is red line, follows PI at low frequencies and PD at high frequencies. Phase is the green line.

Controller:- Magnitude is the orange line, follows an integrator at low frequencies and a differentiator at high frequencies. Phase is the cyan line.

Step Response:- Given by light pink plot for pid and darker pink for pi.

Closed loop response:- Given by light brown line. This system can be unstable and one possible set of parameters is (10.0, 2.5, 4.0, 1.0, 0.26, 1.0, 4.0, x) for instability. The sharp peak in the closed loop response(light brown) indicates an oscillation.

When Ti = 4*Td the zeros are real and identical and the response looks like a first order system eg(20.0, 1.0, 1.0, 2.0, 0.5, 1.0, 1.0, x).
The applet shows the pid and pi phase margins(pm) and crossover frequency "cofpid, cofpi", the 3 closed loop poles as well as the parameters related to the complex conjugate pair of poles for the pid case.

Gif image below show how the applet should appear.

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