Simulation of the step response of a time delay system with a PID controller is contorted.

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s=tf('s');
G=75/(1+40*s)*exp(-60*s); %process with large time delay
F2=0.0141*(1+86.5*s+86.5*21.6*s^2)/86.5/s/(1+0.2*21.6*s); %PID controller (Ziegler Nichols)
Gry2=feedback(G*F2,1);
step(Gry2,0:0.1:800);
The step response gets contorted. Can that be avoided? Get the same problem when using Simulink.
  3 Comments
Michael Tittus
Michael Tittus on 30 Nov 2021
If you simulate with a 2nd order Pade instead of the time delay the simulation is "smooth". The simulation I get has sharp edges. I attach both curves (with Pade and without)

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Answers (1)

Pat Gipper
Pat Gipper on 1 Dec 2021
Those sharp transients in the closed loop response are the echoes of the step input as filtered by the transfer function that are occurring at multiples of the 60 second time delay. The first transient is at 120 seconds, the second is at 180 seconds. It does eventually fade away. Set the time delay to 100 seconds and you will see how they line up on the grid lines of the plot.

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