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

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Michael Tittus 2021-11-30

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https://ww2.mathworks.cn/matlabcentral/answers/1599294-simulation-of-the-step-response-of-a-time-delay-system-with-a-pid-controller-is-contorted

回答： Pat Gipper 2021-12-1

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.

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Noah Tang 2021-11-30

The result seems quite valid (though rather unconventional) for me, but I don't have much experience dealing with systems with large time delay, so maybe I'm missing something...

Michael Tittus 2021-11-30

simulation.fig

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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Answer 1

Pat Gipper 2021-12-1

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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.