How to use the integrating option in a closed-loop PID autotuner?

In a closed-loop PID autotuner block, there is an option called Plant Type. I should select whether the plant is stable or integrating. It says that " If the plant has one or more integrators, select Integrating.". I don't understand this very well and what is reason behind? Is there any example that tells me how to decide which to use?

Answer 1

[Sam Chak]

Here is the difference between stable plants and integrating plants:

%% Stable Plant (all eigenvalues have negative real part)
G   = tf(1, [1 1])

G =
 
    1
  -----
  s + 1
 
Continuous-time transfer function.

eig(G)

ans = -1

G   = tf(1, [1 2 3])

G =
 
        1
  -------------
  s^2 + 2 s + 3
 
Continuous-time transfer function.

eig(G)

ans = 
  -1.0000 + 1.4142i
  -1.0000 - 1.4142i

%% Plant has at least one or more poles at the origin
G   = tf(1, [1 1 0])

G =
 
     1
  -------
  s^2 + s
 
Continuous-time transfer function.

eig(G)

ans = 2×1

0 -1

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G   = tf(1, [1 1 0 0])

G =
 
      1
  ---------
  s^3 + s^2
 
Continuous-time transfer function.

eig(G)

ans = 3×1

0 0 -1

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[Zhi]

Thank you for your answer! I'm now clear with the difference between two plants. But I still don't see much difference if I select the option stable or integrating. I tried some tests with the system with a pole at origin.

sys = tf(1, [1 1 0]);

The expected that the open-loop system should have a gain margin of 10rad/s and phase margin of 45deg. Then I set the Closed-loop PID autotuner in continuous-time domain with sample time 0.01 sec. In the experiment tab, I set the plant type as "Stable" at first and then as "Integrating" and did the same test again. But the output signal waveforms are the same in both cases.

Now it seems that this option doesn't play any role. Is there any further information about the two plant type options?

[Sam Chak]

Hi @Zhi

If you directly use a linear time-invariant (LTI) system with an integrator, the Closed-Loop PID Autotuner block has the capability to detect the system as an integrating plant, regardless of whether you specify the Plant Type as 'Stable' or 'Integrating.' The Autotuner will then automatically tune the PID controller for the LTI plant to produce a stable loop.

However, specifying the Plant Type is particularly useful when the Simulink plant is nonlinear or when the Autotuner block reads the plant output from physical hardware in real time. It helps the Autotuner to decide on the tuning strategy.

If you find the explanation satisfactory, would you please consider clicking 'Accept' ✔ on the answer.

sys = zpk(tf(1, [1 1 0]))

sys =
 
     1
  -------
  s (s+1)
 
Continuous-time zero/pole/gain model.