What do I do wrong when using the stepplot command?

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I have defined a first order system and a PI controller as follows:
and
In matlab code
tau = 0.1;
G_plant = tf(1,[tau 1]);
alpha = -0.1;
Gc = tf([1 alpha],[1 0]);
The controller should also have a gain value and I'm varying it from 0 to 10. My expectation is that, because of the PI-controller, the step response goes to 1 eventually for all gain values I choose. It does so, for gain values up to 8, but for a gain value of 9, I observe something strange. Could you help me explaining this phenomenon?
My code to draw the step responses for the PI-controlled system is
G_openloop = Gc*G_plant;
T = feedback(9*G_openloop,1)
stepplot(T);
Even if I compute the DC gain, it goes to 1, but the stepplot doesn't.
For the green line (K = 9) a strange bending of the curve occurs around time 2 seconds and the green line never goes to its steady state of 1.

Accepted Answer

Pratyush Roy
Pratyush Roy on 11 Jan 2022
Hi Nico,
Although it might seem like the step response for gain values do not approach the steady state value of 1, this might be because it reaches steady state at a later stage due to the value of K chosen. To observe that, we can change the tFinal input argument for the stepplot command final time for step response computation to be a very high value, say 100.
Here is a script that illustrates how to change the tFinal value:
tau = 0.1;
G_plant = tf(1,[tau 1]);
alpha = 0.2;
Gc = tf([1 alpha],[1 0]);
K = 5:0.4:9;
for i=1:length(K)
G_openloop = Gc*G_plant;
T = feedback(K(i)*G_openloop,1);
hold on
stepplot(T,100);
end
hold off
Hope this helps!
  1 Comment
Nico van der Aa
Nico van der Aa on 13 Jan 2022
Thanks Pratyush Roy, apparently I indeed missed the tFinal value, giving the step response only for 0 < t < 1. I did not realize that by using the xlim command, the plot would be extrapolated. Now it is clear, thank you.

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