What do I do wrong when using the stepplot command?

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.

Answer 1

[Pratyush Roy]

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!

[Nico van der Aa]

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.