How to calculate IAE between zero-crossing

I am studying a load disturbance detection procedure presented by Hagglund.

Through simulink I have calculated the control error (it is an array) and I need to calculate the IAE between two consecutive istances of zero crossings as presented in the formula below

In simulink I used a simulation time of 30s and a sampling period of 0.001s.

the question is: how can I calculate the IAE between each zero-crossing and, after each zero-crossing, reset the IAE to 0? Next I need to plot the obtained IAE array.

Answer 1

[Sam Chak]

@PAOLO OLIVIERI

Are you looking for a MATLAB or Simulink solution?

sys = ss([0 1; -1 -1], [0; 1], [1 0], 0);
[y, t] = step(sys, 16);
e   = 1 - y;
subplot(2,1,1)
plot(t, e), grid on, xlabel('t'), ylabel('e(t)'), ylim([-0.5 1.01])
ae  = abs(e);
subplot(2,1,2)
plot(t, ae), grid on, xlabel('t'), ylabel('|e(t)|'), ylim([-0.5 1.01])

J_IAE = trapz(t, ae)

J_IAE = 1.7122

To reset the IAE to 0 after each zero-crossing detection, you probably need some conditional logics. By the way, what does the reset-IAE imply after each zero-crossing detection?

[PAOLO OLIVIERI]

To calculate IAE I used simulink through this scheme:

the result obtained is the same as that using

J_IAE = trapz(t, ae)

Then I obtained this graph

The graph in the article, on the other hand, is this:

so I don't understand if my solution could be correct

[Sam Chak]

Your IAE is increasing over time. This suggests that the error is accumulating and the output did not track the reference signal.