Integrator doesn't work properly

I am working on a controller that calculates the maximum velocity that the actuator can remove from the system so the kinetic energy is zero when achieving the set point. Please see the attachment.

the MATLAB Function block is:

function direction = dircVel(Xd, Xa, Va)

Fmax = 1;

m = 1;

Vmax = sqrt(2 * Fmax * abs(Xd - Xa) / m) * sign(Xd - Xa);

direction = sign(Vmax - Va);

What I expect to see is that the output approaches the setpoint position asymptotically but it diverges to infinity!

the output of the MATLAB function seems OK:

but the output of the first integration is wrong:

red line being what I expected to see.

I would appreciate it if you could help me know what is wrong and how I can resolve it.

P.S. I also posted the question here on Discord and here on Reddit.

Answer 1

[Foad Sojoodi Farimani]

Thanks to this comment on Discord, I could figure the issue out. Basically the Sample rate on the Function block needs to be set manually. Right clock on the function block and select "Block Parameters (Subsystem)":

adjust the Sample time value to something smaller in this case 0.01 worked:

and the result is as expected

Answer 2

[Benjamin Thompson]

The output of your first integrator is always positive. So the second integrator will keep increasing until its input become zero or negative.