limit in PID controller, should we split?

[bnarit]

According to the limit variable, which is used for antiwindup.
The limit variable was used in two conditions, L33 and L41

float integral = integral_prev + I*Ts*0.5f*(error + error_prev); // antiwindup - limit the output integral = _constrain(integral, -limit, limit);

and
// sum all the components float output = proportional + integral + derivative; // antiwindup - limit the output variable output = _constrain(output, -limit, limit);

This is quite incorrect since the anti-windup also has the importance role in reducing the overshoot for the integral term.

And the integral term limit is the result of the multiplication of the I gain, it has a difference reference?

Should we split it into two separated veriable?