[Ether]

I think the following is a correct C implementation of Take-Back-Half:

.

e = S-P;                            // calculate the error;
Y += G*e;                           // integrate the output;
if (Y>1) Y=1; else if (Y<0) Y=0;    // clamp the output to 0..+1;
if (signbit(e)!=signbit(d)){        // if zero crossing,
  Y = b = 0.5*(Y+b);                // then Take Back Half
  d = e;}                           // and save the previous error;

...where:

S is the setpoint (target RPM)
P is the process variable (measured RPM)
G is the integral gain (the tuning parameter)
Y is the output command to the motor controller
e is the error
d is the previous error
b is the TBH variable

Y, d, and b should be initialized.

Would someone be willing to test this and make any necessary corrections and re-post for the benefit of C language teams who might want to try TBH?