JLand
Member
Here we are. It looks very much like all they've done is move the Kp to the outside of the parenthesis.
For the integral error term, the coefficient is 1/(60*Ti), not simply kI. In dependent PID, a larger integral tuning parameter (called reset in dependent form) actually results in integral affecting the final change in controlled output less. It is a common mistake I have seen before and I myself have made.
The reason the coefficient in front of the accumulated error is (1/60*Ti), also sometimes simply represented as (1/Ti), and not simply kI has to do with how the PID equation is derived. The derivation isn't too bad but it uses transfer functions and an inverse Laplace transform so it does rely on some fields of theory that aren't typically taught outside of a 4 year degree program. The math ends up with the tuning parameter for integral being in the denominator of the coefficient and engineers, in all their wisdom, didn't bother to move the tuning parameter to the numerator.
Another reason the integral tuning parameter is in the denominator of the accumulated error coefficient is manually calculating the theoretical ideal tuning parameters gives you the value of denominator of the integral term coefficient. It's trivial to convert coefficient forms, but it is important to know (even though I have manually calculated tuning parameters all of once in my professional life).
2 unrelated things - sorry for making you re-explain why convincing your customer FBD isn't worth it. That customer definitely seems like one worth keeping happy! Lastly, I highly recommend using the velocity form of the PID equation instead of the position form. The velocity form is the one that calculates the change in your controlled output, where the position form is the one that calculates the controlled output directly. Velocity tends to behave better overall and will transition smoothly when the PID loop is taken into and out of manual control as well as when the setpoint is updated.
One last thing - do any of your customers even use dependent forms of the PID equation? I have worked with only one customer who uses it (and they hate it, but they decided it was too late to change). Everyone else uses the much more intuitive independent form.