Finding Kp, Ki, and Kd Values from Bump Test

Hello all,

I had a loop tuning class back before the pandemic, but I never got the chance to put it to practical use, and I've just about forgotten everything I learned.

This is my first time tuning a temperature loop, and the first thing I did was to characterize the system using a bump test. I have collected the process gain, time constant, and dead time, but I have no idea how to use these to derive the tuning values for my ControlLogix PID instruction. It seems like that would be a fairly easy thing to find on the web, but I'm having no luck.

Can anyone point me in the right direction?

Thanks so much.
For the benefit of everyone else, I will publish my findings, thus far:

Using the Process Gain (Kp), time constant (Tau-p), and dead time (Theta-p), I plugged the values into the IMC correlation equations, below:

Loop Tuning Formulas.JPG

The only value that you need in addition to Kp, Tau-p, and Theta-p is Tc.

For aggressive control, Tc is the larger of 0.1*Tp or 0.8*Theta-p
For moderate control, Tc is the larger of 1*Tp or 8*Theta-p
For conservative control, Tc is the larger of 10*Tp or 80*Theta-p

So, using aggressive control, I plugged the numbers in for Ideal PID and obtained Kc = 2.11, Ti = 0.99, and Td = 21.98.

To convert these into Kp, Ki, and Kd values for the PID instruction, I simply remembered that when converting from the dependent form of the PID equation to the independent form:

Kp = Kc
Ki = Kc / Ti
Kd = Kc * Td

Hope this helps.
There is some info on youtube...let me see
Tunning a control loop - the knowledge board. By ABB...the guy is very good. .
Used to know it...but its a case of use it or loose it.
If I remember correctly you need to know what form the PID is.
..but there is a way to convert..from one form to another.
Its all there in his longer tutorials...I'm sure it will all come back to you
Bump test..bit more solid than those other touchy feely methods.
Good luck
The bump test is crude but it works if you excite the system enough.
What isn't clear is what kind of system are you trying to tune?
It makes a HUGE difference.
The equation you post above for PI works well for a FOPDT system. I agree with the formula.
However, everything changes when tuning a SOPDT system
Velocity and position control systems have a different set of formulas.
Also, there is NOTHING magic about the IMC formulas. I can do much better but the formulas for the controller parameter are more complicated. But so what? The parameters only need to be calculated once. The improved performance last until something significant changes.
Here I am comparing my more complex formula to the IMC formula. You can see my pole placement method works a little better than the IMC pole cancelation method. - t0p2 SOPDT CD L-M.pdf
In my example, the dead time is equal to the plants longest time constant.
If the dead time gets to be too large then a Smith Predictor is required.
I have an example for that too.