I have found that using the initial PID tuning values the website provides for the 1st order equation is actually quite accurate for the system I am working on when implemented.
I wanted to know what method the website uses to predict the best PID tuning values are when I first plug in my data?
The PID tuning rules are just given as a tuning starting point. The valuable information are actually the models, you can use any tuning rules over the models to achieve whatever you want with your PID.