Andrew, I calculated PID gains for the second order model that you
calculated. You can see that my PID gains work very well for your
second order model but fail miserably when applied to the actual 5
pole model.
ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20t0p5%20PID%20ITAE%20Andrew.pdf

I have also calculated the PID gains for JCH's 5th order model. You can see they work. ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20t0p5%20PID%20ITAE.pdf

My conclusion is that it is best to have the best model possible.

I used the minimum ITAE ( integrated time absolute error ) method to calculate the PID gains. I am not a big fan of this method but it seemed a fair way to do the comparison.

Peter Nachtwey

I have also calculated the PID gains for JCH's 5th order model. You can see they work. ftp://ftp.deltacompsys.com/public/NG/Mathcad%20-%20t0p5%20PID%20ITAE.pdf

My conclusion is that it is best to have the best model possible.

I used the minimum ITAE ( integrated time absolute error ) method to calculate the PID gains. I am not a big fan of this method but it seemed a fair way to do the comparison.

Peter Nachtwey