Peter Ponders PID - Optimization Routines

[@amwielbinski]

Great stuff Peter, thanks for doing these videos.

[@matthiasfrese5208]

Fascinating video! Do you have any more information about the non-linear model you used for the identification?

[@pnachtwey]

Every non-linear system is going to be different . For this problem I tried perhaps 6 different models. I could see right off that the gain was going to be the biggest problem. I tried 5 segments. I tried f(x)=c0+c1*x+c3*x^3+c5*x^5. The polynomial had be of odd power. It would match the dead band for the valve. I settled on 10 segments with the smaller segments being closer to 0. I once was challenged to determine the diameter and length of horizontal tank. The model I used was that for a horizontal tank. I only had to determine the length and diameter given the volume and height. That was easy but it wasn't linear. My point is that you really need to know the general equations to use for the object you are trying to model. Sometimes you must try multiple models. For instance, Delta Motions auto tuner will try both a motor model and a hydraulic cylinder model. It tries velocity mode and torque mode for the motor. Use the model with the lowest sum of squared errors or mean squared error. You really need to have some idea of what model(s) will work best.