Identification of your controlled system for stability estimation

Look out for papers by Professor Stephen J. Dobbs who has written and lectured on this subject extensively. I hope your math is up to it.

Generally I either model the system from first principals and use and _exceedingly_ conservative controller (because you always miss some important detail when modeling from first principals), or (assuming that it's linear enough) I do a swept-sine measurement of the system's frequency response and use that -- along with the controller's calculated frequency response -- do my design with Bode and Nyquist plots.

Life gets more complicated in the presence of significant nonlinearities.

Do you mean this fellow: ?

--Joel

That's the very person.

Thanks for the question. I tried to find him by the name but its pretty ambiguous.

-- pt

I use Levenberg-Marquardt. Auto tuning is more difficult because you must have a model for each non-li= nearity. The following link shows how a hydraulic actuator with a non-linear valve c= an be modeled. The valve has two gain segments which are clearly seen. I= t is also possible to model the valve as a odd order polynomial with an off= set to model valve with curved responses. All the models must be tested a= nd the one with the lowest error is USUALLY the right one.

Linear temperature systems are easy. I haven't done it yet but properly m= odeling a heat exchanger and taking into account the log mean temperature d= ifference shouldn't be a problem.

Peter Nachtwey

Peter Nachtwey

Peter, I had some trouble getting the LMTD calc to converge, and sought some assistance in a newsgroup, may have been this one or else chem eng related. Charlie W, a regular poster, suggested some small fiddle factors in the calc, that solved the problem and I've been grateful for his assistance ever since. Here's the equation without commentary, if you want any more info revert to here and I can send you more of my code.

Qlmtd = U * A * (at1 - at2 + 1.0E-7 *(at1+at2)) / (log (at1 / at2) +

2.0E-7) ;

Bruce, what software are you using? Do you have your data in a text file in CSV format? I can do this in Scilab. I have a simple FOPDT and SOPDT autotuner here:

wrote this years ago. I would need to change it to make it handle your non-linear case but the idea would be the same.

Charlie W, may be right. I add offset variables to ideal equations since nothing is perfect. You can see where I do that in my Scilab example. In this case the offset is ambient temperature. I know that valves always have a small offset.

Peter Nachtwey

I was looking for online papers of Stephen Dodds but wasn't successfull. Do you have a link to one of them?

-- pt