Identification of your controlled system for stability estimation

• posted
Hi,
which methods are you using to identify the system you try to control?
Often, the controlled system is not simple and can not be derived from
differential equations. Do you just approximate the system with PT2
(maybe with dead time), build the transfer function and continue with
bode?
-- pt
• posted
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.
• posted
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.
• posted
Do you mean this fellow: ?
--Joel
• posted
That's the very person.
• posted
Thanks for the question. I tried to find him by the name but its pretty ambiguous.
-- pt
• posted
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
• posted
I use Levenberg-Marquardt. Auto tuning is more difficult because you must have a model for each non-linearity. The following link shows how a hydraulic actuator with a non-linear valve can be modeled. The valve has two gain segments which are clearly seen. It is also possible to model the valve as a odd order polynomial with an offset to model valve with curved responses. All the models must be tested and the one with the lowest error is USUALLY the right one.
Linear temperature systems are easy. I haven't done it yet but properly modeling a heat exchanger and taking into account the log mean temperature difference shouldn't be a problem.
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) ;
• posted
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: