Extract tranfer function from a graphgreenspun.com : LUSENET : PID Controller Tuning : One Thread
I am an MSc student and my project deal with the investigation of temperature stability in an infant incubator.I have taken some meauserments in different points in the chamber of the incubator and I have plot graphs of TEMP vs TIME.Unfortunately I do not know what is the temperature control system that the incubator is based on.MY question is:How can we understand from the graphs if the system is first-order or second-order and so on, so to extract the appropriate transfer function.Is my sytem linear or non-linear?Note that the temperature control system is based on an electrical heater.
Best regards, Georgios Kouroudis
-- Kouroudis Georgios (firstname.lastname@example.org), July 07, 2000
What are describing is problem in system identification. One of my favorite references in the subject is "Theory and Practice of Recursive Identification" by Lennart Ljung and Torsten Soderstrom (MIT Press ISBN 0-262-12095- X). Basically you have to develop your model and drive it with measured inputs and then compare model outputs with the actual measurements and use a fitting method (Least Squares, Kalman Filter etc) to adjust the model parameters until the outputs match as closely as possible. In your case, you probably need more measurements (room ambient temperature for one). Measureing current on the heater would also be extremely useful. Your model should include all dynamics between the input (ambient temperature) and the output (incubatior temperature). Needless to say this is not a precise science so youhave to keep working with your model until you find a good fit.
-- James Ross (email@example.com), July 07, 2000.
I probable came too late. To answer this question to the one who still interest this question. The order of the process is very high considering it to n-order process but practically we estimate the n-order process to 1st order process. Why is that? If you plot the graph in excel work sheet wiht 1st order form in time domain e(t)=k(1-exp(-t/tau)). This is equvalent to k/(tau*s+1). Observe the response. Then you plot it again in excel sheet in time domail, which is the function of cosine and exponetial. You can compare in case of 2nd order (daping ratio .=1 only). I would like you to notice the shpae of the curve when it starts raising. You will see the difference. Practically, I always estimate it to be 1st order process any error of process identification will be solved by PID or any kind of feedback control. Except some obvious loop like Level Control cascade to Slave Flow Control you may see it behave like 2nd order or higher order with daping ratio less than 1.0. For nonlinear, you can know by doing step test (excite the ssytem with step response at the systm input) at different output value. I experience this: I would like to control the delta temperature in heat exchange to ensure we always have enogh heat transfer. At high delta Temp meaning you have enoigh heat transfet (instrument range 0-25 deg. c). I closed the condensate valve untill the delta Temp is read 10 deg. C, which is consider this is a normal operation. I mad a step test (increase)during normal operation. I got Process Gain = 0.5 Tau=6 min and Dead Time = 2 min. This is the first result. Then I open the outlet condensate valve. the delta Temp is decrease to 3 deg. c. At this delta Temp value 3 deg. c is consider we are losing the condensate level and the condensate flow will become to 2 phase flow. At this staage, the process behavior is change to fast dynamic I mad step test again (increase) at this stage with the same magnitune of control valve openning.I got process parameter as Process Gain = 1.1, Tau= 0.6, Dead Time =0.0 min. You can see that this process is highly non-linear system. At differnt operting point gives different process characteris tic. And most of the real process are non- linear. You can write me the emal of some specific question if I know I will reply.
-- Mongkol Janchookiat (firstname.lastname@example.org), June 25, 2001.