# Heat exchanger identification

I have been developing a digital controller for water cooling system of power electronics converter. This system consists of plate heat exchanger, pipe with demineralized water flow (this fluid is heated by power losses of power transistors of the converter), pipe with common water flow and a control valve which is placed in pipe with common water near the input into the heat exchanger. Controlled variable of this system is temperature of demineralized water at the output of power converter and control variable (action) is position of control valve which sets flow of common water into the exchanger. For controller design I need a transfer function of this system. Because of control valve (it introduces a dead time) I have chosen FOPDT model i.e. $$G(s)=\frac{K_p}{s\cdot T_p+1}\cdot\exp(-T_d\cdot s).$$

Now I would like to identify values of the system gain Kp, system time constant Tp and dead time Td. So I am thinking about sutaible experiment. I have tried to warm demineralized water and then suddenly to fully open the control valve. I have got following response (both values are in per units) . Then I have used Matlab command idproc with argument P1D for identification. The transfer function I have got is following $$G(s)=\frac{1,341}{s\cdot 571,6+1}\cdot\exp(-0,4\cdot s).$$

It is absolutely different than I expected. I don't understand on one hand the large value of time constant and on the other hand small value of dead time. I expected $K_p = 0,1 (-), T_p = 97,3 (s)$ and $T_d = 45,43 (s)$ from rough estimate from directly measured data. I am not sure whether the experiment I have performed is correct. I have heated the demineralized water by hydraulic friction caused by flow of demineralized water through heat exchanger and various folds.The pumps which produces this flow were running also after opening the valve.This hydraulic friction is from control point of view a disturbance signal, but I think that the measurement after opening the valve is relatively quick so I have omitted its influence. Can somebody tell me whether this identification experiment is correct or incorrect? Why there is large difference between Matlab results and expected values? Thanks for any ideas.

• Doesn't the matlab have also a window where you can compare estimated model vs real? I think your model can't be estimated as FOPD, because you can see it does weird thing at the beginning. It seems like something went wrong when opening those valves, looks like two or three systems in cascade. Mar 18, 2016 at 10:45