Why model is not reproducing the output when given the same input (which was used to build model)?

I have built a model from plant data. Plant data are generated by giving PRBS inputs to 4 differential equations (these are derived from first principle as given in research paper)and collecting outputs.output is water level in drum and input is water flow rate. As there is no noise, so i have built oe[2 2 0] model and it fits 90%. But if the same input is given to model it doesn't reproduce the outputs(with which i started). obtained output is very high in magnitude and decreases so rapidly. so i want to know what mistake i have made ? is the water level decreasing because system is unstable?

[Patrik Ek]

What method are you using? I mean, do you use some matlab control method? Some methods induces some noise in the system, some methods are stocastic (like an ARMA estimation which performs a spectral estiamtion and recreates the signal by filtering AWGN). Also, do you ask if your system is unstable? Because I cannot tell without watching some plots.

[Shilochana Dudi]

the following is the code which i used to get model- clear all;clc; load('mat31.mat'); u=input1_q_f; y=output_mat(:,1); dataset=iddata(y,u,1); data=detrend(dataset); figure(1);cra(data) model = pem(data,'na',0,'nb',2,'nc',0,'nd',0,'nf',2,'nk',0); figure(2);resid(model,data) compare(data,model); present(model);

Results -

Discrete-time OE model: y(t) = [B(z)/F(z)]u(t) + e(t) B(z) = -12.33 (+/- 7.668) + 12.13 (+/- 7.729) z^-1

F(z) = 1 - 2 (+/- 4.076e-05) z^-1 + z^-2

in the above data doesn't have noise. i tried with noise of snr 10.

Answer 1

[John]

Because you mention that you have a 90% fit, I assume you have used the Matlab systems identification toolbox (or similar). However if you have differential equations you do not need to use the system identification toolbox, you can determine the state space model analytically. In this way it will have 100% ''fit'' and always return the same values as the differential equations/plant model.

[Shilochana Dudi]

but i did this to get linear transfer function