First order transfer function system identification

I am doing this open loop test in which I am adding constant 561 to every measured output value from the process model and then exporting it for it to be used in model identification.

input is the step response of final value 1.54 and output is the simout cell values in schematic.

In SYSID after estimating first order TF model, fitting is very low(16%). It is passing residual test though.The equation of the model estimated :-

I tried after preprocessing(removing detrends) but the equation of First order TF model estimated after that was way off from this process model used in schematic.

When I used only 29/4s+1 as process model( i.e. not adding 561 to its output) using same procedure in SYSID then 100% fittng model passing residual tests was estimated(without any preprocessing).

Why adding a constant is making such a big difference? Is my process wrong ? How to solve this problem?

Any help would be appreciated.

Thanks in advance:)

[Mathieu NOE]

hello

a process identification is basd on the variation of the outputs vs. the variation of the inputs

if you add on purpose a constant on the outputs it does no more work

the data should content dynamically varying data , constants must be removed first (and kept apart for later)

[Siddhi Satnalika]

Hello

Thanks for helping me out.

But SysID has option of mean removal and I used it in preprocessing ; does that option remove the constant part in input and output and give result in terms of del u & del Y?

The fitting after removing means is estimated to be 58%.(while it was 100% before adding constant 561).

Also, TF equation estimated was way off after means removal

[Mathieu NOE]

again

I would personnaly not make things too complicated and especcially remove constants on the output and add that later on , once the model fit is validated