Why cant I predict kstep ahead when adding System Identification models?

Hello, how are you doing?

I have the following question about System Identification: if I add multiple system identification models, such as ARX models, I obtain as a result a State-space model that ignore the kstep parameter in the prediction.

For example:

load iddata1 z1;
sys = ssest(z1,3);

If i do:

compare(z1,sys,1)

OR

compare(z1,sys,inf)

the results are completely different, as expected!

However, if I have the combination of two models,

sys2 = sys + sys;

when i use compare(z1,sys,inf) or compare(z1,sys,1), the results are the same! It just ignore the kstep parameter!

Can anyone explaine me what is going on? How can I add two systems and still make a 1 step ahead prediction?

PS: sys2 = sys + sys is equivalente to parallel(sys,sys).

Thanks a lot!

Answer 1

[Rajiv Singh]

The issue is that algebra on identified models (plus, minus, series, parallel, feedback, inv etc) are not natively supported. These operations require Control System Toolbox and the result is a model object from that toolbox. So if you do SYS = SYS1+SYS2, where SYS1 and SYS2 are @idss objects, the result SYS is an @ss object of Control System Toolbox. This object is unaware of noise components (K matrix) and hence does not differentiate between prediction and simulation.

If you simply need to add up the outputs of two systems, an easier way is to do horizontal concatenation, as in: SYS = [SYS1, SYS2]. This operation is fully supported and results in SYS being an @idss model with no loss of information.

Answer 2

[Paresh yeole]

https://de.mathworks.com/help/ident/ref/compare.html

Check this link.

It says :

'compare ignores kstep when sys is an iddata object, an FRD model, or a dynamic system with no noise component. compare also ignores kstep when using frequency response validation data. '

[Giulio Cesare Mastrocinque Santo]

Yes, I saw that. But, do you know why adding multiple models I lose the noise components?