L-N-L (Wiener-Hammerstein) system with feedback - recommendation for system ID approach

I have a system model of the attached form that I would like to identify parameters for.

It is a Linear-static nonlinear-linear system with feedback (I have seen it referred to as a Wiener-Hammerstein model with feedback, in contrast with the Hammerstein-Wiener N-L-N model in the system ID toolbox). The static nonlinearity has an approximately known structure, it is like a deadzone, but the middle is not necessarily zero slope.

I am looking for recommendations for a good approach for using the system ID toolbox to identify this system.

Answer 1

[Garmit Pant]

Hello Siva,

I understand that you are trying to identify the parameters to a model that has a Linear – Non-Linear – Linear structure and has feedback.

Please know that as per my findings, System Identification Toolbox and MATLAB do not support this functionality under the current version R2023a.

However, you can identify the parameters of a Non-Linear – Linear – Non-Linear Hammerstein-Wiener models using the ‘idnlhw’ or the ‘nlhw’ functions or using the System Identification App.

You can run the following line on MATLAB command window to open and refer to an example to understand how to estimate Hammerstein-Wiener models:

openExample('ident/EstimateAHammersteinModelWithSaturationExample') 

%Load Data 
load twotankdata; 
z = iddata(y,u,0.2,'Name','Two tank system'); 
z1 = z(1:1000); 
%Create a saturation object with lower limit of 0 and upper limit of 5. 
InputNL = idSaturation('LinearInterval',[0 5]); 
%Estimate model with no output nonlinearity. 
m = nlhw(z1,[2 3 0],InputNL,[]); 

You can also refer to the following MATLAB documentation and resources:

https://in.mathworks.com/help/ident/ref/nlhw.html - documentation for the function to model and estimate parameters for a Hammerstein-Wiener Model.

https://in.mathworks.com/help/ident/ug/what-are-hammerstein-wiener-models.html - documentation about the diverse ways Hammerstein-Wiener models can be solved in MATLAB.

https://in.mathworks.com/help/ident/release-notes.html - release notes for System Identification Toolbox.

I hope you find the above explanation and suggestions useful!