Problem using Hammerstein-Wiener model estimation.

I am working with magnetic levitation system and for the model matching I used identification toolbox. In that toolbox I found Hammerstein-Weiner model to identify i/p-o/p non linearities. I used that this model but I still have doubt about the final transfer function I got. So please tell me steps to find a transfer function which is associated with the i/p-o/p non-linearity according to the Hammerstein-Weiner model.

Answer 1

[Rajiv Singh]

The Hammerstein-Wiener model (idnlhw) contains the linear model as its component. See the "LinearModel" property of the idnlhw object. Or, use the getlinmod method, as in LM = getlinmod(idnlhw_model);

[Harshit Gole]

sir,

Does Hammerstein-Weiner model gives a transfer function which is a approximation of a non-linear system, and includes the nonlinearity??

[Rajiv Singh]

No, it is just the linear component of the model (no nonlinearity). If you want a linear approximation of the whole model, look up idnlhw/linearize and idnlhw/linapp commands.

[Harshit Gole]

Then, how to find the function defining input and output non-linearities?

Because we are trying to find out the non-linear model which exactly defines our real time system.

[Rajiv Singh]

For equations, you must refer to the documentation. In particular, see:

http://www.mathworks.com/help/toolbox/ident/ug/bq2ix15.html

It isn't that complicated. You basically have your input signal modified by a memory-free nonlinear function: w = f(u). The signal w is then used as input to a dynamic linear transfer function B/F whose output is x; x = filter(B,F,w) if you don't worry about initial conditions. Finally the output of the linear block is again modified by a memory-free nonlinear function to produce the final output: y = h(x). If you think of the linear function as an operator L, you have y = h(L(f(u)).