User`s guide

4 Nonlinear Black-Box Model Identification
state values. For m ore information, see “Tangent Linearization of Nonlinear
Black-Box Models” on page 4-35.
Linear Approximation of Nonlinear Black-Box
Models for a Given Input
linapp computes the best linear a pproxi mation—in a mean-square-error
sense—of a nonlinear ARX or Hammerstein-Wiener model for a given input or
a randomly generated input.
linapp estimates the best linear model that is structurally similar to the
origina l non l inear model and provid es the be st fit between a giv en input and
the corresponding simulated response of the nonlinear model.
To compute a linear approximation of a nonlinear black-box model for a g iv en
input, you must h ave the following v ariables in the MATLAB workspace:
• Nonlinear ARX (
idnlarx) or Hammerstein-Weiner (idnlh w) model
• Input signal for which you w ant to obtain a linear approximation, specified
as a real matrix or an
iddata object
You use the specified input signal to compute a linear approximation, as
follows:
• For nonlinear ARX models,
linapp estimates a linear ARX model using the
same model orders
na, nb,andnk as the original model.
• For Hammerstein-W iener models,
linapp estimates a linear Output-Error
(OE)modelusingthesamemodelorders
nb, nf,andnk.
To compute a linear approximation of a nonlinear black-box model for a
randomly generated input, you must also have the minimum and maximum
scalar input values for generating white-noise input with a magnitude in this
rectangular range,
umin and umax in the M A TLAB w orkspace.
For more information, se e the
linapp reference page.
The resulting linear model is only valid for the same input signal as you the
one you used to generate the linear approximation.
4-34