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Hammerstein-Wiener Models

Connection of linear dynamic systems with static nonlinearities such as saturation and dead zone

Apps

System Identification Identify models of dynamic systems from measured data

Functions

nlhw Estimate Hammerstein-Wiener model
idnlhw Hammerstein-Wiener model
pem Prediction error estimate for linear and nonlinear model
customnet Custom nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
deadzone Create a dead-zone nonlinearity estimator object
poly1d Class representing single-variable polynomial nonlinear estimator for Hammerstein-Wiener models
pwlinear Create a piecewise-linear nonlinearity estimator object
saturation Create a saturation nonlinearity estimator object
sigmoidnet Class representing sigmoid network nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
unitgain Specify absence of nonlinearities for specific input or output channels in Hammerstein-Wiener models
wavenet Create a wavelet network nonlinearity estimator object
evaluate Value of nonlinearity estimator at given input
plot Plot input and output nonlinearity, and linear responses of Hammerstein-Wiener model
sim Simulate response of identified model
findop Compute operating point for Hammerstein-Wiener model
operspec Construct operating point specification object for idnlhw model
linearize Linearize Hammerstein-Wiener model
linapp Linear approximation of nonlinear ARX and Hammerstein-Wiener models for given input
findstates Estimate initial states of model
init Set or randomize initial parameter values
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
nlhwOptions Option set for nlhw
findopOptions Option set for findop
findstatesOptions Option set for findstates
simOptions Option set for sim

Examples and How To

Estimate Hammerstein-Wiener Models in the App

Estimate Hammerstein-Wiener models in the System Identification app.

Estimate Hammerstein-Wiener Models at the Command Line

Configure Hammerstein-Wiener model estimation at the command line.

Estimate Hammerstein-Wiener Models Using Linear OE Models

This example shows how to estimate Hammerstein-Wiener models using linear OE models.

Low-level Simulation of Hammerstein-Wiener Model

This example shows how the software evaluates the simulated output by first computing the output of the input and output nonlinearity estimators.

Concepts

Structure of Hammerstein-Wiener Models

Understand the structure of a Hammerstein-Wiener model.

Using Linear Model for Hammerstein-Wiener Estimation

You can use a polynomial model of Output-Error (OE) structure (idpoly) or state-space model with no disturbance component (idss model with K = 0) for Hammerstein-Wiener estimation.

Nonlinearity Estimators for Hammerstein-Wiener Models

System Identification Toolbox™ software provides several scalar nonlinearity estimators F(x) for Hammerstein-Wiener models.

Applications of Hammerstein-Wiener Models

When the output of a system depends nonlinearly on its inputs, sometimes it is possible to decompose the input-output relationship into two or more interconnected elements.

Ways to Configure Hammerstein-Wiener Estimation

Configure Hammerstein-Wiener estimation.

Estimation Options for Hammerstein-Wiener Models

Estimation of Hammerstein-Wiener models uses iterative search to minimize the simulation error between the model output and the measured output.

How the Software Computes Hammerstein-Wiener Model Output

How the software evaluates the output of nonlinearity estimators and uses this output to compute the model response.

Validating Hammerstein-Wiener Models

Plot model nonlinearities, analyze residuals, and simulate and predict model output.

Using Hammerstein-Wiener Models

Simulate and predict model output, linearize Hammerstein-Wiener models, and import estimated models into the Simulink® software.

Linear Approximation of Nonlinear Black-Box Models

Choose the approach for computing linear approximations, compute operating points for linearization, and linearize your model.

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