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Hammerstein-Wiener Models

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

Use Hammerstein-Wiener models to estimate static nonlinearities in an otherwise linear system. In the toolbox, these models are represented as idnlhw objects. You can estimate Hammerstein-Wiener models in the System Identification app, or at the command line using the nlhw command.


System IdentificationIdentify models of dynamic systems from measured data


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idnlhwHammerstein-Wiener model
nlhwEstimate Hammerstein-Wiener model
nlhwOptionsOption set for nlhw
initSet or randomize initial parameter values
getpvecObtain model parameters and associated uncertainty data
setpvecModify values of model parameters
idCustomNetworkCustom network function for nonlinear ARX and Hammerstein-Wiener models
idDeadZoneCreate a dead-zone nonlinearity estimator object
idPolynomial1DClass representing single-variable polynomial nonlinear estimator for Hammerstein-Wiener models
idPiecewiseLinearCreate a piecewise-linear nonlinearity estimator object
idSaturationCreate a saturation nonlinearity estimator object
idSigmoidNetworkSigmoid network function for nonlinear ARX and Hammerstein-Wiener models
idUnitGainSpecify absence of nonlinearities for specific input or output channels in Hammerstein-Wiener models
idWaveletNetworkWavelet network function for nonlinear ARX and Hammerstein-Wiener models
evaluateValue of nonlinearity estimator at given input
simSimulate response of identified model
simOptionsOption set for sim
compareCompare identified model output and measured output
compareOptionsOption set for compare
plotPlot input and output nonlinearity, and linear responses of Hammerstein-Wiener model
evaluateValue of nonlinearity estimator at given input
findopCompute operating point for Hammerstein-Wiener model
findopOptionsOption set for findop
operspecConstruct operating point specification object for idnlhw model
linearizeLinearize Hammerstein-Wiener model
linappLinear approximation of nonlinear ARX and Hammerstein-Wiener models for given input


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Hammerstein-Wiener ModelSimulate Hammerstein-Wiener model in Simulink software
Iddata SinkExport simulation data as iddata object to MATLAB workspace
Iddata SourceImport time-domain data stored in iddata object in MATLAB workspace


What are Hammerstein-Wiener Models?

Understand the structure of Hammerstein-Wiener models.

Available Nonlinearity Estimators for Hammerstein-Wiener Models

Choose from piecewise linear, sigmoid, wavelet, saturation, dead zone, polynomial, and custom network nonlinearities.

Identifying Hammerstein-Wiener Models

Specify the Hammerstein-Wiener model structure, and configure the estimation algorithm.

Validating Hammerstein-Wiener Models

Plot model nonlinearities, analyze residuals, and simulate 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.

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.

Featured Examples