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. You can use the Hammerstein-Wiener structure to capture physical nonlinear effects in sensors and actuators that affect the input and output of a linear system, such as dead zones and saturation. To estimate Hammerstein-Wiener models, use the System Identification app or the nlhw function.

Apps

System Identification

Identify models of dynamic systems from measured data

Functions

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Model Estimation

`idnlhw`	Hammerstein-Wiener Model
`nlhw`	Estimate Hammerstein-Wiener model
`nlhwOptions`	Option set for `nlhw`
`init`	Set or randomize initial parameter values
`getpvec`	Obtain model parameters and associated uncertainty data
`setpvec`	Modify values of model parameters

Nonlinearity Representation

`idCustomNetwork`	Custom network function for nonlinear ARX and Hammerstein-Wiener models
`idDeadZone`	Create a dead-zone nonlinearity estimator object
`idPolynomial1D`	Class representing single-variable polynomial nonlinear estimator for Hammerstein-Wiener models
`idPiecewiseLinear`	Create a piecewise-linear nonlinearity estimator object
`idSaturation`	Create a saturation nonlinearity estimator object
`idSigmoidNetwork`	Sigmoid network function for nonlinear ARX and Hammerstein-Wiener models
`idUnitGain`	Specify absence of nonlinearities for specific input or output channels in Hammerstein-Wiener models
`idWaveletNetwork`	Wavelet network function for nonlinear ARX and Hammerstein-Wiener models
`idGaussianProcess`	Gaussian process regression mapping function for nonlinear ARX and Hammerstein-Wiener models (requires Statistics and Machine Learning Toolbox) (Since R2021b)
`idNeuralNetwork`	Multilayer neural network mapping function for nonlinear ARX models and Hammerstein-Wiener models (requires Statistics and Machine Learning Toolbox or Deep Learning Toolbox) (Since R2023b)
`evaluate`	Evaluate output values of `idnlarx` or `idnlhw` mapping object array for given set of input values

Simulation and Validation

`sim`	Simulate response of identified model
`simOptions`	Option set for `sim`
`compare`	Compare identified model output with measured output
`compareOptions`	Option set for `compare`
`nlhwPlot`	Plot input and output nonlinearity, and linear responses of Hammerstein-Wiener model (Since R2023a)
`evaluate`	Evaluate output values of `idnlarx` or `idnlhw` mapping object array for given set of input values

Linearization

`idnlhw/findop`	Compute operating point for Hammerstein-Wiener model
`findopOptions`	Option set for `findop`
`idnlhw/operspec`	Construct operating point specification object for `idnlhw` model
`idnlhw/linearize`	Linearize Hammerstein-Wiener model
`linapp`	Linear approximation of nonlinear ARX and Hammerstein-Wiener models for given input

Blocks

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Simulation

Hammerstein-Wiener Model	Simulate Hammerstein-Wiener model in Simulink software
Iddata Sink	Export simulation data as `iddata` object to MATLAB workspace
Iddata Source	Import time-domain data stored in `iddata` object in MATLAB workspace

Topics

What Are Hammerstein-Wiener Models?
Understand the structure of Hammerstein-Wiener models.
Available Nonlinearity Estimators for Hammerstein-Wiener Models
Choose from a set of scalar nonlinearity estimators that you can use for both input and output estimators in Hammerstein-Wiener models.
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

A Tutorial on Identification of Nonlinear ARX and Hammerstein-Wiener Models

Identify single-input-single-output (SISO) nonlinear black box models using measured input-output data.

Open Script

Create Black-Box Models of a Robotic Arm System Using Neural Networks

Use neural networks as the nonlinear function when you model nonlinear ARX and Hammerstein-Wiener models. It compares the nonlinear systems estimated using different types of neural networks, activation functions, and number of layers.

Open Live Script

Hammerstein-Wiener Model of SI Engine Torque Dynamics

Describes modeling the nonlinear torque dynamics of a spark-ignition (SI) engine as a Hammerstein-Wiener model. The identified model can be used for hardware-in-the-loop (HIL) testing, powertrain control, diagnostic, and training algorithm design. For example, you can use the model for aftertreatment control and diagnostics algorithm development. For more information on Hammerstein-Wiener models, see Hammerstein-Wiener Models.

Open Live Script