idSaturation

Create a saturation nonlinearity estimator object

Description

idSaturation is an object that stores the saturation nonlinearity estimator for estimating Hammerstein-Wiener models.

Use idSaturation to define a nonlinear function $$y=F(x,\theta )$$, where y and x are scalars, and θ represents the parameters a and b that define the linear interval, [a,b].

The saturation nonlinearity function has the following characteristics:

$$\begin{array}{l}a\le x<bF(x)=x\\ a>xF(x)=a\\ b\le xF(x)=b\end{array}$$

For example, in the following plot, the linear interval is [-4,3].

The value F(x) is computed by evaluate(NL,x), where NL is the idSaturation object.

For idSaturation object properties, see Properties.

Creation

Syntax

NL = idSaturation

NL = idSaturation('LinearInterval',[a,b])

Description

NL = idSaturation creates a default saturation nonlinearity estimator object for estimating Hammerstein-Wiener models. The linear interval is set to [NaN NaN]. The initial value of the linear interval is determined from the estimation data range during estimation using nlhw. Use dot notation to customize the object properties, if needed.

NL = idSaturation('LinearInterval',[a,b]) creates a saturation nonlinearity estimator object initialized with linear interval, [a,b].

Alternatively, use NL = idSaturation([a,b]).

Properties

[a,b] — Linear interval

[NaN NaN] (default) | 2–element row vector

Linear interval of the saturation, specified as a 2–element row vector of doubles.

The saturation nonlinearity is initialized at the interval [a,b]. The interval values are adjusted to the estimation data by nlhw. To remove the lower limit, set a to -Inf. The lower limit is not adjusted during estimation. To remove the upper limit, set b to Inf. The upper limit is not adjusted during estimation.

When the interval is [NaN NaN], the initial value of the linear interval is determined from the estimation data range during estimation using nlhw.

Example: [-2 1]

LinearInterval — Linear interval of the saturation

[NaN NaN] (default) | row vector

Linear interval of the saturation, specified as a 2–element row vector of doubles.

Free — Option to fix or free parameters of property LinearInterval

[true true] (default) | logical row vector

Option to fix or free the parameters of LinearInterval, specified as a 2–element logical row vector. When you set an element of Free to false, the corresponding value in LinearInterval remains fixed during estimation to the initial value that you specify.

Examples

Create a Default Saturation Nonlinearity Estimator

NL = idSaturation;

Specify the linear interval.

NL.LinearInterval = [-4,5];

Estimate a Hammerstein Model with Saturation

Load data.

load twotankdata;
z = iddata(y,u,0.2,'Name','Two tank system');
z1 = z(1:1000);

Create a saturation object with lower limit of 0 and upper limit of 5.

InputNL = idSaturation('LinearInterval',[0 5]);

Estimate model with no output nonlinearity.

m = nlhw(z1,[2 3 0],InputNL,[]);

Estimate MIMO Hammerstein-Wiener Model

Load the estimation data.

load motorizedcamera;

Create an iddata object.

z = iddata(y,u,0.02,'Name','Motorized Camera','TimeUnit','s');

z is an iddata object with six inputs and two outputs.

Specify the model orders and delays.

Orders = [ones(2,6),ones(2,6),ones(2,6)];

Specify the same nonlinearity estimator for each input channel.

InputNL = idWaveletNetwork;

Specify different nonlinearity estimators for each output channel.

 OutputNL = [idDeadZone,idWaveletNetwork];

Estimate the Hammerstein-Wiener model.

sys = nlhw(z,Orders,InputNL,OutputNL);

To see the shape of the estimated input and output nonlinearities, plot the nonlinearities.

plot(sys)

Click on the input and output nonlinearity blocks on the top of the plot to see the nonlinearities.

Version History

Introduced in R2007a

R2021b: Use of previous idnlarx and idnlhw mapping object names is not recommended.

Starting in R2021b, the mapping objects (also known as nonlinearities) used in the nonlinear components of the idnlarx and idnlhw objects have been renamed. The following table lists the name changes.

Pre-R2021b Name	R2021b Name
wavenet	idWaveletNetwork
sigmoidnet	idSigmoidNetwork
treepartition	idTreePartition
customnet	idCustomNetwork
saturation	idSaturation
deadzone	idDeadZone
pwlinear	idPiecewiseLinear
poly1d	idPolynomial1D
unitgain	idUnitGain
linear	idLinear
neuralnet	idFeedforwardNetwork

Scripts with the old names still run normally, although they will produce a warning. Consider using the new names for continuing compatibility with newly developed features and algorithms. There are no plans to exclude the use of these object names at this time.