# saturation

Create a saturation nonlinearity estimator object

## Syntax

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

## Description

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

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

## Object Description

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

Use saturation to define a nonlinear function $y=F\left(x,\theta \right)$, 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:

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 saturation object.

For saturation object properties, see Properties.

## Examples

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NL = saturation;

Specify the linear interval.

NL.LinearInterval = [-4,5];

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 = saturation('LinearInterval',[0 5]);

Estimate model with no output nonlinearity.

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

Create an iddata object.

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

z is an iddata object with 6 inputs and 2 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 = saturation;

Specify different nonlinearity estimators for each output channel.

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.

## Input Arguments

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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]

## Properties

 LinearInterval Linear interval of the saturation, specified as a 2–element row vector of doubles. Default: [NaN NaN]

## Output Arguments

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Saturation nonlinearity estimator object, returned as a saturation object.