idDeadZone

Create a dead-zone nonlinearity estimator object

Description

idDeadZone is an object that stores the dead-zone nonlinearity estimator for estimating Hammerstein-Wiener models.

Use idDeadZone to define a nonlinear function $$y=F(x,\theta )$$, where y and x are scalars, and θ represents the parameters a and b, which define the zero interval.

The dead-zone nonlinearity function has the following characteristics:

$$\begin{array}{l}a\le x<bF(x)=0\\ x<aF(x)=x-a\\ x\ge bF(x)=x-b\end{array}$$

For example, in the following plot, the dead-zone is in the interval [-4,4].

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

For idDeadZone object properties, see Properties.

Creation

Syntax

NL = idDeadZone

NL = idDeadZone('ZeroInterval',[a,b])

Description

NL = idDeadZone creates a default dead-zone nonlinearity estimator object for estimating Hammerstein-Wiener models. The interval in which the dead-zone exists (zero interval) is set to [NaN NaN]. The initial value of the zero interval is determined from the estimation data range, during estimation using nlhw. Use dot notation to customize the object properties, if needed.

NL = idDeadZone('ZeroInterval',[a,b]) creates a dead-zone nonlinearity estimator object initialized with zero interval, [a,b].

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

Properties

[a,b] — Zero interval

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

Zero interval of the dead-zone, specified as a 2–element row vector of doubles.

The dead-zone 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 zero interval is determined from the estimation data range during estimation using nlhw.

Example: [-2 1]

ZeroInterval — Zero interval of the dead-zone

[NaN NaN] (default) | row vector

Zero interval of the dead-zone, specified as a 2–element row vector of doubles.

Free — Option to fix or free the parameters of the property ZeroInterval

[true true] (default) | row vector

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

Examples

Create a Default Dead-Zone Nonlinearity Estimator

NL = idDeadZone;

Specify the zero interval.

NL.ZeroInterval = [-4,5];

Estimate a Hammerstein-Wiener Model with Dead-zone Nonlinearity

Load estimation data.

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

Create an idDeadZone object, and specify the initial guess for the zero-interval.

OutputNL = idDeadZone('ZeroInterval',[-0.1 0.1]);

Estimate model with no input nonlinearity.

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

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.