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# idpoly

Polynomial model with identifiable parameters

## Syntax

``sys = idpoly(A,B,C,D,F,NoiseVariance,Ts)``
``sys = idpoly(A,B,C,D,F,NoiseVariance,Ts,Name,Value)``
``sys = idpoly(A)``
``sys = idpoly(A,[],C,D,[],NoiseVariance,Ts)``
``sys = idpoly(A,[],C,D,[],NoiseVariance,Ts,Name,Value)``
``sys = idpoly(sys0)``
``sys = idpoly(sys0,'split')``

## Description

````sys = idpoly(A,B,C,D,F,NoiseVariance,Ts)` creates a polynomial model with identifiable coefficients. `A`, `B`, `C`, `D`, and `F` specify the initial values of the coefficients. `NoiseVariance` specifies the initial value of the variance of the white noise source. `Ts` is the model sample time. ```
````sys = idpoly(A,B,C,D,F,NoiseVariance,Ts,Name,Value)` creates a polynomial model using additional options specified by one or more `Name,Value` pair arguments.```
````sys = idpoly(A)` creates a time-series model with only an autoregressive term. In this case, `sys` represents the AR model given by A(q–1) y(t) = e(t). The noise e(t) has variance 1. `A` specifies the initial values of the estimable coefficients. ```
````sys = idpoly(A,[],C,D,[],NoiseVariance,Ts)` creates a time-series model with an autoregressive and a moving average term. The inputs `A`, `C`, and `D`, specify the initial values of the estimable coefficients. `NoiseVariance` specifies the initial value of the noise e(t). `Ts` is the model sample time. (Omit `NoiseVariance` and `Ts` to use their default values.) If `D = []`, then `sys` represents the ARMA model given by:$A\left({q}^{-1}\right)y\left(t\right)=C\left({q}^{-1}\right)e\left(t\right).$```
````sys = idpoly(A,[],C,D,[],NoiseVariance,Ts,Name,Value)` creates a time-series model using additional options specified by one or more `Name,Value` pair arguments.```
````sys = idpoly(sys0)` converts any dynamic system model, `sys0`, to `idpoly` model form. ```
````sys = idpoly(sys0,'split')` converts `sys0` to `idpoly` model form, and treats the last Ny input channels of `sys0` as noise channels in the returned model. `sys0` must be a numeric (nonidentified) `tf`, `zpk`, or `ss` model object. Also, `sys0` must have at least as many inputs as outputs.```

## Object Description

An `idpoly` model represents a system as a continuous-time or discrete-time polynomial model with identifiable (estimable) coefficients.

A polynomial model of a system with input vector u, output vector y, and disturbance e takes the following form in discrete time:

`$A\left(q\right)y\left(t\right)=\frac{B\left(q\right)}{F\left(q\right)}u\left(t\right)+\frac{C\left(q\right)}{D\left(q\right)}e\left(t\right)$`

In continuous time, a polynomial model takes the following form:

`$A\left(s\right)Y\left(s\right)=\frac{B\left(s\right)}{F\left(s\right)}U\left(s\right)+\frac{C\left(s\right)}{D\left(s\right)}E\left(s\right)$`

U(s) are the Laplace transformed inputs to `sys`. Y(s) are the Laplace transformed outputs. E(s) is the Laplace transform of the disturbance.

For `idpoly` models, the coefficients of the polynomials A, B, C, D, and F can be estimable parameters. The `idpoly` model stores the values of these matrix elements in the `A`, `B`, `C`, `D`, and `F` properties of the model.

Time-series models are special cases of polynomial models for systems without measured inputs. For AR models, `B` and `F` are empty, and `C` and `D` are 1 for all outputs. For ARMA models, `B` and `F` are empty, while `D` is 1.

There are three ways to obtain an `idpoly` model:

• Estimate the `idpoly` model based on output or input-output measurements of a system, using commands such as `polyest`, `arx`, `armax`, `oe`, `bj`, `iv4`, or `ivar`. These commands estimate the values of the free polynomial coefficients. The estimated values are stored in the `A`, `B`, `C`, `D`, and `F` properties of the resulting `idpoly` model. The `Report` property of the resulting model stores information about the estimation, such as handling of initial conditions and options used in estimation.

When you obtain an `idpoly` model by estimation, you can extract estimated coefficients and their uncertainties from the model using commands such as `polydata`, `getpar`, or `getcov`.

• Create an `idpoly` model using the `idpoly` command. You can create an `idpoly` model to configure an initial parameterization for estimation of a polynomial model to fit measured response data. When you do so, you can specify constraints on the polynomial coefficients. For example, you can fix the values of some coefficients, or specify minimum or maximum values for the free coefficients. You can then use the configured model as an input argument to `polyest` to estimate parameter values with those constraints.

• Convert an existing dynamic system model to an `idpoly` model using the `idpoly` command.

## Examples

collapse all

Create an `idpoly` model representing the one-input, two-output ARMAX model described by the following equations:

`$\begin{array}{l}{y}_{1}\left(t\right)+0.5{y}_{1}\left(t-1\right)+0.9{y}_{2}\left(t-1\right)+0.1{y}_{2}\left(t-2\right)=\\ \phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}u\left(t\right)+5u\left(t-1\right)+2u\left(t-2\right)+{e}_{1}\left(t\right)+0.01{e}_{1}\left(t-1\right)\\ {y}_{2}\left(t\right)+0.05{y}_{2}\left(t-1\right)+0.3{y}_{2}\left(t-2\right)=\\ \phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}\phantom{\rule{1em}{0ex}}10u\left(t-2\right)+{e}_{2}\left(t\right)+0.1{e}_{2}\left(t-1\right)+0.02{e}_{2}\left(t-2\right).\end{array}$`

${y}_{1}$ and ${y}_{2}$ are the two outputs, and $u$ is the input. ${e}_{1}$ and ${e}_{2}$ are the white noise disturbances on the outputs ${y}_{1}$ and ${y}_{2}$ respectively.

To create the `idpoly` model, define the `A`, `B`, and `C` polynomials that describe the relationships between the outputs, inputs, and noise values. (Because there are no denominator terms in the system equations, `B` and `F` are 1.)

Define the cell array containing the coefficients of the `A` polynomials.

```A = cell(2,2); A{1,1} = [1 0.5]; A{1,2} = [0 0.9 0.1]; A{2,1} = ; A{2,2} = [1 0.05 0.3];```

You can read the values of each entry in the `A` cell array from the left side of the equations describing the system. For example, `A{1,1}` describes the polynomial that gives the dependence of ${y}_{1}$ on itself. This polynomial is ${A}_{11}=1+0.5{q}^{-1}$, because each factor of ${q}^{-1}$ corresponds to a unit time decrement. Therefore, `A{1,1} = [1 0.5]`, giving the coefficients of ${A}_{11}$ in increasing exponents of ${q}^{-1}$.

Similarly, `A{1,2}` describes the polynomial that gives the dependence of ${y}_{1}$ on ${y}_{2}$. From the equations, ${A}_{12}=0+0.9{q}^{-1}+0.1{q}^{-2}$. Thus, `A{1,2} = [0 0.9 0.1]`.

The remaining entries in `A` are similarly constructed.

Define the cell array containing the coefficients of the `B` polynomials.

```B = cell(2,1); B{1,1} = [1 5 2]; B{2,1} = [0 0 10];```

`B` describes the polynomials that give the dependence of the outputs ${y}_{1}$ and ${y}_{2}$ on the input $u$. From the equations, ${B}_{11}=1+5{q}^{-1}+2{q}^{-2}$. Therefore, `B{1,1} = [1 5 2]`.

Similarly, from the equations, ${B}_{21}=0+0{q}^{-1}+10{q}^{-2}$. Therefore, `B{2,1} = [0 0 10]`.

Define the cell array containing the coefficients of the `C` polynomials.

```C = cell(2,1); C{1,1} = [1 0.01]; C{2,1} = [1 0.1 0.02];```

`C` describes the polynomials that give the dependence of the outputs ${y}_{1}$ and ${y}_{2}$ on the noise terms ${e}_{1}$ and ${e}_{2}$. The entries of `C` can be read from the equations similarly to those of `A` and `B`.

Create an `idpoly` model with the specified coefficients.

`sys = idpoly(A,B,C)`
```sys = Discrete-time ARMAX model: Model for output number 1: A(z)y_1(t) = - A_i(z)y_i(t) + B(z)u(t) + C(z)e_1(t) A(z) = 1 + 0.5 z^-1 A_2(z) = 0.9 z^-1 + 0.1 z^-2 B(z) = 1 + 5 z^-1 + 2 z^-2 C(z) = 1 + 0.01 z^-1 Model for output number 2: A(z)y_2(t) = B(z)u(t) + C(z)e_2(t) A(z) = 1 + 0.05 z^-1 + 0.3 z^-2 B(z) = 10 z^-2 C(z) = 1 + 0.1 z^-1 + 0.02 z^-2 Sample time: unspecified Parameterization: Polynomial orders: na=[1 2;0 2] nb=[3;1] nc=[1;2] nk=[0;2] Number of free coefficients: 12 Use "polydata", "getpvec", "getcov" for parameters and their uncertainties. Status: Created by direct construction or transformation. Not estimated. ```

The display shows all the polynomials and allows you to verify them. The display also states that there are 12 free coefficients. Leading terms of diagonal entries in `A` are always fixed to 1. Leading terms of all other entries in `A` are always fixed to 0.

You can use `sys` to specify an initial parametrization for estimation with such commands as `polyest` or `armax`.

## Input Arguments

`A,B,C,D,F`

Initial values of polynomial coefficients.

For SISO models, specify the initial values of the polynomial coefficients as row vectors. Specify the coefficients in order of:

• Ascending powers of z–1 or q–1 (for discrete-time polynomial models).

• Descending powers of s or p (for continuous-time polynomial models).

The leading coefficients of `A`, `C`, `D`, and `F` must be 1. Use `NaN` for any coefficient whose initial value is not known.

For MIMO models with Ny outputs and Nu inputs, `A`, `B`, `C`, `D`, and `F` are cell arrays of row vectors. Each entry in the cell array contains the coefficients of a particular polynomial that relates input, output, and noise values.

PolynomialDimensionRelation Described
`A`Ny-by-Ny array of row vectors`A{i,j}` contains coefficients of relation between output yi and output yj
`B,F`Ny-by-Nu array of row vectors`B{i,j}` and `F{i,j}`contain coefficients of relations between output yi and input uj
`C,D`Ny-by-1 array of row vectors`C{i}` and `D{i}`contain coefficients of relations between output yi and noise ei

The leading coefficients of the diagonal entries of `A` (`A{i,i},i=1:Ny`) must be 1. The leading coefficients of the off-diagonal entries of `A` must be zero, for causality. The leading coefficients of all entries of `C`, `D`, and `F` , must be 1.

Use `[]` for any polynomial that is not present in the wanted model structure. For example, to create an ARX model, use `[]` for `C`, `D`, and `F`. For an ARMA time series, use `[]` for `B` and `F`.

Default: `B = []`; `C = 1` for all outputs; `D = 1` for all outputs; `F = []`

`Ts`

Sample time. For continuous-time models, `Ts = 0`. For discrete-time models, `Ts` is a positive scalar representing the sample time expressed in the unit specified by the `TimeUnit` property of the model. To denote a discrete-time model with unspecified sample time, set `Ts = -1`.

Default: –1 (discrete-time model with unspecified sample time)

`NoiseVariance`

The variance (covariance matrix) of the model innovations e.

An identified model includes a white, Gaussian noise component e(t). `NoiseVariance` is the variance of this noise component. Typically, a model estimation function (such as `polyest`) determines this variance. Use this input to specify an initial value for the noise variance when you create an `idpoly` model.

For SISO models, `NoiseVariance` is a scalar. For MIMO models, `NoiseVariance` is a Ny-by-Ny matrix, where Ny is the number of outputs in the system.

Default: Ny-by-Ny identity matrix

`sys0`

Dynamic system.

Any dynamic system to be converted into an `idpoly` object.

When `sys0` is an identified model, its estimated parameter covariance is lost during conversion. If you want to translate the estimated parameter covariance during the conversion, use `translatecov`.

For the syntax `sys = idpoly(sys0,'split')`, `sys0` must be a numeric (non-identified) `tf`, `zpk`, or `ss` model object. Also, `sys0` must have at least as many inputs as outputs. Finally, the subsystem `sys0(:,Ny+1:Nu)` must be biproper.

### Name-Value Pair Arguments

Specify optional comma-separated pairs of `Name,Value` arguments. `Name` is the argument name and `Value` is the corresponding value. `Name` must appear inside quotes. You can specify several name and value pair arguments in any order as `Name1,Value1,...,NameN,ValueN`.

Use `Name,Value` arguments to specify additional properties of `idpoly` models during model creation. For example, `idpoly(A,B,C,D,F,1,0,'InputName','Voltage')` creates an `idpoly` model with the `InputName` property set to `Voltage`.

## Properties

`idpoly` object properties include:

`A,B,C,D,F`

Values of polynomial coefficients.

If you create an `idpoly` model `sys` using the `idpoly` command, `sys.A`, `sys.B`, `sys.C`, `sys.D`, and `sys.F` contain the initial coefficient values that you specify with the `A`, `B`, `C`, `D`, and `F` input arguments, respectively.

If you obtain an `idpoly` model by identification, then `sys.A`, `sys.B`, `sys.C`, `sys.D`, and `sys.F` contain the estimated values of the coefficients.

For an `idpoly` model `sys`, each property `sys.A`, `sys.B`, `sys.C`, `sys.D`, and `sys.F` is an alias to the corresponding `Value` entry in the `Structure` property of `sys`. For example, `sys.A` is an alias to the value of the property `sys.Structure.A.Value`.

For SISO polynomial models, the values of the numerator coefficients are stored as a row vector in order of:

• Ascending powers of z–1 or q–1 (for discrete-time transfer functions).

• Descending powers of s or p (for continuous-time transfer functions).

The leading coefficients of `A`, `C`, and `D` are fixed to 1. Any coefficient whose initial value is not known is stored as `NaN`.

For MIMO models with Ny outputs and Nu inputs, `A`, `B`, `C`, `D`, and `F` are cell arrays of row vectors. Each entry in the cell array contains the coefficients of a particular polynomial that relates input, output, and noise values.

PolynomialDimensionRelation Described
`A`Ny-by-Ny array of row vectors`A{i,j}` contains coefficients of relation between output yi and output yj
`B,F`Ny-by-Nu array of row vectors`B{i,j}` and `F{i,j}`contain coefficients of relations between output yi and input uj
`C,D`Ny-by-1 array of row vectors`C{i}` and `D{i}`contain coefficients of relations between output yi and noise ei

The leading coefficients of the diagonal entries of `A` (```A{i,i}, i=1:Ny```) are fixed to 1. The leading coefficients of the off-diagonal entries of `A` are fixed to zero. The leading coefficients of all entries of `C`, `D`, and `F` , are fixed to 1.

For a time series (a model with no measured inputs), ```B = []``` and `F = []`.

Default: `B = []`; `C = 1` for all outputs; `D = 1` for all outputs; `F = []`

`Variable`

Polynomial model display variable, specified as one of the following values:

• `'z^-1'` — Default for discrete-time models

• `'q^-1'` — Equivalent to `'z^-1'`

• `'s'` — Default for continuous-time models

• `'p'` — Equivalent to `'s'`

The value of `Variable` is reflected in the display, and also affects the interpretation of the `A`, `B`, `C`, `D`, and `F` coefficient vectors for discrete-time models. For `Variable = 'z^-1'` or `'q^-1'`, the coefficient vectors are ordered as ascending powers of the variable.

`IODelay`

Transport delays. `IODelay` is a numeric array specifying a separate transport delay for each input/output pair.

If you create an `idpoly` model `sys` using the `idpoly` command, `sys.IODelay` contains the initial values of the transport delay that you specify with a `Name,Value` argument pair.

For an `idpoly` model `sys`, the property `sys.IODelay` is an alias to the value of the property `sys.Structure.IODelay.Value`.

For continuous-time systems, transport delays are expressed in the time unit stored in the `TimeUnit` property. For discrete-time systems, transport delays are expressed as integers denoting delay of a multiple of the sample time `Ts`.

For a MIMO system with `Ny` outputs and `Nu` inputs, set `IODelay` is a `Ny`-by-`Nu` array, where each entry is a numerical value representing the transport delay for the corresponding input/output pair. You can set `IODelay` to a scalar value to apply the same delay to all input/output pairs.

Default: 0 for all input/output pairs

`IntegrateNoise`

Logical vector, denoting presence or absence of integration on noise channels.

Specify `IntegrateNoise` as a logical vector of length equal to the number of outputs.

`IntegrateNoise(i) = true` indicates that the noise channel for the ith output contains an integrator. In this case, the corresponding D polynomial contains an additional term which is not represented in the property `sys.D`. This integrator term is equal to `[1 0]` for continuous-time systems, and equal to `[1 -1]` for discrete-time systems.

Default: 0 for all output channels

`Structure`

Information about the estimable parameters of the `idpoly` model. `sys.Structure.A`, `sys.Structure.B`, `sys.Structure.C`, `sys.Structure.D`, and `sys.Structure.F` contain information about the polynomial coefficients. `sys.Structure.IODelay` contains information about the transport delay. `sys.Structure.IntegrateNoise` contain information about the integration terms on the noise. Each contains the following fields:

• `Value` — Parameter values. For example, `sys.Structure.A.Value` contains the initial or estimated values of the A coefficients.

`NaN` represents unknown parameter values.

For SISO models, each property `sys.A`, `sys.B`, `sys.C`, `sys.D`, `sys.F`, and `sys.IODelay` is an alias to the corresponding `Value` entry in the `Structure` property of `sys`. For example, `sys.A` is an alias to the value of the property `sys.Structure.A.Value`

For MIMO models, `sys.A{i,j}` is an alias to `sys.Structure.A(i,j).Value`, and similarly for the other identifiable coefficient values.

• `Minimum` — Minimum value that the parameter can assume during estimation. For example, ```sys.Structure.IODelay.Minimum = 0.1``` constrains the transport delay to values greater than or equal to 0.1.

`sys.Structure.IODelay.Minimum` must be greater than or equal to zero.

• `Maximum` — Maximum value that the parameter can assume during estimation.

• `Free` — Logical value specifying whether the parameter is a free estimation variable. If you want to fix the value of a parameter during estimation, set the corresponding ```Free = false```. For example, if B is a 3-by-3 matrix, `sys.Structure.B.Free = eyes(3)` fixes all of the off-diagonal entries in B to the values specified in `sys.Structure.B.Value`. In this case, only the diagonal entries in B are estimable.

For fixed values, such as the leading coefficients in `sys.Structure.B.Value`, the corresponding value of `Free` is always `false`.

• `Scale` — Scale of the parameter’s value. `Scale` is not used in estimation.

• `Info` — Structure array for storing parameter units and labels. The structure has `Label` and `Unit` fields.

Specify parameter units and labels as character vectors. For example, `'Time'`.

For a MIMO model with `Ny` outputs and `Nu` inputs, the dimensions of the `Structure` elements are as follows:

• `sys.Structure.A``Ny`-by-`Ny`

• `sys.Structure.B``Ny`-by-`Nu`

• `sys.Structure.C``Ny`-by-`1`

• `sys.Structure.D``Ny`-by-`1`

• `sys.Structure.F``Ny`-by-`Nu`

An inactive polynomial, such as the `B` polynomial in a time-series model, is not available as a parameter in the `Structure` property. For example, `sys = idpoly([1 -0.2 0.5])` creates an AR model. `sys.Structure` contains the fields `sys.Structure.A`, `sys.Structure.IODelay`, and `sys.Structure.IntegrateNoise`. However, there is no field in `sys.Structure` corresponding to `B`, `C`, `D`, or `F`.

`NoiseVariance`

The variance (covariance matrix) of the model innovations e.

An identified model includes a white Gaussian noise component e(t). `NoiseVariance` is the variance of this noise component. Typically, the model estimation function (such as `arx`) determines this variance.

For SISO models, `NoiseVariance` is a scalar. For MIMO models, `NoiseVariance` is a Ny-by-Ny matrix, where Ny is the number of outputs in the system.

`Report`

Summary report that contains information about the estimation options and results when the polynomial model is obtained using estimation commands, such as `polyest`, `armax`, `oe`, and `bj`. Use `Report` to query a model for how it was estimated, including its:

• Estimation method

• Estimation options

• Search termination conditions

• Estimation data fit and other quality metrics

The contents of `Report` are irrelevant if the model was created by construction.

```m = idpoly({[1 0.5]},{[1 5]},{[1 0.01]}); m.Report.OptionsUsed```
```ans = []```

If you obtain the polynomial model using estimation commands, the fields of `Report` contain information on the estimation data, options, and results.

```load iddata2 z2; m = polyest(z2,[2 2 3 3 2 1]); m.Report.OptionsUsed```
```Option set for the polyest command: InitialCondition: 'auto' Focus: 'prediction' EstimateCovariance: 1 Display: 'off' InputOffset: [] OutputOffset: [] Regularization: [1x1 struct] SearchMethod: 'auto' SearchOptions: [1x1 idoptions.search.identsolver] Advanced: [1x1 struct]```

`Report` is a read-only property.

For more information on this property and how to use it, see the Output Arguments section of the corresponding estimation command reference page and Estimation Report.

`InputDelay`

Input delay for each input channel, specified as a scalar value or numeric vector. For continuous-time systems, specify input delays in the time unit stored in the `TimeUnit` property. For discrete-time systems, specify input delays in integer multiples of the sample time `Ts`. For example, ```InputDelay = 3``` means a delay of three sample times.

For a system with `Nu` inputs, set `InputDelay` to an `Nu`-by-1 vector. Each entry of this vector is a numerical value that represents the input delay for the corresponding input channel.

You can also set `InputDelay` to a scalar value to apply the same delay to all channels.

Default: 0

`OutputDelay`

Output delays.

For identified systems, such as `idpoly`, `OutputDelay` is fixed to zero.

`Ts`

Sample time. For continuous-time models, `Ts = 0`. For discrete-time models, `Ts` is a positive scalar representing the sample time expressed in the unit specified by the `TimeUnit` property of the model. To denote a discrete-time model with unspecified sample time, set `Ts = -1`.

Changing this property does not discretize or resample the model. Use `c2d` and `d2c` to convert between continuous- and discrete-time representations. Use `d2d` to change the sample time of a discrete-time system.

Default: –1 (discrete-time model with unspecified sample time)

`TimeUnit`

Units for the time variable, the sample time `Ts`, and any time delays in the model, specified as one of the following values:

• `'nanoseconds'`

• `'microseconds'`

• `'milliseconds'`

• `'seconds'`

• `'minutes'`

• `'hours'`

• `'days'`

• `'weeks'`

• `'months'`

• `'years'`

Changing this property has no effect on other properties, and therefore changes the overall system behavior. Use `chgTimeUnit` to convert between time units without modifying system behavior.

Default: `'seconds'`

`InputName`

Input channel names, specified as one of the following:

• Character vector — For single-input models, for example, `'controls'`.

• Cell array of character vectors — For multi-input models.

Alternatively, use automatic vector expansion to assign input names for multi-input models. For example, if `sys` is a two-input model, enter:

`sys.InputName = 'controls';`

The input names automatically expand to `{'controls(1)';'controls(2)'}`.

When you estimate a model using an `iddata` object, `data`, the software automatically sets `InputName` to `data.InputName`.

You can use the shorthand notation `u` to refer to the `InputName` property. For example, `sys.u` is equivalent to `sys.InputName`.

Input channel names have several uses, including:

• Identifying channels on model display and plots

• Extracting subsystems of MIMO systems

• Specifying connection points when interconnecting models

Default: `''` for all input channels

`InputUnit`

Input channel units, specified as one of the following:

• Character vector — For single-input models, for example, `'seconds'`.

• Cell array of character vectors — For multi-input models.

Use `InputUnit` to keep track of input signal units. `InputUnit` has no effect on system behavior.

Default: `''` for all input channels

`InputGroup`

Input channel groups. The `InputGroup` property lets you assign the input channels of MIMO systems into groups and refer to each group by name. Specify input groups as a structure. In this structure, field names are the group names, and field values are the input channels belonging to each group. For example:

```sys.InputGroup.controls = [1 2]; sys.InputGroup.noise = [3 5];```

creates input groups named `controls` and `noise` that include input channels 1, 2 and 3, 5, respectively. You can then extract the subsystem from the `controls` inputs to all outputs using:

`sys(:,'controls')`

Default: Struct with no fields

`OutputName`

Output channel names, specified as one of the following:

• Character vector — For single-output models. For example, `'measurements'`.

• Cell array of character vectors — For multi-output models.

Alternatively, use automatic vector expansion to assign output names for multi-output models. For example, if `sys` is a two-output model, enter:

`sys.OutputName = 'measurements';`

The output names automatically expand to `{'measurements(1)';'measurements(2)'}`.

When you estimate a model using an `iddata` object, `data`, the software automatically sets `OutputName` to `data.OutputName`.

You can use the shorthand notation `y` to refer to the `OutputName` property. For example, `sys.y` is equivalent to `sys.OutputName`.

Output channel names have several uses, including:

• Identifying channels on model display and plots

• Extracting subsystems of MIMO systems

• Specifying connection points when interconnecting models

Default: `''` for all output channels

`OutputUnit`

Output channel units, specified as one of the following:

• Character vector — For single-output models. For example, `'seconds'`.

• Cell array of character vectors — For multi-output models.

Use `OutputUnit` to keep track of output signal units. `OutputUnit` has no effect on system behavior.

Default: `''` for all output channels

`OutputGroup`

Output channel groups. The `OutputGroup` property lets you assign the output channels of MIMO systems into groups and refer to each group by name. Specify output groups as a structure. In this structure, field names are the group names, and field values are the output channels belonging to each group. For example:

```sys.OutputGroup.temperature = ; sys.InputGroup.measurement = [3 5];```

creates output groups named `temperature` and `measurement` that include output channels 1, and 3, 5, respectively. You can then extract the subsystem from all inputs to the `measurement` outputs using:

`sys('measurement',:)`

Default: Struct with no fields

`Name`

System name, specified as a character vector. For example, `'system_1'`.

Default: `''`

`Notes`

Any text that you want to associate with the system, stored as a string or a cell array of character vectors. The property stores whichever data type you provide. For instance, if `sys1` and `sys2` are dynamic system models, you can set their `Notes` properties as follows:

```sys1.Notes = "sys1 has a string."; sys2.Notes = 'sys2 has a character vector.'; sys1.Notes sys2.Notes```
```ans = "sys1 has a string." ans = 'sys2 has a character vector.' ```

Default: `[0×1 string]`

`UserData`

Any type of data you want to associate with system, specified as any MATLAB® data type.

Default: `[]`

`SamplingGrid`

Sampling grid for model arrays, specified as a data structure.

For arrays of identified linear (IDLTI) models that are derived by sampling one or more independent variables, this property tracks the variable values associated with each model. This information appears when you display or plot the model array. Use this information to trace results back to the independent variables.

Set the field names of the data structure to the names of the sampling variables. Set the field values to the sampled variable values associated with each model in the array. All sampling variables should be numeric and scalar valued, and all arrays of sampled values should match the dimensions of the model array.

For example, if you collect data at various operating points of a system, you can identify a model for each operating point separately and then stack the results together into a single system array. You can tag the individual models in the array with information regarding the operating point:

```nominal_engine_rpm = [1000 5000 10000]; sys.SamplingGrid = struct('rpm', nominal_engine_rpm)```

where `sys` is an array containing three identified models obtained at rpms 1000, 5000 and 10000, respectively.

For model arrays generated by linearizing a Simulink® model at multiple parameter values or operating points, the software populates `SamplingGrid` automatically with the variable values that correspond to each entry in the array. For example, the Simulink Control Design™ commands `linearize` and `slLinearizer` populate `SamplingGrid` in this way.

Default: `[]`

## Tips

• Although `idpoly` supports continuous-time models, `idtf` and `idproc` enable more choices for estimation of continuous-time models. Therefore, for some continuous-time applications, these model types are preferable.

#### Introduced before R2006a

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