# idtf

Transfer function model with identifiable parameters

## Syntax

• `sys = idtf(num,den)`
• `sys = idtf(num,den,Ts)`
• `sys = idtf(___,Name,Value)`
• `sys = idtf(sys0)`

## Description

````sys = idtf(num,den)` creates a continuous-time transfer function with identifiable parameters (an `idtf` model). `num` specifies the current values of the transfer function numerator coefficients. `den` specifies the current values of the transfer function denominator coefficients.```
````sys = idtf(num,den,Ts)` creates a discrete-time transfer function with identifiable parameters. `Ts` is the sample time. ```
````sys = idtf(___,Name,Value)` creates a transfer function with properties specified by one or more `Name,Value` pair arguments.```
````sys = idtf(sys0)` converts any dynamic system model, `sys0`, to `idtf` model form.```

## Object Description

An `idtf` model represents a system as a continuous-time or discrete-time transfer function with identifiable (estimable) coefficients.

A SISO transfer function is a ratio of polynomials with an exponential term. In continuous time,

$G\left(s\right)={e}^{-\tau s}\frac{{b}_{n}{s}^{n}+{b}_{n-1}{s}^{n-1}+...+{b}_{0}}{{s}^{m}+{a}_{m-1}{s}^{m-1}+...+{a}_{0}}.$

In discrete time,

$G\left({z}^{-1}\right)={z}^{-k}\frac{{b}_{n}{z}^{-n}+{b}_{n-1}{z}^{-n+1}+...+{b}_{0}}{{z}^{-m}+{a}_{m-1}{z}^{-m+1}+...+{a}_{0}}.$

In discrete time, zk represents a time delay of kTs, where Ts is the sample time.

For `idtf` models, the denominator coefficients a0,...,am–1 and the numerator coefficients b0,...,bn can be estimable parameters. (The leading denominator coefficient is always fixed to 1.) The time delay τ (or kin discrete time) can also be an estimable parameter. The `idtf` model stores the polynomial coefficients a0,...,am–1 and b0,...,bn in the `den` and `num` properties of the model, respectively. The time delay τ or k is stored in the `ioDelay` property of the model.

A MIMO transfer function contains a SISO transfer function corresponding to each input-output pair in the system. For `idtf` models, the polynomial coefficients and transport delays of each input-output pair are independently estimable parameters.

There are three ways to obtain an `idtf` model.

• Estimate the `idtf` model based on input-output measurements of a system, using `tfest`. The `tfest` command estimates the values of the transfer function coefficients and transport delays. The estimated values are stored in the `num`, `den`, and `ioDelay` properties of the resulting `idtf` 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 `idtf` model by estimation, you can extract estimated coefficients and their uncertainties from the model. To do so, use commands such as `tfdata`, `getpar`, or `getcov`.

• Create an `idtf` model using the `idtf` command.

You can create an `idtf` model to configure an initial parameterization for estimation of a transfer function to fit measured response data. When you do so, you can specify constraints on such values as the numerator and denominator coefficients and transport delays. For example, you can fix the values of some parameters, or specify minimum or maximum values for the free parameters. You can then use the configured model as an input argument to `tfest` to estimate parameter values with those constraints.

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

 Note:   Unlike `idss` and `idpoly`, `idtf` uses a trivial noise model and does not parameterize the noise.So, H = 1 in $y=Gu+He$.

## Examples

collapse all

### Continuous-Time Transfer Function

Specify a continuous-time, single-input, single-output (SISO) transfer function with estimable parameters. The initial values of the transfer function are:

$G\left(s\right)=\frac{s+4}{{s}^{2}+20s+5}$

```num = [1 4]; den = [1 20 5]; G = idtf(num,den);```

`G` is an `idtf` model. `num` and `den` specify the initial values of the numerator and denominator polynomial coefficients in descending powers of s. The numerator coefficients having initial values 1 and 4 are estimable parameters. The denominator coefficient having initial values 20 and 5 are also estimable parameters. The leading denominator coefficient is always fixed to 1.

You can use `G` to specify an initial parametrization for estimation with `tfest`.

### Transfer Function with Known Input Delay and Specified Attributes

Specify a continuous-time, SISO transfer function with known input delay. The transfer function initial values are given by:

$G\left(s\right)={e}^{-5.8s}\frac{5}{s+5}$

Label the input of the transfer function with the name `'Voltage'` and specify the input units as `volt`.

Use `Name,Value` input pairs to specify the delay, input name, and input unit.

```num = 5; den = [1 5]; input_delay = 5.8; input_name = 'Voltage'; input_unit = 'volt'; G = idtf(num,den,'InputDelay',input_delay,... 'InputName',input_name,'InputUnit',input_unit);```

G is an `idtf` model. You can use `G` to specify an initial parametrization for estimation with `tfest`. If you do so, model properties such as `InputDelay`, `InputName`, and `InputUnit` are applied to the estimated model. The estimation process treats `InputDelay` as a fixed value. If you want to estimate the delay and specify an initial value of 5.8 s, use the `ioDelay` property instead.

### Discrete-Time Transfer Function

Specify a discrete-time SISO transfer function with estimable parameters. The initial values of the transfer function are:

$H\left(z\right)=\frac{z-0.1}{z+0.8}$

Specify the sample time as 0.2 seconds.

```num = [1 -0.1]; den = [1 0.8]; Ts = 0.2 H = idtf(num,den,Ts);```

`num` and `den` are the initial values of the numerator and denominator polynomial coefficients. For discrete-time systems, specify the coefficients in ascending powers of z–1.

`Ts` specifies the sample time for the transfer function as 0.2 seconds.

`H` is an `idtf` model. The numerator and denominator coefficients are estimable parameters (except for the leading denominator coefficient, which is fixed to 1).

### MIMO Discrete-Time Transfer Function

Specify a discrete-time, two-input, two-output transfer function. The initial values of the MIMO transfer function are:

$H\left(z\right)=\left[\begin{array}{cc}\frac{1}{z+0.2}& \frac{z}{z+0.7}\\ \frac{-z+2}{z-0.3}& \frac{3}{z+0.3}\end{array}\right]$

Specify the sample time as 0.2 seconds.

```nums = {1,[1,0];[-1,2],3}; dens = {[1,0.2],[1,0.7];[1,-0.3],[1,0.3]}; Ts = 0.2 H = idtf(nums,dens,Ts);```

`nums` and `dens` specify the initial values of the coefficients in cell arrays. Each entry in the cell array corresponds to the numerator or denominator of the transfer function of one input-output pair. For example, the first row of `nums` is `{1,[1,0]}`. This cell array specifies the numerators across the first row of transfer functions in `H`. Likewise, the first row of `dens`, `{[1,0.2],[1,0.7]}`, specifies the denominators across the first row of `H`.

`Ts` specifies the sample time for the transfer function as 0.2 seconds.

`H` is an `idtf` model. All of the polynomial coefficients are estimable parameters, except for the leading coefficient of each denominator polynomial. These coefficients are always fixed to 1.

### Specify q^-1 as Transfer Function Variable

Specify the following discrete-time transfer function in terms of `q^-1`:

$H\left({q}^{-1}\right)=\frac{1+.4{q}^{-1}}{1+.1{q}^{-1}-.3{q}^{-2}}$

Specify the sample time as 0.1 seconds.

```num = [1 .4]; den = [1 .1 -.3]; Ts = 0.1; convention_variable = 'q^-1'; H = idtf(num,den,Ts,'Variable',convention_variable); ```

Use a `Name,Value` pair argument to specify the variable `q^-1`.

`num` and `den` are the numerator and denominator polynomial coefficients in ascending powers of q–1.

`Ts` specifies the sample time for the transfer function as 0.1 seconds.

`H` is an `idtf` model.

### Gain Matrix Transfer Function

Specify a transfer function with estimable coefficients whose initial value is the static gain matrix:

$H\left(s\right)=\left[\begin{array}{ccc}1& 0& 1\\ 1& 1& 0\\ 3& 0& 2\end{array}\right]$

```M = [1 0 1; 1 1 0; 3 0 2]; H = idtf(M);```

`H` is an `idtf` model that describes a three input (`Nu=3`), three output (`Ny=3`) transfer function. Each input/output channel is an estimable static gain. The initial values of the gains are given by the values in the matrix `M`.

### Convert Identifiable State-Space Model to Identifiable Transfer Function

Convert a state-space model with identifiable parameters to a transfer function with identifiable parameters.

Convert the following identifiable state-space model to an identifiable transfer function.

$\begin{array}{l}\stackrel{˜}{x}\left(t\right)=\left[\begin{array}{cc}-0.2& 0\\ 0& -0.3\end{array}\right]x\left(t\right)+\left[\begin{array}{c}-2\\ 4\end{array}\right]u\left(t\right)+\left[\begin{array}{c}.1\\ .2\end{array}\right]e\left(t\right)\\ y\left(t\right)=\left[\begin{array}{cc}1& 1\end{array}\right]x\left(t\right)\end{array}$

```A = [-0.2, 0; 0, -0.3]; B = [2;4]; C=[1, 1]; D = 0; K = [.1; .2]; sys0 = idss(A,B,C,D,K,'NoiseVariance',0.1); sys = idtf(sys0);```

`A`,`B`,`C`,`D` and `K` are matrices that specify `sys0`, an identifiable state-space model with a noise variance of 0.1.

`sys = idtf(sys0)` creates an `idtf` model, `sys`.

### Obtain a Transfer Function by Estimation

Identify a transfer function containing a specified number of poles for given data.

Load time-domain system response data and use it to estimate a transfer function for the system.

```load iddata1 z1; np = 2; sys = tfest(z1,np);```

`z1` is an `iddata` object that contains time-domain, input-output data.

`np` specifies the number of poles in the estimated transfer function.

`sys` is an `idtf` model containing the estimated transfer function.

To see the numerator and denominator coefficients of the resulting estimated model `sys`, enter:

```sys.num sys.den```

To view the uncertainty in the estimates of the numerator and denominator and other information, use `tfdata`.

### Obtain a Transfer Function with Prior Knowledge of Model Structure and Constraints

Identify a transfer function for given data by providing its expected structure and coefficient constraints

```load iddata1 z1; z1.y = cumsum(z1.y); ```

`cumsum` integrates the output data of `z1`. The estimated transfer function should therefore contain an integrator.

Create a transfer function model with the expected structure.

`init_sys = idtf([100 1500],[1 10 10 0]);`

`int_sys` is an `idtf` model with three poles and one zero. The denominator coefficient for the `s^0` term is zero. Therefore, `int_sys` contains an integrator.

Specify constraints on the numerator and denominator coefficients of the transfer function model. To do so, configure fields in the `Structure` property:

```init_sys.Structure.num.Minimum = eps; init_sys.Structure.den.Minimum = eps; init_sys.Structure.den.Free(end) = false;```

The constraints specify that the numerator and denominator coefficients are nonnegative. Additionally, the last element of the denominator coefficients (associated with the `s^0` term) is not an estimable parameter. This constraint forces one of the estimated poles to be at `s = 0`.

Create an estimation option set that specifies using the Levenberg–Marquardt search method.

`opt = tfestOptions('SearchMethod', 'lm');`

Estimate a transfer function for `z1` using `init_sys` and the estimation option set.

`sys = tfest(z1,init_sys,opt);`

`tfest` uses the coefficients of `init_sys` to initialize the estimation of `sys`. Additionally, the estimation is constrained by the constraints you specify in the `Structure` property of `init_sys`. The resulting `idtf` model `sys` contains the parameter values that result from the estimation.

### Array of Transfer Function Models

Create an array of transfer function models with identifiable coefficients. Each transfer function in the array is of the form:

$H\left(s\right)=\frac{a}{s+a}.$

The initial value of the coefficient a varies across the array, from 0.1 to 1.0, in increments of 0.1.

```H = idtf(zeros(1,1,10)); for k = 1:10 num = k/10; den = [1 k/10]; H(:,:,k) = idtf(num,den); end```

The first command preallocates a one-dimensional, 10-element array, `H`, and fills it with empty `idtf` models.

The first two dimensions of a model array are the output and input dimensions. The remaining dimensions are the array dimensions. `H(:,:,k)` represents the `k`th model in the array. Thus, the `for` loop replaces the `k`th entry in the array with a transfer function whose coefficients are initialized with a = k/10.

## Input Arguments

 `num` Initial values of transfer function numerator coefficients. For SISO transfer functions, specify the initial values of the numerator coefficients `num` as a row vector. Specify the coefficients in order of: Descending powers of s or p (for continuous-time transfer functions)Ascending powers of z–1 or q–1 (for discrete-time transfer functions) Use `NaN` for any coefficient whose initial value is not known. For MIMO transfer functions with `Ny` outputs and `Nu` inputs, `num` is a `Ny`-by-`Nu` cell array of numerator coefficients for each input/output pair. `den` Initial values of transfer function denominator coefficients. For SISO transfer functions, specify the initial values of the denominator coefficients `den` as a row vector. Specify the coefficients in order of: Descending powers of s or p (for continuous-time transfer functions)Ascending powers of z–1 or q–1 (for discrete-time transfer functions) The leading coefficient in `den` must be 1. Use `NaN` for any coefficient whose initial value is not known. For MIMO transfer functions with `Ny` outputs and `Nu` inputs, `den` is a `Ny`-by-`Nu` cell array of denominator coefficients for each input/output pair. `Ts` Sample time. For continuous-time models, `Ts = 0`. For discrete-time models, `Ts` is a positive scalar representing the sampling period. This value is 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: `0` (continuous time) `sys0` Dynamic system. Any dynamic system to convert to an `idtf` model. 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`.

### 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 single 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 `idtf` models during model creation. For example, `idtf(num,den,'InputName','Voltage')` creates an `idtf` model with the `InputName` property set to `Voltage`.

## Properties

`idtf` object properties include:

 `num` Values of transfer function numerator coefficients. If you create an `idtf` model `sys` using the `idtf` command, `sys.num` contains the initial values of numerator coefficients that you specify with the `num` input argument. If you obtain an `idtf` model by identification using `tfest`, then `sys.num` contains the estimated values of the numerator coefficients. For an `idtf` model `sys`, the property `sys.num` is an alias for the value of the property `sys.Structure.num.Value`. For SISO transfer functions, the values of the numerator coefficients are stored as a row vector in order of: Descending powers of s or p (for continuous-time transfer functions)Ascending powers of z–1 or q–1 (for discrete-time transfer functions) Any coefficient whose initial value is not known is stored as `NaN`. For MIMO transfer functions with `Ny` outputs and `Nu` inputs, `num` is a `Ny`-by-`Nu` cell array of numerator coefficients for each input/output pair. `den` Values of transfer function denominator coefficients. If you create an `idtf` model `sys` using the `idtf` command, `sys.den` contains the initial values of denominator coefficients that you specify with the `den` input argument. If you obtain an `idtf` model `sys` by identification using `tfest`, then `sys.den` contains the estimated values of the denominator coefficients. For an `idtf` model `sys`, the property `sys.den` is an alias for the value of the property `sys.Structure.den.Value`. For SISO transfer functions, the values of the denominator coefficients are stored as a row vector in order of: Descending powers of s or p (for continuous-time transfer functions)Ascending powers of z–1 or q–1 (for discrete-time transfer functions) The leading coefficient in `den` is fixed to 1. Any coefficient whose initial value is not known is stored as `NaN`. For MIMO transfer functions with `Ny` outputs and `Nu` inputs, `den` is a `Ny`-by-`Nu` cell array of denominator coefficients for each input/output pair. `Variable` String specifying the transfer function display variable. `Variable` requires one of the following values:`'s'` — Default for continuous-time models`'p'` — Equivalent to `'s'``'z^-1'` — Default for discrete-time models`'q^-1'` — Equivalent to `'z^-1'` The value of `Variable` is reflected in the display, and also affects the interpretation of the `num` and `den` 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 `idtf` model `sys` using the `idtf` command, `sys.ioDelay` contains the initial values of the transport delay that you specify with a `Name,Value` argument pair. If you obtain an `idtf` model `sys` by identification using `tfest`, then `sys.ioDelay` contains the estimated values of the transport delay. For an `idtf` model `sys`, the property `sys.ioDelay` is an alias for 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, specify transport 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` as a `Ny`-by-`Nu` array. Each entry of this array 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 `Structure` Information about the estimable parameters of the `idtf` model. `Structure.num`, `Structure.den`, and `Structure.ioDelay` contain information about the numerator coefficients, denominator coefficients, and transport delay, respectively. Each contains the following fields: `Value` — Parameter values. For example, `sys.Structure.num.Value` contains the initial or estimated values of the numerator coefficients. `NaN` represents unknown parameter values. For denominators, the value of the leading coefficient, specified by `sys.Structure.den.Value(1)` is fixed to 1.For SISO models, `sys.num`, `sys.den`, and `sys.ioDelay` are aliases for `sys.Structure.num.Value`, `sys.Structure.den.Value`, and `sys.Structure.ioDelay.Value`, respectively.For MIMO models, `sys.num{i,j}` is an alias for `sys.Structure(i,j).num.Value`, and `sys.den{i,j}` is an alias for `sys.Structure(i,j).den.Value`. Additionally, `sys.ioDelay(i,j)` is an alias for `sys.Structure(i,j).ioDelay.Value``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` — Boolean 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, ```sys.Structure.den.Free = false``` fixes all of the denominator coefficients in `sys` to the values specified in `sys.Structure.den.Value`.For denominators, the value of `Free` for the leading coefficient, specified by `sys.Structure.den.Free(1)`, is always `false` (the leading denominator coefficient is always fixed to 1).`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.Use these fields for your convenience, to store strings that describe parameter units and labels. For a MIMO model with `Ny` outputs and `Nu` input, `Structure` is an `Ny`-by-`Nu` array. The element `Structure(i,j)` contains information corresponding to the transfer function for the `(i,j)` input-output pair. `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 `tfest`) 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` Information about the estimation process. `Report` contains the following fields: `InitMethod` — Method used to initialize model coefficients before iterative prediction error minimization`N4Weight` — Subspace algorithm option value used by `n4sid`estimator (see `n4sidOptions`)`N4Horizon` — Forward and backward prediction horizons used by `n4sid` (see `n4sidOptions`)`InitialCondition` — Whether estimation estimated initial conditions or fixed them at zero`Fit` — Quantitative quality assessment of estimation, including percent fit to data and final prediction error`Parameters` — Estimated values of model parameters and their covariance`OptionsUsed` — Options used during estimation (see `tfestOptions`)`RandState` — Random number stream state at start of estimation`Status` — Whether model was obtained by construction, estimated, or modified after estimation`Method` — Name of estimation method used`DataUsed` — Attributes of data used for estimation, such as name and sample time`Termination` — Termination conditions for the iterative search scheme used for prediction error minimization, such as final cost value or stopping criterion `InputDelay` Input delays. `InputDelay` is a numeric vector specifying a time delay for each input channel. 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 representing 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. Estimation treats `InputDelay` as a fixed constant of the model. Estimation uses the `ioDelay` property for estimating time delays. To specify initial values and constraints for estimation of time delays, use `sys.Structure.ioDelay`. Default: `0` for all input channels `OutputDelay` Output delays. For identified systems, like `idtf`, `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 sampling period. This value is 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: `0` (continuous time) `TimeUnit` String representing the unit of the time variable. This property specifies the units for the time variable, the sample time `Ts`, and any time delays in the model. Use any 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. Set `InputName` to a string for single-input model. For a multi-input model, set `InputName` to a cell array of strings. 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 plotsExtracting subsystems of MIMO systemsSpecifying connection points when interconnecting models Default: Empty string `''` for all input channels `InputUnit` Input channel units. Use `InputUnit` to keep track of input signal units. For a single-input model, set `InputUnit` to a string. For a multi-input model, set `InputUnit` to a cell array of strings. `InputUnit` has no effect on system behavior. Default: Empty string `''` 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. Set `OutputName` to a string for single-output model. For a multi-output model, set `OutputName` to a cell array of strings. 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 plotsExtracting subsystems of MIMO systemsSpecifying connection points when interconnecting models Default: Empty string `''` for all output channels `OutputUnit` Output channel units. Use `OutputUnit` to keep track of output signal units. For a single-output model, set `OutputUnit` to a string. For a multi-output model, set `OutputUnit` to a cell array of strings. `OutputUnit` has no effect on system behavior. Default: Empty string `''` 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 = [1]; 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. Set `Name` to a string to label the system. Default: `''` `Notes` Any text that you want to associate with the system. Set `Notes` to a string or a cell array of strings. Default: `{}` `UserData` Any type of data you wish to associate with system. Set `UserData` to 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: `[]`