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# ltiblock.tf

Tunable transfer function with fixed number of poles and zeros

## Syntax

blk = ltiblock.tf(name,Nz,Np)
blk = ltiblock.tf(name,Nz,Np,Ts)
blk = ltiblock.tf(name,sys)

## Description

Model object for creating tunable SISO transfer function models of fixed order. ltiblock.tf lets you parametrize a transfer function of a given orderfor parameter studies or for automatic tuning with Robust Control Toolbox™ tuning commands such as systune or looptune.

ltiblock.tf is part of the Control Design Block family of parametric models. Other Control Design Blocks includeltiblock.pid, ltiblock.ss, and ltiblock.gain.

## Construction

blk = ltiblock.tf(name,Nz,Np) creates the parametric SISO transfer function:

$blk=\frac{{a}_{m}{s}^{m}+{a}_{m-1}{s}^{m-1}+\dots +{a}_{1}s+{a}_{0}}{{s}^{n}+{b}_{n-1}{s}^{n-1}+\dots +{b}_{1}s+{b}_{0}}.$

n = Np is the maximum number of poles of blk, and m = Nz is the maximum number of zeros. The tunable parameters are the numerator and denominator coefficients a0, ..., am and b0, ..., bn–1. The leading coefficient of the denominator is fixed to 1.

blk = ltiblock.tf(name,Nz,Np,Ts) creates a discrete-time parametric transfer function with sampling time Ts.

blk = ltiblock.tf(name,sys) uses the tf model sys to set the number of poles, number of zeros, sampling time, and initial parameter values.

### Input Arguments

 name String specifying the Name of the parametric transfer function blk. (See Properties.) Nz Nonnegative integer specifying the number of zeros of the parametric transfer function blk. Np Nonnegative integer specifying the number of poles of the parametric transfer function blk. Ts Scalar sampling time. sys tf model providing number of poles, number of zeros, sampling time, and initial values of the parameters of blk.

## Properties

num, den

Parametrization of the numerator coefficients am, ..., a0 and the denominator coefficients 1,bn–1, ..., b0 of the tunable transfer function blk.

blk.num and blk.den are param.Continuous objects. For general information about the properties of these param.Continuous objects, see the param.Continuousparam.Continuous object reference page.

The following fields of blk.num and blk.den are used when you tune blk using hinfstruct:

FieldDescription
ValueArray of current values of the numerator am, ..., a0 or the denominator coefficients 1,bn–1, ..., b0. blk.num.Value has length Nz + 1. blk.den.Value has length Np + 1. The leading coefficient of the denominator (blk.den.Value(1)) is always fixed to 1.
By default, the coefficients initialize to values that yield a stable, strictly proper transfer function. Use the input sys to initialize the coefficients to different values.
hinfstruct tunes all values except those whose Free field is zero.
FreeArray of logical values determining whether the coefficients are fixed or tunable. For example,
• If blk.num.Free(j) = 1, then blk.num.Value(j) is tunable.

• If blk.num.Free(j) = 0, then blk.num.Value(j) is fixed.

Default: blk.den.Free(1) = 0; all other entries are 1.
MinimumMinimum value of the parameter. This property places a lower bound on the tuned value of the parameter. For example, setting blk.num.Minimum(1) = 0 ensures that the leading coefficient of the numerator remains positive.
Default: -Inf.
MaximumMaximum value of the parameter. This property places an upper bound on the tuned value of the parameter. For example, setting blk.num.Maximum(1) = 1 ensures that the leading coefficient of the numerator does not exceed 1.
Default: Inf.

Ts

Sampling 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 sampling 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 sampling 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 sampling 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)'}.

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: 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 to automatically expand to {'measurements(1)';'measurements(2)'}.

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: Empty string '' for all input 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 input 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: []

## Examples

Create a parametric SISO transfer function with two zeros, four poles, and at least one integrator.

A transfer function with an integrator includes a factor of 1/s. Therefore, to ensure that a parametrized transfer function has at least one integrator regardless of the parameter values, fix the lowest-order coeffiecient of the denominator to zero.

```  blk = ltiblock.tf('tfblock',2,4);  % two zeros, four poles
blk.den.Value(end) = 0;   % set last denominator entry to zero
blk.den.Free(end) = 0;    % fix it to zero```

Create a parametric transfer function, and assign names to the input and output.

```blk = ltiblock.tf('tfblock',2,3);