# tunableTF

Tunable transfer function with fixed number of poles and zeros

## Syntax

blk = tunableTF(name,Nz,Np)
blk = tunableTF(name,Nz,Np,Ts)
blk = tunableTF(name,sys)

## Description

Model object for creating tunable SISO transfer function models of fixed order. tunableTF lets you parameterize a transfer function of a given order for parameter studies or for automatic tuning with tuning commands such as systune or looptune.

tunableTF is part of the Control Design Block family of parametric models. Other Control Design Blocks include tunablePID, tunableSS, and tunableGain.

## Construction

blk = tunableTF(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 = tunableTF(name,Nz,Np,Ts) creates a discrete-time parametric transfer function with sample time Ts.

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

### Input Arguments

 name Parametric transfer function Name, specified as a character vector such as 'filt' or 'DM'. (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 sample time. sys tf model providing number of poles, number of zeros, sample time, and initial values of the parameters of blk.

## Properties

Numerator, Denominator

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

blk.Numerator and blk.Denominator are param.Continuous objects. For general information about the properties of these param.Continuous objects, see the param.Continuous (Simulink Design Optimization) object reference page.

The following fields of blk.Numerator and blk.Denominator are used when you tune blk using hinfstruct:

FieldDescription
Value

Array of current values of the numerator am, ..., a0 or the denominator coefficients 1,bn–1, ..., b0. blk.Numerator.Value has length Nz + 1. blk.Denominator.Value has length Np + 1. The leading coefficient of the denominator (blk.Denominator.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 (Robust Control Toolbox) tunes all values except those whose Free field is zero.

Free

Array of logical values determining whether the coefficients are fixed or tunable. For example:

• If blk.Numerator.Free(j) = 1, then blk.Numerator.Value(j) is tunable.

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

Default: blk.Denominator.Free(1) = 0; all other entries are 1.

Minimum

Minimum value of the parameter. This property places a lower bound on the tuned value of the parameter. For example, setting blk.Numerator.Minimum(1) = 0 ensures that the leading coefficient of the numerator remains positive.

Default: -Inf

Maximum

Maximum value of the parameter. This property places an upper bound on the tuned value of the parameter. For example, setting blk.Numerator.Maximum(1) = 1 ensures that the leading coefficient of the numerator does not exceed 1.

Default: Inf

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.

Default: 0 (continuous 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)'}.

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)'}.

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 = [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, 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: []

## 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 parameterized transfer function has at least one integrator regardless of the parameter values, fix the lowest-order coefficient of the denominator to zero.

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

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

blk = tunableTF('tfblock',2,3);
blk.OutputName = {'control'};    % assign output name

## Tips

• To convert a tunableTF parametric model to a numeric (non-tunable) model object, use model commands such as tf, zpk, or ss.

## Compatibility Considerations

expand all

Behavior changed in R2016a

| | | | | | | (Robust Control Toolbox)

### Topics

Introduced in R2016a