Tunable Generalized LTI models represent systems having both fixed and tunable (or parametric) coefficients.

You can use tunable Generalized LTI models to:

Model a tunable (or parametric) component of a control system, such as a tunable low-pass filter.

Model a control system that contains both:

Fixed components, such as plant dynamics and sensor dynamics

Tunable components, such as filters and compensators

You can use tunable Generalized LTI models for parameter studies.
For an example, see Study Parameter Variation by Sampling Tunable Model.
You can also use tunable Generalized LTI models for tuning fixed control
structures using tuning commands such as `systune`

or
the Control System Tuner app. See Multiloop, Multiobjective Tuning.

Control System Toolbox™ includes tunable components with predefined structure called Control Design Blocks. You can use tunable Control Design Blocks to model any tunable component that fits one of the predefined structures.

To create tunable components with a specific custom structure that is not covered by the Control Design Blocks:

Use the tunable real parameter

`realp`

or the generalized matrix`genmat`

to represent the tunable coefficients of your component.Use the resulting

`realp`

or`genmat`

objects as inputs to`tf`

or`ss`

to model the component. The result is a generalized state-space (`genss`

) model of the component.

For examples of creating such custom tunable components, see:

To construct a tunable Generalized LTI model representing a control system with both fixed and tunable components:

Model the nontunable components of your system using numeric LTI models.

Model each tunable component using Control Design Blocks or expressions involving such blocks. See Modeling Tunable Components.

Use model interconnection commands such as

`series`

,`parallel`

or`connect`

, or the arithmetic operators`+`

,`-`

,`*`

,`/`

,`\`

, and`^`

, to combine all the components of your system.

The resulting model is:

A

`genss`

model, if none of the nontunable components is a frequency response data model (for example,`frd`

)A

`genfrd`

model, if the nontunable component is a`frd`

model

For an example of constructing a `genss`

model
of a control system with both fixed and tunable components, see Control System with Tunable Components.

A Generalized model separately stores the numeric and parametric
portions of the model by structuring the model in *Standard
Form*, as shown in the following illustration.

*w* and *z* represent the
inputs and outputs of the Generalized model.

*H* represents all portions of the Generalized
model that have fixed (non-parametric) coefficients. *H* is:

A state-space (

`ss`

) model, for`genss`

modelsA frequency response data (

`frd`

) model, for`genfrd`

modelsA matrix, for

`genmat`

models

*B* represents the parametric components of
the Generalized model, which are the Control Design Blocks *B*_{1}, . . . , *B _{N}*. The

`Blocks`

property
of the Generalized model stores a list of the names of these blocks.
If the Generalized model has blocks that occur multiple times in `Blocks`

property.To access the internal representation of a Generalized model,
including `H`

and `B`

, use the `getLFTModel`

command.

This Standard Form can represent any control structure. To understand why, consider the control structure as an aggregation of fixed-coefficient elements interacting with the parametric elements:

To rewrite this in Standard Form, define

$$\begin{array}{l}u:=\left[{u}_{1},\dots ,{u}_{N}\right]\\ y:=\left[{y}_{1},\dots ,{y}_{N}\right],\end{array}$$

and group the tunable control elements *B*_{1}, . . . , *B _{N}* into the
block-diagonal configuration

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