# Model Reducer

Reduce complexity of linear time-invariant (LTI) models

## Description

The Model Reducer app lets you compute reduced-order approximations of high-order models. Working with lower-order models can simplify analysis and control design. Simpler models are also easier to understand and manipulate. You can reduce a plant model to focus on relevant dynamics before designing a controller for the plant. Or, you can use model reduction to simplify a full-order controller.

Using any of the following methods, Model Reducer helps you reduce model order while preserving model characteristics that are important to your application:

• Balanced Truncation — Remove states with relatively small energy contributions.

• Mode Selection — Select modes by specifying a frequency range of interest.

• Pole-Zero Simplification — Eliminate canceling or near-canceling pole-zero pairs.

Model Reducer provides response plots and error plots to help ensure that the reduced-order model preserves important dynamics. For more information on model reduction and why it is useful, see Model Reduction Basics.

For an alternative to the Model Reducer app that lets you interactively perform model reduction and generate code for a live script, see the Reduce Model Order task in the Live Editor.

## Open the Model Reducer App

• MATLAB® Toolstrip: On the Apps tab, under Control System Design and Analysis, click the app icon.

• MATLAB command prompt: Enter `modelReducer`.

## Parameters

Balanced Truncation Tab

Specify the model you want to reduce by selecting from the Model drop-down list. The list includes all models currently in the Data Browser. To get a model from the MATLAB workspace into the Data Browser, on the Model Reducer tab, click Import Model. You can import any:

• `tf`, `ss`, or `zpk` model that is proper. The model can be SISO or MIMO, and continuous or discrete.

• Continuous-time models must not have time delays. To reduce a continuous-time model with time delays, first use `pade` to approximate the time delays as model dynamics.

• Discrete-time models can have time delays. For the Balanced Truncation reduction method, the app uses `absorbDelay` to convert the delay into poles at z = 0 before reducing the model. The additional states are reflected in the response plot and Hankel singular-value plot.

• Generalized model such as a `genss` model. The Model Reducer app uses the current or nominal value of all control design blocks in `model` (see `getValue`).

Note

Model Reducer assumes that the model time unit (specified in the `TimeUnit` property of the model) is seconds. If your model does not have `TimeUnit = 'seconds'`, use `chgTimeUnit` to convert the model to seconds.

Specify the number of states in the reduced-order model. Any value is permitted that falls between the number of unstable states in the model and the number of states in the original model. If you specify a single value, Model Reducer computes and displays the responses of a model of that order. If you specify multiple values, Model Reducer computes models of all specified orders and displays their responses on the same plot. To store reduced models in the Data Browser, click .

For more information, see Balanced Truncation Model Reduction.

Example: `5`

Example: `4:7`

Example: `[3,7,10]`

You can choose between absolute and relative errors by selecting the appropriate option in Error Bound. Setting it to `absolute` controls the absolute error ${‖G-{G}_{r}‖}_{\infty }$ while setting it to `relative` controls the relative error ${‖{G}^{-1}\left(G-{G}_{r}\right)‖}_{\infty }$. Relative error gives a better match across frequency while absolute error emphasizes areas with most gain.

For more information, see Balanced Truncation Model Reduction.

When Preserve DC Gain is checked, the DC gain of the reduced model equals the DC gain of the original model. When the DC behavior of the model is important in your application, leave this option checked. Uncheck the option to get better matching of higher-frequency behavior.

For more information, see Balanced Truncation Model Reduction.

By default, Model Reducer analyzes Hankel singular values across all frequencies. Restricting this analysis to a particular frequency range is useful when you know the model has modes outside the region of interest to your particular application. When you apply a frequency limit, Model Reducer determines which states are the low-energy states to truncate based on their energy contribution within the specified frequency range only. Focus on range is only available when Error Bound is set to `absolute`.

To limit the analysis of state contributions to a particular frequency range, check Focus on range. Then, drag the vertical cursors on the response plot to specify the frequency range of interest. Alternatively, enter a frequency range in the text box as a vector of the form `[fmin,fmax]`. Units are `rad/TimeUnit`, where `TimeUnit` is the `TimeUnit` property of the model you are reducing.

Mode Selection Tab

Specify the model you want to reduce by selecting from the Model drop-down list. The list includes all models currently in the Data Browser. To get a model from the MATLAB workspace into the Data Browser, on the Model Reducer tab, click Import Model. You can import any:

• `tf`, `ss`, or `zpk` model that is proper. The model can be SISO or MIMO, and continuous or discrete.

• Continuous-time models must not have time delays. To reduce a continuous-time model with time delays, first use `pade` to approximate the time delays as model dynamics.

• Discrete-time models can have time delays. For the Balanced Truncation reduction method, the app uses `absorbDelay` to convert the delay into poles at z = 0 before reducing the model. The additional states are reflected in the response plot and Hankel singular-value plot.

• Generalized model such as a `genss` model. The Model Reducer app uses the current or nominal value of all control design blocks in `model` (see `getValue`).

For more information, see Mode-Selection Model Reduction.

Note

Reduce Model Order assumes that the model time unit (specified in the `TimeUnit` property of the model) is seconds. If your model does not have ```TimeUnit = 'seconds'```, use `chgTimeUnit` to convert the model to seconds.

Enter the frequency of the slowest dynamics to preserve in the reduced model. Poles with natural frequency below this cutoff are eliminated from the reduced model.

Enter the frequency of the fastest dynamics to preserve in the reduced model. Poles with natural frequency above this cutoff are eliminated from the reduced model.

Pole/Zero Simplification Tab

Specify the model you want to reduce by selecting from the Model drop-down list. The list includes all models currently in the Data Browser. To get a model from the MATLAB workspace into the Data Browser, on the Model Reducer tab, click Import Model. You can import any:

• `tf`, `ss`, or `zpk` model that is proper. The model can be SISO or MIMO, and continuous or discrete.

• Continuous-time models must not have time delays. To reduce a continuous-time model with time delays, first use `pade` to approximate the time delays as model dynamics.

• Discrete-time models can have time delays. For the Balanced Truncation reduction method, the app uses `absorbDelay` to convert the delay into poles at z = 0 before reducing the model. The additional states are reflected in the response plot and Hankel singular-value plot.

• Generalized model such as a `genss` model. The Model Reducer app uses the current or nominal value of all control design blocks in `model` (see `getValue`).

Set the tolerance for pole-zero cancellation by using the slider or entering a value in the text box. The value determines how close together a pole and zero must be for Model Reducer to eliminate them from the reduced model. Moving the slider to the left or entering a smaller value in the text box simplifies the model less, by cancelling fewer poles and zeros. Moving the slider to the right, or entering a larger value, simplifies the model more by cancelling poles and zeros that are further apart.

## Programmatic Use

expand all

`modelReducer` opens the Model Reducer app with no models in the Data Browser. To import a model from the MATLAB workspace, click Import Model.

`modelReducer(model)` opens app and imports the specified LTI model. `model` can be a:

• `tf`, `ss`, or `zpk` model that is proper. The model can be SISO or MIMO, and continuous or discrete.

• Continuous-time models must not have time delays. To reduce a continuous-time model with time delays, first use `pade` to approximate the time delays as model dynamics.

• Discrete-time models can have time delays. For the Balanced Truncation reduction method, the app uses `absorbDelay` to convert the delay into poles at z = 0 before reducing the model. The additional states are reflected in the response plot and Hankel singular-value plot.

• Generalized model such as a `genss` model. The Model Reducer app uses the current or nominal value of all control design blocks in `model` (see `getValue`).

`modelReducer(model1,...,modelN)` opens the app and imports the specified models.

`modelReducer(sessionFile)` opens the app and loads a previously saved session. `sessionFile` is the name of a session data file in the current working directory or on the MATLAB path.

To save session data to disk, in the Model Reducer app, on the Model Reducer tab, click Save Session. The saved session data includes the current plot configuration and all models in the Data Browser.

### Live Editor Tasks

Introduced in R2016a