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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.

Examples

Parameters

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Balanced Truncation Tab

`Model` — Currently selected model for reduction
model name

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.

`Reduced orders` — Number of states in reduced model
integer | integer array

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]

`Error Bound` — Type of error bound
`absolute` (default) | `relative`

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 ${‖ G^{- 1} (G - G_{r}) ‖}_{\infty}$ . Relative error gives a better match across frequency while absolute error emphasizes areas with most gain.

For more information, see Balanced Truncation Model Reduction.

`Preserve DC Gain` — Match DC gain of reduced model to original model
checked (default) | unchecked

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.

`Focus on range` — Limit analysis to specified frequencies
unchecked (default) | checked

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

`Model` — Currently selected model for reduction
model name

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.

`Lower Cutoff` — Lowest mode frequency
positive scalar

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.

`Upper Cutoff` — Highest mode frequency
positive scalar

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

`Model` — Currently selected model for reduction
model name

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).

`Simplification of Pole-Zero Pairs` — Tolerance for pole-zero cancellation
positive scalar

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.

For more information, see Pole-Zero Simplification.

Programmatic Use

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`modelReducer`

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)`

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)`

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

`modelReducer(sessionFile)`

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.

Version History

Introduced in R2016a

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R2023b: Generates code using new model order reduction workflow

The Model Reducer app now generates code using the new model order reduction workflows. For example, this table describes the change in the model order reduction workflow in the generated code.

Method	Generated Code before R2023b	Generated Code in R2023b
Balanced Truncation	%% Reduce LTI model order using balanced truncation System = G; % Define System to reduce Order = 14; % Create option set for balred command Options = balredOptions(); % Offset for the stable/unstable boundary Options.Offset = 1e-05; % Compute reduced order approximation ReducedSystem = balred(System,Order,Options); % Create comparison plot bode(System,ReducedSystem);	%% Reduce LTI model order using balanced truncation System = G; % Define System to reduce % Compute reduced order approximation R = reducespec(System,'balanced'); % Set options for Balanced Truncation specification % Offset for the stable/unstable boundary R.Options.Offset = 1e-05; % Compute MOR data once R = process(R); % Get reduced-order model ReducedSystem = getrom(R,Order=14); % Create comparison plot bode(System,ReducedSystem);
Mode Selection	%% Reduce LTI model order using mode selection System = G; % Define System to reduce UpperCutoffFrequency = 100; LowerCutoffFrequency = 10; % Create option set for freqsep command Options = freqsepOptions(); % Accuracy loss factor for stable/unstable decomposition Options.SepTol = 100; % Select modes between lower and upper cutoff frequencies ReducedSystem = freqsep(System,... [LowerCutoffFrequency UpperCutoffFrequency],Options); % Create comparison plot bode(System,ReducedSystem);	%% Reduce LTI model order using mode selection System = G; % Define System to reduce % Select modes between lower and upper cutoff frequencies R = reducespec(System,'modal'); % Set options for Modal Truncation specification % Accuracy loss factor for stable/unstable decomposition R.Options.SepTol = 1e-11; % Compute MOR data once R = process(R); % Get reduced-order model ReducedSystem = getrom(R,Frequency=[10 100],Method='truncate'); % Create comparison plot bode(System,ReducedSystem);

Method

Generated Code before R2023b

Generated Code in R2023b

Balanced Truncation

%% Reduce LTI model order using balanced truncation
System = G; % Define System to reduce
Order = 14;
 
% Create option set for balred command
Options = balredOptions();
% Offset for the stable/unstable boundary
Options.Offset = 1e-05;
 
% Compute reduced order approximation
ReducedSystem = balred(System,Order,Options);
 
% Create comparison plot
bode(System,ReducedSystem);

%% Reduce LTI model order using balanced truncation
System = G; % Define System to reduce
 
% Compute reduced order approximation
R = reducespec(System,'balanced');
% Set options for Balanced Truncation specification
% Offset for the stable/unstable boundary
R.Options.Offset = 1e-05;
% Compute MOR data once
R = process(R);
% Get reduced-order model
ReducedSystem = getrom(R,Order=14);
 
% Create comparison plot
bode(System,ReducedSystem);

Mode Selection

%% Reduce LTI model order using mode selection
System = G; % Define System to reduce
UpperCutoffFrequency = 100;
LowerCutoffFrequency = 10;
 
% Create option set for freqsep command
Options = freqsepOptions();
% Accuracy loss factor for stable/unstable decomposition
Options.SepTol = 100;
 
% Select modes between lower and upper cutoff frequencies
ReducedSystem = freqsep(System,...
    [LowerCutoffFrequency UpperCutoffFrequency],Options);
 
% Create comparison plot
bode(System,ReducedSystem);

%% Reduce LTI model order using mode selection
System = G; % Define System to reduce
 
% Select modes between lower and upper cutoff frequencies
R = reducespec(System,'modal');
% Set options for Modal Truncation specification
% Accuracy loss factor for stable/unstable decomposition
R.Options.SepTol = 1e-11;
% Compute MOR data once
R = process(R);
% Get reduced-order model
ReducedSystem = getrom(R,Frequency=[10 100],Method='truncate');
 
% Create comparison plot
bode(System,ReducedSystem);

For more information about the new workflow, see reducespec and Task-Based Model Order Reduction Workflow.

Model Reducer

Description

Open the Model Reducer App

Examples

Parameters

`Model` — Currently selected model for reduction
model name

`Reduced orders` — Number of states in reduced model
integer | integer array

`Error Bound` — Type of error bound
`absolute` (default) | `relative`

`Preserve DC Gain` — Match DC gain of reduced model to original model
checked (default) | unchecked

`Focus on range` — Limit analysis to specified frequencies
unchecked (default) | checked

`Model` — Currently selected model for reduction
model name

`Lower Cutoff` — Lowest mode frequency
positive scalar

`Upper Cutoff` — Highest mode frequency
positive scalar

`Model` — Currently selected model for reduction
model name

`Simplification of Pole-Zero Pairs` — Tolerance for pole-zero cancellation
positive scalar

Programmatic Use

`modelReducer`

`modelReducer(model)`

`modelReducer(model1,...,modelN)`

`modelReducer(sessionFile)`

Version History

R2023b: Generates code using new model order reduction workflow

See Also

Functions

Live Editor Tasks

Model Reducer

Description

Open the Model Reducer App

Examples

Parameters

Model — Currently selected model for reduction model name

Reduced orders — Number of states in reduced model integer | integer array

Error Bound — Type of error bound absolute (default) | relative

Preserve DC Gain — Match DC gain of reduced model to original model checked (default) | unchecked

Focus on range — Limit analysis to specified frequencies unchecked (default) | checked

Model — Currently selected model for reduction model name

Lower Cutoff — Lowest mode frequency positive scalar

Upper Cutoff — Highest mode frequency positive scalar

Model — Currently selected model for reduction model name

Simplification of Pole-Zero Pairs — Tolerance for pole-zero cancellation positive scalar

Programmatic Use

modelReducer

modelReducer(model)

modelReducer(model1,...,modelN)

modelReducer(sessionFile)

Version History

R2023b: Generates code using new model order reduction workflow

See Also

Functions

Live Editor Tasks

`Model` — Currently selected model for reduction
model name

`Reduced orders` — Number of states in reduced model
integer | integer array

`Error Bound` — Type of error bound
`absolute` (default) | `relative`

`Preserve DC Gain` — Match DC gain of reduced model to original model
checked (default) | unchecked

`Focus on range` — Limit analysis to specified frequencies
unchecked (default) | checked

`Model` — Currently selected model for reduction
model name

`Lower Cutoff` — Lowest mode frequency
positive scalar

`Upper Cutoff` — Highest mode frequency
positive scalar

`Model` — Currently selected model for reduction
model name

`Simplification of Pole-Zero Pairs` — Tolerance for pole-zero cancellation
positive scalar

`modelReducer`

`modelReducer(model)`

`modelReducer(model1,...,modelN)`

`modelReducer(sessionFile)`