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
Related Examples
Parameters
Balanced Truncation TabModel — 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, orzpkmodel 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
padeto approximate the time delays as model dynamics.Discrete-time models can have time delays. For the Balanced Truncation reduction method, the app uses
absorbDelayto 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
genssmodel. The Model Reducer app uses the current or nominal value of all control design blocks inmodel(seegetValue).
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 model 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]
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.
Select frequency 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.
To limit the analysis of state contributions to a particular frequency
range, check Select frequency 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.
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, orzpkmodel 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
padeto approximate the time delays as model dynamics.Discrete-time models can have time delays. For the Balanced Truncation reduction method, the app uses
absorbDelayto 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
genssmodel. The Model Reducer app uses the current or nominal value of all control design blocks inmodel(seegetValue).
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.
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, orzpkmodel 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
padeto approximate the time delays as model dynamics.Discrete-time models can have time delays. For the Balanced Truncation reduction method, the app uses
absorbDelayto 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
genssmodel. The Model Reducer app uses the current or nominal value of all control design blocks inmodel(seegetValue).
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
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)
model)modelReducer( opens app and
imports the specified LTI model. model)model can be a:
tf,ss, orzpkmodel 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
padeto approximate the time delays as model dynamics.Discrete-time models can have time delays. For the Balanced Truncation reduction method, the app uses
absorbDelayto 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
genssmodel. The Model Reducer app uses the current or nominal value of all control design blocks inmodel(seegetValue).
modelReducer(model1,...,modelN)
model1,...,modelN)modelReducer(
opens the app and imports the specified models.model1,...,modelN)
modelReducer(sessionFile)
sessionFile)modelReducer( opens the app
and loads a previously saved session. sessionFile)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.