Model Order Reduction

Obtain low-order approximations of complex models

Working with low-order models can simplify analysis and control design. Simpler models are also easier to understand and manipulate than high-order models. You can get high-order models when you linearize complex Simulink^® or Partial Differential Equation Toolbox™ models, interconnect model elements, or use other processes that produce states that do not contribute much to the dynamics of particular interest to your application. Using Control System Toolbox™ software, you can obtain low-order models for ordinary LTI models or large-scale sparse LTI models.

To obtain low-order models, you can:

Discard modes (poles) that fall outside a specific frequency range or region of interest using freqsep or modalsep.
Compute low-order approximations of LTI or sparse LTI models using various techniques and criteria, such as balanced truncation and proper orthogonal decomposition (POD). Use reducespec as the entry point for these workflows.

In addition, you can simplify models by canceling pole-zero pairs or eliminating low-contribution states using functions such as minreal, sminreal, or xelim.

You can also interactively reduce model order using the Model Reducer app and the Reduce Model Order task in Live Editor.

For more information about ways to reduce model order, see Model Reduction Basics.

Apps

Model Reducer

Reduce complexity of linear time-invariant (LTI) models

Live Editor Tasks

Reduce Model Order

Reduce complexity of linear time-invariant (LTI) models in the Live Editor

Functions

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Model Simplification

`minreal`	Minimal realization or pole-zero cancellation
`sminreal`	Eliminates structurally disconnected states, delays, and blocks
`xelim`	Eliminate states from state-space models (Since R2023b)
`sminDAE`	Reduce algebraic states in sparse state-space models while preserving sparsity (Since R2024b)

Modal and Spectral Decompositions

`modalsep`	Compute modal decomposition (Since R2023b)
`modalsum`	Sum of modal components (Since R2023b)
`stabsep`	Stable-unstable decomposition
`freqsep`	Slow-fast decomposition

Model Reduction

`reducespec`	Create model order reduction specifications (Since R2023b)
`process`	Run model order reduction algorithm (Since R2023b)
`view (balanced)`	Plot state contributions when using balanced truncation method (Since R2023b)
`getrom (balanced)`	Obtain reduced-order models when using balanced truncation method (Since R2023b)
`view (ncf)`	Plot state contributions when using balanced truncation of normalized coprime factors method (Since R2023b)
`getrom (ncf)`	Obtain reduced-order models when using balanced truncation of normalized coprime factors method (Since R2023b)
`view (modal)`	Plot mode information when using modal truncation method (Since R2023b)
`getrom (modal)`	Obtain reduced-order models when using modal truncation method (Since R2023b)
`view (pod)`	Plot state contributions when using proper orthogonal decomposition (POD) method (Since R2024b)
`getrom (pod)`	Obtain reduced-order models when using proper orthogonal decomposition method (Since R2024b)

Incremental POD Analysis

`update`	Update URV approximation given new snapshots for POD (Since R2024b)
`getUR`	Obtain U and R factors from incremental proper orthogonal decomposition (Since R2024b)
`svd`	Compute truncated SVD of state-data matrix (Since R2024b)
`merge`	Combine incremental proper orthogonal decomposition results (Since R2024b)
`lsim`	Compute time response simulation data of dynamic system to arbitrary inputs

Objects

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Balanced Truncation

`BalancedTruncation`	Balanced truncation model order reduction (Since R2023b)
`BalancedTruncationOptions`	Options for model order reduction with balanced truncation (Since R2023b)
`NCFBalancedTruncation`	Balanced truncation of normalized coprime factors model order reduction specification (Since R2023b)
`SparseBalancedTruncation`	Sparse balanced truncation model order reduction object (Since R2023b)
`SparseBalancedTruncationOptions`	Options for sparse model order reduction with balanced truncation method (Since R2023b)

Modal Truncation

`ModalTruncation`	Modal truncation model order reduction specification (Since R2023b)
`ModalTruncationOptions`	Options for model order reduction with modal truncation (Since R2023b)
`SparseModalTruncation`	Sparse modal truncation model order reduction specification (Since R2023b)
`SparseModalTruncationOptions`	Options for sparse model order reduction with modal truncation method (Since R2023b)

Proper Orthogonal Decomposition

`ProperOrthogonalDecomposition`	Proper orthogonal decomposition model order reduction (Since R2024b)
`ProperOrthogonalDecompositionOptions`	Options for model order reduction with proper orthogonal decomposition (Since R2024b)
`incrementalPOD`	Incremental Proper Orthogonal Decomposition (POD) (Since R2024b)

Topics

Model Reduction Workflows

Model Reduction Basics
Model-order reduction can simplify analysis and control design by providing simpler models that are easier to understand and manipulate.
Task-Based Model Order Reduction Workflow
Learn how to create custom reduction criteria to obtain reduced-order models.

LTI Model Order Reduction

Approximate Model by Balanced Truncation at the Command Line
Compute a reduced-order approximation of a model at the command line.
Compare Truncated and DC Matched Low-Order Model Approximations
Compute a low-order approximation in two ways and compare the results.
Approximate Model with Unstable or Near-Unstable Pole
Compute a reduced-order approximation of a system when the system has unstable or near-unstable poles.
Frequency-Limited Balanced Truncation
Reduce a high-order model by removing states of relatively low energy within a particular frequency interval.

Sparse LTI Model Order Reduction

Sparse Modal Truncation of Linearized Structural Beam Model
Compute a low-order approximation of a sparse state-space model obtained from linearizing a structural beam model. (Since R2023b)
Sparse Balanced Truncation of Thermal Model
Balanced truncation of a sparse state-space model obtained from linearizing a thermal model. (Since R2023b)

Interactive Workflows

Import and Export Data in Model Reducer
Import and export model data in Model Reducer.
Specify Options for Balanced Truncation in Model Reducer
Specify options to customize Balanced Truncation model order reduction.
Specify Options for Modal Truncation in Model Reducer
Specify options to customize Modal Truncation model order reduction.
Reduce Model Order Using Model Reducer App
Interactively reduce model order while preserving important dynamics.
Model Reduction in the Live Editor
Interactively perform model reduction and generate code in a live script using the Reduce Model Order task.
Pole-Zero Simplification
Reduce model order by canceling pole-zero pairs or eliminating states that have no effect on the overall model response.
Balanced Truncation Model Reduction
Compute lower order approximations of higher order models by removing states with lower energy contributions.
Modal Truncation Model Reduction
Reduce model order by eliminating poles that fall outside a specific frequency range.
Visualize Reduced-Order Models in Model Reducer App
Examine and compare time-domain and frequency-domain responses of the original and reduced models.