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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. 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 ReducerReduce complexity of linear time-invariant (LTI) models

Live Editor Tasks

Reduce Model OrderReduce complexity of linear time-invariant (LTI) models in the Live Editor (Since R2019b)

Functions

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minrealMinimal realization or pole-zero cancellation
sminrealEliminates structurally disconnected states, delays, and blocks
xelimEliminate states from state-space models (Since R2023b)
modalsepCompute modal decomposition (Since R2023b)
modalsumSum of modal components (Since R2023b)
stabsepStable-unstable decomposition
freqsepSlow-fast decomposition
reducespecCreate model order reduction specifications (Since R2023b)
processRun 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)

Objects

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BalancedTruncationBalanced truncation model order reduction (Since R2023b)
BalancedTruncationOptionsOptions for model order reduction with balanced truncation (Since R2023b)
NCFBalancedTruncationBalanced truncation of normalized coprime factors model order reduction specification (Since R2023b)
ModalTruncationModal truncation model order reduction specification (Since R2023b)
ModalTruncationOptionsOptions for model order reduction with modal truncation (Since R2023b)
SparseBalancedTruncationSparse balanced truncation model order reduction object (Since R2023b)
SparseBalancedTruncationOptionsOptions for sparse model order reduction with balanced truncation method (Since R2023b)
SparseModalTruncationSparse modal truncation model order reduction specification (Since R2023b)
SparseModalTruncationOptionsOptions for sparse model order reduction with modal truncation method (Since R2023b)

Topics

Model Reduction Workflows

LTI Model Order Reduction

Sparse LTI Model Order Reduction

Interactive Workflows