# Model Order Reduction

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

## Objects

## 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.