# 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. 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 (Since R2019b) |

## 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.

### Model Simplification

**Pole-Zero Simplification**

Reduce model order by canceling pole-zero pairs or eliminating states that have no effect on the overall model response.**Mode-Selection Model Reduction**

Reduce model order by eliminating poles that fall outside a specific frequency range.

### 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

**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.**Balanced Truncation Model Reduction**

Compute lower order approximations of higher order models by removing states with lower energy contributions.**Visualize Reduced-Order Models in Model Reducer App**

Examine and compare time-domain and frequency-domain responses of the original and reduced models.