Linearization Basics

Define system to linearize, plot linear response, validate linearization results

You can linearize a Simulink^® model at the default operating point defined in the model. For more information, see Linearize Simulink Model at Model Operating Point. You can also specify an operating point found using an optimization-based search or at a simulation time.

To extract the linearized response of a portion of your model, you can define specific linearization input and output points. For more information, see Specify Portion of Model to Linearize. After linearization, you can analyze and validate your results in both the time domain and frequency domain.

Apps

Model Linearizer

Linearize Simulink models

Tools

Control Design Onramp with Simulink

Interactive training course included with Simulink Control Design license

Functions

`linearize`	Linear approximation of Simulink model or subsystem
`getlinio`	Obtain linear analysis points from Simulink model, Linear Analysis Plots block, or Model Verification block
`linio`	Create linear analysis point for Simulink model, Linear Analysis Plots block, or Model Verification block
`setlinio`	Save linear analysis points to Simulink model, Linear Analysis Plots block, or Model Verification block
`linlft`	Linearize model while removing contribution of specified blocks
`linlftfold`	Combine linearization results from specified blocks and model
`linearizeOptions`	Set linearization options
`fastRestartForLinearAnalysis`	Fast restart for linear analysis

Topics

Getting Started

Linearize Nonlinear Models

Obtain a linear approximation of a nonlinear system that is valid in a small region around an operating point.

Choose Linearization Tools

Simulink Control Design™ software lets you perform linear analysis of nonlinear models using a user interface, functions, or blocks.

Exact Linearization Algorithm

Simulink Control Design software linearizes models using a block-by-block approach. The software individually linearizes each block in a Simulink model and produces the linearization of the overall system by combining the individual block linearizations.

Linearize Simulink Model at Model Operating Point

Linearize a model at the operating point specified in the model. The model operating point consists of the model initial state values and input signals.

Linearize Plant

You can linearize a block or subsystem in your Simulink model without defining separate analysis points for the block inputs and outputs. The specified block or subsystem is isolated from the rest of the model before linearization.

Compute Open-Loop Response

You can analyze and compute the combined response of the plant and controller, excluding the effects of the feedback loop.

Order States in Linearized Model

You can control the order of the states in a linearized model. This state order appears in linearization results.

Operating Point Specification

Linearize at Trimmed Operating Point

You can linearize a Simulink model at an operating point that meets specified input, output, or state constraints.

Linearize at Simulation Snapshot

Simulate a Simulink model and extract the state and input levels of the system at specified simulation times.

Linearize at Triggered Simulation Events

You can linearize a Simulink model at specific events in time. Linearization events can be trigger-based events or function-call events.

Specify Portion of Model

Specify Portion of Model to Linearize

Specify the subsystem, loop, or block to linearize using linear analysis points.

How the Software Treats Loop Openings

Loop openings affect only how the software recombines linearized blocks, not how the software linearizes each block. The software ignores openings when computing operating points.

Models with Special Characteristics

Linearization of Models with Delays

When linearizing a Simulink model with continuous-time delay blocks, you can either approximate the delays or represent the delays exactly.

Linearize Multirate Models

You can linearize a Simulink model that contains blocks with different sample times.

Linearization of Models with Model References

To achieve an accurate block-by-block linearization of a model reference subsystem, first set it to run its simulation in normal mode.

Linearize Simscape Networks

You can linearize models with Simscape™ components using Simulink Control Design software.

Analysis and Validation

Analyze Results Using Model Linearizer Response Plots

Analyze the time-domain and frequency-domain responses of linearized models. You can compare the responses of multiple models and view system characteristics such as stability margins and settling time.

View Linearized Model Equations Using Model Linearizer

You can view the state-space equations of your linearized model in the Model Linearizer.

Validate Linearization In Frequency Domain

You can assess the accuracy of your linearization results by estimating the frequency response of the nonlinear model and comparing the result with the response of the linearized model.

Validate Linearization In Time Domain

You can assess the accuracy of your linearization results by comparing the simulated output of the nonlinear model and the linearized model.

Code Generation

Generate MATLAB Code for Linearization from Model Linearizer

To reproduce your interactive linearization results at the command line, you can generate MATLAB^® scripts or functions using the Model Linearizer.

Featured Examples

Trimming and Linearizing an Airframe

Trim and linearize an airframe. We first need to find the elevator deflection and the resulting trimmed body rate (q) that will generate a given incidence value when the airframe is traveling at a set speed. Once we find the trim condition, we can derive a linear model for the dynamics of the states around the trim condition.

Open Script

Linearization of Pneumatic System at Simulation Snapshots

Use the time based operating point snapshot feature in Simulink Control Design. This example uses a model of the dynamics of filling a cylinder with compressed air.