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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.

Graphical Tools

Linear Analysis Tool Linearize Simulink models

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

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 linearization I/Os 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.

Linearization of Multirate Models

You can linearize Simulink models that include states with different sampling rates.

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.

Analysis and Validation

Analyze Results With Linear Analysis Tool 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.

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 Linear Analysis Tool

To reproduce your linearization results, you can generate MATLAB® scripts or functions using the Linear Analysis Tool.

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