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Grey-Box Model Estimation

Estimate coefficients of linear and nonlinear differential, difference and state-space equations

Functions

`greyest`	Estimate ODE parameters of linear grey-box model
`nlgreyest`	Estimate nonlinear grey-box model parameters
`idgrey`	Linear ODE (grey-box model) with identifiable parameters
`idnlgrey`	Nonlinear grey-box model
`pem`	Prediction error minimization for refining linear and nonlinear models

`findstates`	Estimate initial states of model
`init`	Set or randomize initial parameter values
`getinit`	Values of `idnlgrey` model initial states
`setinit`	Set initial states of `idnlgrey` model object
`getpar`	Parameter values and properties of `idnlgrey` model parameters
`setpar`	Set initial parameter values of `idnlgrey` model object
`getpvec`	Obtain model parameters and associated uncertainty data
`setpvec`	Modify values of model parameters
`sim`	Simulate response of identified model

`greyestOptions`	Option set for `greyest`
`nlgreyestOptions`	Option set for `nlgreyest`
`findstatesOptions`	Option set for `findstates`
`simOptions`	Option set for `sim`

Examples and How To

Estimate Linear Grey-Box Models
How to define and estimate linear grey-box models at the command line.
Estimate Continuous-Time Grey-Box Model for Heat Diffusion
This example shows how to estimate the heat conductivity and the heat-transfer coefficient of a continuous-time grey-box model for a heated-rod system.
Estimate Discrete-Time Grey-Box Model with Parameterized Disturbance
This example shows how to create a single-input and single-output grey-box model structure when you know the variance of the measurement noise.
Estimate Coefficients of ODEs to Fit Given Solution
Estimate model parameters using linear and nonlinear grey-box modeling.
Estimate Model Using Zero/Pole/Gain Parameters
This example shows how to estimate a model that is parameterized by poles, zeros, and gains.
Estimate Nonlinear Grey-Box Models
How to define and estimate nonlinear grey-box models at the command line.
Creating IDNLGREY Model Files
This example shows how to write ODE files for nonlinear grey-box models as MATLAB® and C MEX files.
Estimate State-Space Models with Structured Parameterization
Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values.
Building Structured and User-Defined Models Using System Identification Toolbox
This example shows how to estimate parameters in user-defined model structures.

Concepts

Supported Grey-Box Models
Types of supported grey-box models.
Data Supported by Grey-Box Models
Types of supported data for estimating grey-box models.
Choosing idgrey or idnlgrey Model Object
Difference between idgrey and idnlgrey model objects for representing grey-box model objects.
Identifying State-Space Models with Separate Process and Measurement Noise Descriptions
An identified linear model is used to simulate and predict system outputs for given input and noise signals.
Loss Function and Model Quality Metrics
Configure the loss function that is minimized during parameter estimation. After estimation, use model quality metrics to assess the quality of identified models.
Estimation Report
The estimation report contains information about the results and options used for a model estimation.
Regularized Estimates of Model Parameters
Regularization is the technique for specifying constraints on the flexibility of a model, thereby reducing uncertainty in the estimated parameter values.

Featured Examples

Modeling a Vehicle Dynamics System

Nonlinear grey-box modeling of vehicle dynamics.

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Modeling an Aerodynamic Body

The grey-box modeling of a large and complex nonlinear system.

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Modeling an Industrial Robot Arm

Grey-box modeling of the dynamics of an industrial robot arm.

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Represent Nonlinear Dynamics Using MATLAB File for Grey-Box Estimation

Construct, estimate, and analyze nonlinear grey-box models.

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Two Tank System: C MEX-File Modeling of Time-Continuous SISO System

Perform IDNLGREY modeling based on C MEX model files.

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Three Ecological Population Systems: MATLAB and C MEX-File Modeling of Time-Series

Create nonlinear grey box time series models.

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Narendra-Li Benchmark System: Nonlinear Grey Box Modeling of a Discrete-Time System

Identify the parameters of a complex yet artificial nonlinear discrete-time system with one input and one output.

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Friction Modeling: MATLAB File Modeling of Static SISO System

Grey-box modeling of a static single-input, single-output system using a MATLAB function as the ODE file.

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Signal Transmission System: C MEX-File Modeling Using Optional Input Arguments

Provide optional input arguments to IDNLGREY models.

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Dry Friction Between Two Bodies: Parameter Estimation Using Multiple Experiment Data

Estimate parameters of a nonlinear grey box model using multiple experiment data.

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Industrial Three-Degrees-of-Freedom Robot: C MEX-File Modeling of MIMO System Using Vector/Matrix Parameters

Design C-MEX model files that involve scalar, vector, and matrix parameters.

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Non-Adiabatic Continuous Stirred Tank Reactor: MATLAB File Modeling with Simulations in Simulink

Include and simulate an IDNLGREY model in Simulink^®.

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Classical Pendulum: Some Algorithm-Related Issues

How the estimation algorithm choices may impact the results for a nonlinear grey box model estimation.

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