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線形モデル同定の基礎

線形モデルの同定、ブラックボックスのモデル化、モデル構造の選択、正則化

例および操作のヒント

Identify Linear Models Using System Identification App

Identifying linear black-box models from single-input/single-output (SISO) data using the System Identification app.

Identify Linear Models Using the Command Line

Identifying linear models from multiple-input/single-output (MISO) data using System Identification Toolbox™ commands.

Transfer Function Structure Specification

Specify the values and constraints for the numerator, denominator and transport delays.

Specifying Initial Conditions for Iterative Estimation of Transfer Functions

Specify how initial conditions are handled during model estimation in the app and at the command line.

Model Structure Selection: Determining Model Order and Input Delay

This example shows some methods for choosing and configuring the model structure. Estimation of a model using measurement data requires selection of a model structure (such as state-space or transfer function) and its order (e.g., number of poles and zeros) in advance. This choice is influenced by prior knowledge about the system being modeled, but can also be motivated by an analysis of data itself. This example describes some options for determining model orders and input delay.

Frequency Domain Identification: Estimating Models Using Frequency Domain Data

This example shows how to estimate models using frequency domain data. The estimation and validation of models using frequency domain data work the same way as they do with time domain data. This provides a great amount of flexibility in estimation and analysis of models using time and frequency domain as well as spectral (FRF) data. You may simultaneously estimate models using data in both domains, compare and combine these models. A model estimated using time domain data may be validated using spectral data or vice-versa.

Regularized Identification of Dynamic Systems

This example shows the benefits of regularization for identification of linear and nonlinear models.

Estimate Regularized ARX Model Using System Identification App

This example shows how to estimate regularized ARX models using automatically generated regularization constants in the System Identification app.

概念

Types of Model Objects

Model object types include numeric models, for representing systems with fixed coefficients, and generalized models for systems with tunable or uncertain coefficients.

About Identified Linear Models

System Identification Toolbox software uses objects to represent a variety of linear and nonlinear model structures.

Available Linear Models

A linear model is often sufficient to accurately describe the system dynamics and, in most cases, you should first try to fit linear models. Available linear structures include transfer functions and state-space models, summarized in the following table.

Linear Model Structures

Linear Model Structures

Black-Box Modeling

Black-box modeling is useful when your primary interest is in fitting the data regardless of a particular mathematical structure of the model.

Recommended Model Estimation Sequence

Recommended model estimation sequence, from the simplest to the more complex model structures.

Imposing Constraints on Model Parameter Values

All identified linear (IDLTI) models, except idfrd, contain a Structure property. The Structure property contains the adjustable entities (parameters) of the model. Each parameter has attributes such as value, minimum/maximum bounds, and free/fixed status that allow you to constrain them to desired values or a range of values during estimation. You use the Structure property to impose constraints on the values of various model parameters.

Determining Model Order and Delay

Estimation requires you to specify the model order and delay. Many times, these values are not known.

Effect of Input Intersample Behavior on Continuous-Time Models

The intersample behavior of the input signals influences the estimation, simulation and prediction of continuous-time models. A sampled signal is characterized only by its values at the sampling instants. However, when you apply a continuous-time input to a continuous-time system, the output values at the sampling instants depend on the inputs at the sampling instants and on the inputs between these points.

Modeling Multiple-Output Systems

Supported models for multiple-output systems.

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.

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.

Estimation Report

The estimation report contains information about the results and options used for a model estimation. This report is stored in the Report property of the estimated model. The exact contents of the report depend on the estimator function you use to obtain the model.

Next Steps After Getting an Accurate Model

How you can work with identified models.

注目の例