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状態空間モデル

フリー、正準、構造化のパラメーター化をもつ状態空間モデル、等価の ARMAX モデルおよび OE モデル

アプリ

System IdentificationIdentify models of dynamic systems from measured data

関数

ssestEstimate state-space model using time-domain or frequency-domain data
ssregestEstimate state-space model by reduction of regularized ARX model
n4sidEstimate state-space model using subspace method
idssState-space model with identifiable parameters
pemPrediction error estimate for linear and nonlinear model
delayestEstimate time delay (dead time) from data
getpvecModel parameters and associated uncertainty data
setpvecModify value of model parameters
getparObtain attributes such as values and bounds of linear model parameters
setparSet attributes such as values and bounds of linear model parameters
ssformQuick configuration of state-space model structure
initSet or randomize initial parameter values
idparCreate parameter for initial states and input level estimation
idssdataState-space data of identified system
findstatesEstimate initial states of model
ssestOptionsOption set for ssest
ssregestOptionsOption set for ssregest
n4sidOptionsOption set for n4sid
findstatesOptionsOption set for findstates

例および操作のヒント

Estimate State-Space Model With Order Selection

To estimate a state-space model, you must provide a value of its order, which represents the number of states. When you do not know the order, you can search and select an order using the following procedures.

Estimate State-Space Models in System Identification App

Import data into the System Identification app. See データの表現. For supported data formats, see Data Supported by State-Space Models.

Estimate State-Space Models at the Command Line

Perform black-box or structured estimation.

Estimate State-Space Models with Free-Parameterization

The default parameterization of the state-space matrices A, B, C, D, and K is free; that is, any elements in the matrices are adjustable by the estimation routines. Because the parameterization of A, B, and C is free, a basis for the state-space realization is automatically selected to give well-conditioned calculations.

Estimate State-Space Models with Canonical Parameterization

Canonical parameterization represents a state-space system in a reduced parameter form where many elements of A, B and C matrices are fixed to zeros and ones. The free parameters appear in only a few of the rows and columns in state-space matrices A, B, C, D, and K. The free parameters are identifiable — they can be estimated to unique values. The remaining matrix elements are fixed to zeros and ones.

Estimate State-Space Models with Structured Parameterization

Structured parameterization lets you exclude specific parameters from estimation by setting these parameters to specific values. This approach is useful when you can derive state-space matrices from physical principles and provide initial parameter values based on physical insight. You can use this approach to discover what happens if you fix specific parameter values or if you free certain parameters.

Estimate State-Space Equivalent of ARMAX and OE Models

This example shows how to estimate ARMAX and OE-form models using the state-space estimation approach.

概念

What Are State-Space Models?

State-space models are models that use state variables to describe a system by a set of first-order differential or difference equations, rather than by one or more nth-order differential or difference equations. State variables x(t) can be reconstructed from the measured input-output data, but are not themselves measured during an experiment.

Data Supported by State-Space Models

You can use time-domain and frequency-domain data that is real or complex and has single or multiple outputs.

Supported State-Space Parameterizations

System Identification Toolbox™ software supports the following parameterizations that indicate which parameters are estimated and which remain fixed at specific values:

Specifying Initial States for Iterative Estimation Algorithms

When you estimate state-space models, you can specify how the algorithm treats initial states. This information supports the estimation procedures Estimate State-Space Models in System Identification App and Estimate State-Space Models at the Command Line.

State-Space Model Estimation Methods

Choose between noniterative subspace methods, iterative method that uses prediction error minimization algorithm, and noniterative method.

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. The input signals are measured while the noise signals are only known via their statistical mean and variance. The general form of the state-space model, often associated with Kalman filtering, is an example of such a model, and is defined as: