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Input-Output Polynomial Models

Input-output polynomial models, including ARX, ARMAX, output-error, and Box-Jenkins model structures

A polynomial model uses a generalized notion of transfer functions to express the relationship between the input,u(t), the outputy(t), and the noisee(t) using an equation of the form:

A ( q ) y ( t ) = B ( q ) F ( q ) u ( t − n k ) + C ( q ) D ( q ) e ( t )

A(q),B(q),F(q),C(q) andD(q) are polynomial matrices in terms of the time-shift operatorq-1.u(t) is the input, andnkis the input delay.y(t) is the output ande(t) is the disturbance signal.

Each polynomial has an independentorder, or number of estimable coefficients. For example, ifA(q) has an order of 2, then theA多项式的形式A(q) = 1 +a1q-1+a2q-2.

In practice, not all the polynomials are simultaneously active. Simpler polynomial forms, such as ARX, ARMAX, Output-Error, and Box-Jenkins provide model structures suitable for specific objectives such as handling nonstationary disturbances or providing completely independent parameterization for dynamics and noise. For more information about these model types, seeWhat Are Polynomial Models?

Apps

System Identification Identify models of dynamic systems from measured data

Functions

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idpoly Polynomial model with identifiable parameters
arx Estimate parameters of ARX, ARIX, AR, or ARI model
armax Estimate parameters of ARMAX, ARIMAX, ARMA, or ARIMA model using time-domain data
bj Estimate Box-Jenkins polynomial model using time domain data
iv4 ARX model estimation using four-stage instrumental variable method
ivx ARX model estimation using instrumental variable method with arbitrary instruments
oe Estimate output-error polynomial model using time-domain or frequency-domain data
polyest Estimate polynomial model using time- or frequency-domain data
pem Prediction error minimization for refining linear and nonlinear models
arxstruc Compute loss functions for single-output ARX models
ivstruc Compute loss functions for sets of ARX model structures using instrumental variable method
selstruc Select model order for single-output ARX models
struc Generate model-order combinations for single-output ARX model estimation
arxRegul Determine regularization constants for ARX model estimation
delayest Estimate time delay (dead time) from data
初始化 Set or randomize initial parameter values
polydata Access polynomial coefficients and uncertainties of identified model
getpvec Obtain model parameters and associated uncertainty data
setpvec Modify values of model parameters
getpar Obtain attributes such as values and bounds of linear model parameters
setpar Set attributes such as values and bounds of linear model parameters
setPolyFormat Specify format forBandFpolynomials of multi-input polynomial model
armaxOptions Option set forarmax
arxOptions Option set forarx
arxRegulOptions Option set forarxRegul
bjOptions Option set forbj
iv4Options Option set foriv4
oeOptions Option set foroe
polyestOptions Option set forpolyest

Topics

Polynomial Model Basics

Estimate Polynomial Models

Set Polynomial Model Options