Input-Output Polynomial Models
A polynomial model uses a generalized notion of transfer functions to express the relationship between the input, u(t), the output y(t), and the noise e(t) using an equation of the form:
F(q), C(q) and
D(q) are polynomial matrices in terms of the
time-shift operator q-1.
u(t) is the input, and
nk is the
input delay. y(t) is the output and
e(t) is the disturbance signal.
Each polynomial has an independent order, or number of estimable coefficients. For example, if A(q) has an order of 2, then theA polynomial has the form 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, see What Are Polynomial Models?
|System Identification||Identify models of dynamic systems from measured data|
Create Polynomial Model
|Polynomial model with identifiable parameters|
|Estimate parameters of ARX, ARIX, AR, or ARI model|
|Estimate parameters of ARMAX, ARIMAX, ARMA, or ARIMA model using time-domain data|
|Estimate Box-Jenkins polynomial model using time-domain data|
|ARX model estimation using four-stage instrumental variable method|
|ARX model estimation using instrumental variable method with arbitrary instruments|
|Estimate output-error polynomial model using time-domain or frequency-domain data|
|Estimate polynomial model using time- or frequency-domain data|
|Prediction error minimization for refining linear and nonlinear models|
Find Best ARX Model-Order Combination
Model Initialization and Structure Parameters
Extract or Set Model Parameters
|Access polynomial coefficients and uncertainties of identified model|
|Obtain model parameters and associated uncertainty data|
|Modify values of model parameters|
|Obtain attributes such as values and bounds of linear model parameters|
|Set attributes such as values and bounds of linear model parameters|
|Specify format for B and F polynomials of multi-input polynomial model|
Polynomial Model Basics
Estimate Polynomial Models
- Preliminary Step – Estimating Model Orders and Input Delays
To estimate polynomial models, you must provide input delays and model orders.
- Estimate Polynomial Models in the App
Import data into the app, specify model orders, delays and estimation options.
- Estimate Polynomial Models at the Command Line
Specify model orders, delays, and estimation options.
- Polynomial Sizes and Orders of Multi-Output Polynomial Models
Size of A, B, C, D, and F polynomials for multi-output models.
- Estimate Models Using armax
This example shows how to estimate a linear, polynomial model with an ARMAX structure for a three-input and single-output (MISO) system using the iterative estimation method
Set Polynomial Model Options
- Specifying Initial States for Iterative Estimation Algorithms
When you use the
polyestfunctions to estimate ARMAX, Box-Jenkins (BJ), Output-Error (OE), you must specify how the algorithm treats initial conditions.
- Polynomial Model Estimation Algorithms
Choose between the ARX and IV algorithms for ARX and AR model estimation.