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|
|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|
|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|
To estimate polynomial models, you must provide input delays and model orders.
Import data into the app, specify model orders, delays and estimation options.
Specify model orders, delays, and estimation options.
Size of A, B, C, D, and F polynomials for multi-output models.
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
When you use the
polyest functions to estimate ARMAX, Box-Jenkins (BJ), Output-Error (OE), you
must specify how the algorithm treats initial conditions.
Choose between the ARX and IV algorithms for ARX and AR model estimation.