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:
A(q), B(q),
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 structures including ARX, ARMAX, output-error, and Box-Jenkins.
Data Supported by Polynomial Models
Use time-domain and frequency-domain data to estimate discrete-time and continuous-time 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.
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 armax
.
Specifying Initial States for Iterative Estimation Algorithms
When you use the pem
or polyest
functions 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.