1
2
3
4
5
6
7
8
9
10
11
12
13
14
15
16
17
18
19
20
21
22
23
24
25
26
27
28
29
30
31
32
33
34
35
36
37
38
39
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
61
|
% Generated by roxygen2 (4.1.1): do not edit by hand
% Please edit documentation in R/estpoly.R
\name{arx}
\alias{arx}
\title{Estimate ARX Models}
\usage{
arx(x, order = c(0, 1, 0))
}
\arguments{
\item{x}{an object of class \code{idframe}}
\item{order:}{Specification of the orders: the three integer components
(na,nb,nk) are the order of polynolnomial A, (order of polynomial B + 1) and
the input-output delay}
}
\value{
An object of class \code{estPoly} containing the following elements:
\tabular{ll}{
\code{coefficients} \tab an \code{idpoly} object containing the
fitted coefficients \cr
\code{vcov} \tab the covariance matrix of the fitted coefficients\cr
\code{sigma} \tab the standard deviation of the innovations\cr
\code{df} \tab the residual degrees of freedom \cr
\code{fitted.values} \tab the predicted response \cr
\code{residuals} \tab the residuals \cr
\code{call} \tab the matched call \cr
\code{time} \tab the time of the data used \cr
\code{input} \tab the input data used
}
}
\description{
Fit an ARX model of the specified order given the input-output data
}
\details{
SISO ARX models are of the form
\deqn{
y[k] + a_1 y[k-1] + \ldots + a_{na} y[k-na] = b_{nk} u[k-nk] +
\ldots + b_{nk+nb} u[k-nk-nb] + e[k]
}
The function estimates the coefficients using linear least squares (with
no regularization). Future versions may include regularization
parameters as well
\\
The data is expected to have no offsets or trends. They can be removed
using the \code{\link{detrend}} function.
}
\examples{
data(arxsim)
model <- arx(data,c(2,1,1))
summary(model) # obtain estimates and their covariances
plot(model) # plot the predicted and actual responses
}
\references{
Arun K. Tangirala (2015), \emph{Principles of System Identification:
Theory and Practice}, CRC Press, Boca Raton. Section 21.6.1
Lennart Ljung (1999), \emph{System Identification: Theory for the User},
2nd Edition, Prentice Hall, New York. Section 10.1
}
|
