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Diffstat (limited to 'man/arx.Rd')
| -rw-r--r-- | man/arx.Rd | 25 |
1 files changed, 13 insertions, 12 deletions
@@ -1,4 +1,4 @@ -% Generated by roxygen2 (4.1.1): do not edit by hand +% Generated by roxygen2: do not edit by hand % Please edit documentation in R/estpoly.R \name{arx} \alias{arx} @@ -9,15 +9,15 @@ 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 +\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{sys} \tab an \code{idpoly} object containing the + \code{sys} \tab an \code{idpoly} object containing the fitted ARX coefficients \cr \code{fitted.values} \tab the predicted response \cr \code{residuals} \tab the residuals \cr @@ -27,7 +27,7 @@ An object of class \code{estpoly} containing the following elements: \tabular{ll}{ \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 + \code{df} \tab the residual degrees of freedom } } } @@ -35,16 +35,16 @@ An object of class \code{estpoly} containing the following elements: Fit an ARX model of the specified order given the input-output data } \details{ -SISO ARX models are of the form +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] + 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 +no regularization). Future versions may include regularization parameters as well \\ -The data is expected to have no offsets or trends. They can be removed +The data is expected to have no offsets or trends. They can be removed using the \code{\link{detrend}} function. } \examples{ @@ -52,12 +52,13 @@ data(arxsim) model <- arx(data,c(2,1,1)) model plot(model) # plot the predicted and actual responses + } \references{ -Arun K. Tangirala (2015), \emph{Principles of System Identification: +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}, +Lennart Ljung (1999), \emph{System Identification: Theory for the User}, 2nd Edition, Prentice Hall, New York. Section 10.1 } |