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#' @export
sim <- function(model,input,sigma=0) UseMethod("sim")
#' @export
sim.default <- function(model,input,sigma=0){
print("The sim method is not developed for the current class of the object")
}
#' Simulate from an ARX Model
#'
#' Simulate the response of an ARX system, given the input
#'
#' @param model an object of class \code{arx} containing the coefficients
#' @param input a vector/matrix containing the input
#' @param sigma standard deviation of the innovations (Default= \code{0})
#'
#' @return
#' a vector containing the output
#'
#' @details
#' The routine is currently built only for SISO systems. Future Versions will
#' include support for MIMO systems
#'
#' @seealso
#' \code{\link{arx}} for defining ARX models
#'
#' @examples
#' u <- rnorm(200,sd=1)
#' model <- arx(A=c(1,-1.5,0.7),B=c(0.8,-0.25),ioDelay=1)
#' y <- sim(model,u,sigma=0.1)
#'
#' @export
sim.arx <- function(model,input,sigma=0){
na <- length(model$A) - 1; nk <- model$ioDelay;
nb <- length(model$B) - nk; nb1 <- nb+nk
n <- max(na,nb1)
coef <- matrix(c(model$A[-1],model$B),nrow=na+nb1)
y <- rep(0,length(input)+n)
u <- c(rep(0,n),input)
ek <- rnorm(length(input),sd=sigma)
# padLeftZeros <- function(x) c(rep(0,n),x)
# u <- apply(input,2,padLeftZeros)
for(i in n+1:length(input)){
if(nk==0) v <- u[i-0:(nb-1)] else v <- u[i-nk:nb1]
reg <- matrix(c(-(y[i-1:na]),v),ncol=na+nb1)
y[i] <- reg%*%coef + ek[i-n]
}
return(y[n+1:length(input)])
}
#' Simulate from a Polynomial Model
#'
#' Simulate the response of a system system governed by a polynomial model
#' , given the input
#'
#' @param model an object of class \code{idpoly} containing the coefficients
#' @param input a vector/matrix containing the input
#' @param sigma standard deviation of the innovations (Default= \code{0})
#'
#' @return
#' a vector containing the output
#'
#' @details
#' The routine is currently built only for SISO systems. Future Versions will
#' include support for MIMO systems
#'
#' @seealso
#' \code{\link{idpoly}} for defining polynomial models
#'
#' @examples
#' u <- rnorm(200,sd=1)
#' model <- idpoly(A=c(1,-1.5,0.7),B=c(0.8,-0.25),C=1,D=1,F1=1,ioDelay=1)
#' y <- sim(model,u,sigma=0.1)
#'
#' @export
sim.idpoly <- function(model,input,sigma=1){
require(signal);require(polynom)
n <- length(input)[1]
ek <- rnorm(n,sd=sigma)
den1 <- as.numeric(polynomial(model$A)*polynomial(model$D))
filt1 <- Arma(b=model$C,a=den1)
vk <- signal::filter(filt1,ek)
B <- c(rep(0,model$ioDelay),model$B)
den2 <- as.numeric(polynomial(model$A)*polynomial(model$F1))
filt2 <- Arma(b=B,a=den2)
ufk <- signal::filter(filt2,input)
yk <- as.numeric(ufk) + as.numeric(vk)
return(as.numeric(yk))
}
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