| Type: | Package |
| Title: | System Identification in R |
| Version: | 1.0.4 |
| Date: | 2017-01-06 |
| Author: | Suraj Yerramilli, Arun Tangirala |
| Maintainer: | Suraj Yerramilli <surajyerramilli@gmail.com> |
| Description: | Provides functions for constructing mathematical models of dynamical systems from measured input-output data. |
| License: | GPL-3 |
| Depends: | R (≥ 3.1) |
| Imports: | signal,tframe, ggplot2 (≥ 2.1.0), reshape2, polynom, bitops, zoo |
| RoxygenNote: | 5.0.1 |
| NeedsCompilation: | no |
| Packaged: | 2017-01-07 18:42:13 UTC; suraj |
| Repository: | CRAN |
| Date/Publication: | 2017-01-07 20:00:56 |
Multiple assignment operator
Description
Assign multiple variables from a list or function return object
Usage
l %=% r
Arguments
l |
the variables to be assigned |
r |
the list or function-return object |
Estimate ARMAX Models
Description
Fit an ARMAX model of the specified order given the input-output data
Usage
armax(x, order = c(0, 1, 1, 0), init_sys = NULL, intNoise = FALSE,
options = optimOptions())
Arguments
x |
an object of class |
order |
Specification of the orders: the four integer components (na,nb,nc,nk) are the order of polynolnomial A, order of polynomial B + 1, order of the polynomial C,and the input-output delay respectively |
init_sys |
Linear polynomial model that configures the initial parameterization.
Must be an ARMAX model. Overrules the |
intNoise |
Logical variable indicating whether to add integrators in
the noise channel (Default= |
options |
Estimation Options, setup using |
Details
SISO ARMAX models are of the form
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] + c_{1} e[k-1] + \ldots c_{nc} e[k-nc]
+ e[k]
The function estimates the coefficients using non-linear least squares
(Levenberg-Marquardt Algorithm)
The data is expected to have no offsets or trends. They can be removed
using the detrend function.
Value
An object of class estpoly containing the following elements:
sys |
an |
fitted.values |
the predicted response |
residuals |
the residuals |
input |
the input data used |
call |
the matched call |
stats |
A list containing the following fields: |
options |
Option set used for estimation. If no custom options were configured, this is a set of default options |
termination |
Termination conditions for the iterative
search used for prediction error minimization:
|
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Sections 14.4.1, 21.6.2
Examples
data(armaxsim)
z <- dataSlice(armaxsim,end=1533) # training set
mod_armax <- armax(z,c(1,2,1,2))
mod_armax
Data simulated from an ARMAX model
Description
This dataset contains 2555 samples simulated from the following ARMAX model:
y[k] = \frac{0.6q^{-2} - 0.2q^{-3}}{1 - 0.5q^{-1}} u[k] +
\frac{1-0.3q^{-1}}{1 - 0.5q^{-1}} e[k]
Usage
armaxsim
Format
an idframe object with 2555 samples, one input and one
output
Details
The model is simulated with a 2555 samples long full-band PRBS input. The noise variance is set to 0.1
Estimate ARX Models
Description
Fit an ARX model of the specified order given the input-output data
Usage
arx(x, order = c(1, 1, 1), lambda = 0.1, intNoise = FALSE, fixed = NULL)
Arguments
x |
an object of class |
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 |
lambda |
Regularization parameter(Default= |
intNoise |
Logical variable indicating whether to add integrators in
the noise channel (Default= |
fixed |
list containing fixed parameters. If supplied, only |
Details
SISO ARX models are of the form
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
regularization).
The data is expected to have no offsets or trends. They can be removed
using the detrend function.
To estimate finite impulse response(FIR) models, specify the first
order to be zero.
Value
An object of class estpoly containing the following elements:
sys |
an |
fitted.values |
the predicted response |
residuals |
the residuals |
input |
the input data used |
call |
the matched call |
stats |
A list containing the following fields: |
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Section 21.6.1
Lennart Ljung (1999), System Identification: Theory for the User, 2nd Edition, Prentice Hall, New York. Section 10.1
Examples
data(arxsim)
mod_arx <- arx(arxsim,c(1,2,2))
mod_arx
plot(mod_arx) # plot the predicted and actual responses
Data simulated from an ARX model
Description
This dataset contains 2555 samples simulated from the following ARX model:
y[k] = \frac{0.6q^{-2} - 0.2q^{-3}}{1 - 0.5q^{-1}} u[k] +
\frac{1}{1 - 0.5q^{-1}} e[k]
Usage
arxsim
Format
an idframe object with 2555 samples, one input and one
output
Details
The model is simulated with a 2555 samples long full-band PRBS input. The noise variance is set to 0.1
Estimate Box-Jenkins Models
Description
Fit a box-jenkins model of the specified order from input-output data
Usage
bj(z, order = c(1, 1, 1, 1, 0), init_sys = NULL, options = optimOptions())
Arguments
z |
an |
order |
Specification of the orders: the five integer components (nb,nc,nd,nf,nk) are order of polynomial B + 1, order of the polynomial C, order of the polynomial D, order of the polynomial F, and the input-output delay respectively |
init_sys |
Linear polynomial model that configures the initial parameterization.
Must be a BJ model. Overrules the |
options |
Estimation Options, setup using
|
Details
SISO BJ models are of the form
y[k] = \frac{B(q^{-1})}{F(q^{-1})}u[k-nk] +
\frac{C(q^{-1})}{D(q^{-1})} e[k]
The orders of Box-Jenkins model are defined as follows:
B(q^{-1}) = b_1 + b_2q^{-1} + \ldots + b_{nb} q^{-nb+1}
C(q^{-1}) = 1 + c_1q^{-1} + \ldots + c_{nc} q^{-nc}
D(q^{-1}) = 1 + d_1q^{-1} + \ldots + d_{nd} q^{-nd}
F(q^{-1}) = 1 + f_1q^{-1} + \ldots + f_{nf} q^{-nf}
The function estimates the coefficients using non-linear least squares
(Levenberg-Marquardt Algorithm)
The data is expected to have no offsets or trends. They can be removed
using the detrend function.
Value
An object of class estpoly containing the following elements:
sys |
an |
fitted.values |
the predicted response |
residuals |
the residuals |
input |
the input data used |
call |
the matched call |
stats |
A list containing the following fields: |
options |
Option set used for estimation. If no custom options were configured, this is a set of default options |
termination |
Termination conditions for the iterative
search used for prediction error minimization:
|
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Sections 14.4.1, 17.5.2, 21.6.3
Examples
data(bjsim)
z <- dataSlice(bjsim,end=1500) # training set
mod_bj <- bj(z,c(2,1,1,1,2))
mod_bj
residplot(mod_bj) # residual plots
Data simulated from an BJ model
Description
This dataset contains 2046 samples simulated from the following BJ model:
y[k] = \frac{0.6q^{-2} - 0.2q^{-3}}{1 - 0.5q^{-1}} u[k] +
\frac{1+0.2q^{-1}}{1 - 0.3q^{-1}} e[k]
Usage
bjsim
Format
an idframe object with 2046 samples, one input and one
output
Details
The model is simulated with a 2046 samples long full-band PRBS input. The noise variance is set to 0.1
Compare the measured output and the predicted output(s)
Description
Plots the output predictions of model(s) superimposed over validation data, data, for comparison.
Usage
compare(data, nahead = 1, ...)
Arguments
data |
validation data in the form of an |
nahead |
number of steps ahead at which to predict (Default:1). For infinite-
step ahead predictions, supply |
... |
models whose predictions are to be compared |
See Also
predict.estpoly for obtaining model predictions
Examples
data(arxsim)
mod1 <- arx(arxsim,c(1,2,2))
mod2 <- oe(arxsim,c(2,1,1))
compare(arxsim,nahead=Inf,mod1,mod2)
Continuous stirred tank reactor data (idframe)
Description
The Process is a model of a Continuous Stirring Tank Reactor,
where the reaction is exothermic and the concentration is
controlled by regulating the coolant flow.
Usage
cstr
Format
an idframe object with 7500 samples, one input and two
outputs
Details
Inputs: q, Coolant Flow l/min Outputs:
- Ca
Concentration mol/l
- T
Temperature Kelvin
Continuous stirred tank reactor data (data.frame)
Description
The Process is a model of a Continuous Stirring Tank Reactor,
where the reaction is exothermic and the concentration is
controlled by regulating the coolant flow.
Usage
cstrData
Format
an data.frame object with 7500 rows and three columns:
q, Ca and T
Details
Inputs: q, Coolant Flow l/min Outputs:
- Ca
Concentration mol/l
- T
Temperature Kelvin
Source
ftp://ftp.esat.kuleuven.be/pub/SISTA/data/process_industry/cstr.dat.gz
Continuous stirred tank reactor data with missing values
Description
This dataset is derived from the cstr dataset with few samples
containing missing values, in one or all variables. It is used to
demonstrate the capabilities of the misdata routine.
Usage
cstr_mis
Format
an idframe object with 7500 samples, one input and two
outputs
See Also
Subset or Resample idframe data
Description
dataSlice is a subsetting method for objects of class idframe. It
extracts the subset of the object data observed between indices start
and end. If a frequency is specified, the series is then re-sampled at the
new frequency.
Usage
dataSlice(data, start = NULL, end = NULL, freq = NULL)
Arguments
data |
an object of class |
start |
the start index |
end |
the end index |
freq |
fraction of the original frequency at which the series to be sampled. |
Details
The dataSlice function extends the window
function for idframe objects
Value
an idframe object
See Also
Examples
data(cstr)
cstrsub <- dataSlice(cstr,start=200,end=400) # extract between indices 200 and 400
cstrTrain <- dataSlice(cstr,end=4500) # extract upto index 4500
cstrTest <- dataSlice(cstr,start=6501) # extract from index 6501 till the end
cstr_new <- dataSlice(cstr,freq=0.5) # resample data at half the original frequency
Remove offsets and linear trends
Description
Removes offsets or trends from data
Usage
detrend(x, type = 0)
Arguments
x |
an object of class |
type |
argument indicating the type of trend to be removed (Default=
|
Details
R by default doesn't allow return of multiple objects. The %=%
operator and g function in this package facillitate this behaviour. See
the examples section for more information.
Value
A list containing two objects: the detrended data and the trend information
See Also
Examples
data(cstr)
datatrain <- dataSlice(cstr,end=4500)
datatest <- dataSlice(cstr,4501)
g(Ztrain,tr) %=% detrend(datatrain) # Remove means
g(Ztest) %=% detrend(datatest,tr)
Estimated polynomial object
Description
Estimated discrete-time polynomial model returned from an estimation routine.
Usage
estpoly(sys, fitted.values, residuals, options = NULL, call, stats,
termination = NULL, input)
Arguments
sys |
an |
fitted.values |
1-step ahead predictions on the training dataset |
residuals |
1-step ahead prediction errors |
options |
optimization specification ser used (applicable for non-linear least squares) |
call |
the matched call |
stats |
a list containing estimation statistics |
termination |
termination criteria for optimization |
input |
input signal of the training data-set |
Details
Do not use estpoly for directly specifing an input-output polynomial model.
idpoly is to be used instead
Estimate empirical transfer function
Description
Estimates the emperical transfer function from the data by taking the ratio of the fourier transforms of the output and the input variables
Usage
etfe(data, n = 128)
Arguments
data |
an object of class |
n |
frequency spacing (Default: |
Value
an idfrd object containing the estimated frequency response
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Sections 5.3 and 20.4.2
See Also
Examples
data(arxsim)
frf <- etfe(arxsim)
Fit Characteristics
Description
Returns quantitative assessment of the estimated model as a list
Usage
fitch(x)
Arguments
x |
the estimated model |
Value
A list containing the following elements
MSE |
Mean Square Error measure of how well the response of the model fits the estimation data |
FPE |
Final Prediction Error |
FitPer |
Normalized root mean squared error (NRMSE) measure of how well the response of the model fits the estimation data, expressed as a percentage. |
AIC |
Raw Akaike Information Citeria (AIC) measure of model quality |
AICc |
Small sample-size corrected AIC |
nAIC |
Normalized AIC |
BIC |
Bayesian Information Criteria (BIC) |
Frequency response data
Description
This dataset contains frequency response data of an unknown SISO system.
Usage
frd
Format
an idfrd object with response at 128 frequency points
Parameter covariance of the identified model
Description
Obtain the parameter covariance matrix of the linear, identified parametric model
Usage
getcov(sys)
Arguments
sys |
a linear, identified parametric model |
S3 class for storing input-output data.
Description
idframe is an S3 class for storing and manipulating input-ouput data. It supports discrete time and frequency domain data.
Usage
idframe(output, input = NULL, Ts = 1, start = 0, end = NULL,
unit = c("seconds", "minutes", "hours", "days")[1])
Arguments
output |
dataframe/matrix/vector containing the outputs |
input |
dataframe/matrix/vector containing the inputs |
Ts |
sampling interval (Default: 1) |
start |
Time of the first observation |
end |
Time of the last observation Optional Argument |
unit |
Time unit (Default: "seconds") |
Value
an idframe object
See Also
plot.idframe, the plot method for idframe objects
Examples
dataMatrix <- matrix(rnorm(1000),ncol=5)
data <- idframe(output=dataMatrix[,3:5],input=dataMatrix[,1:2],Ts=1)
S3 class constructor for storing frequency response data
Description
S3 class constructor for storing frequency response data
Usage
idfrd(respData, freq, Ts, spec = NULL, covData = NULL, noiseCov = NULL)
Arguments
respData |
frequency response data. For SISO systems, supply a vector of frequency response values. For MIMO systems with Ny outputs and Nu inputs, supply an array of size c(Ny,Nu,Nw). |
freq |
frequency points of the response |
Ts |
sampling time of data |
spec |
power spectra and cross spectra of the system output disturbances (noise). Supply an array of size (Ny,Ny,Nw) |
covData |
response data covariance matrices. Supply an array of size (Ny,Nu,Nw,2,2). covData[ky,ku,kw,,] is the covariance matrix of respData[ky,ku,kw] |
noiseCov |
power spectra variance. Supply an array of size (Ny,Ny,Nw) |
Value
an idfrd object
See Also
plot.idfrd for generating bode plots,
spa and etfe for estimating the
frequency response given input/output data
function to generate input singals (rgs/rbs/prbs/sine)
Description
idinput is a function for generating input signals (rgs/rbs/prbs/sine) for identification purposes
Usage
idinput(n, type = "rgs", band = c(0, 1), levels = c(-1, 1))
Arguments
n |
integer length of the input singal to be generated |
type |
the type of input signal to be generated. 'rgs' - generates random gaussian signal 'rbs' - generates random binary signal 'prbs' - generates pseudorandom binary signal 'sine' - generates a signal that is a sum of sinusoids Default value is type='rgs' |
band |
determines the frequency content of the signal. For type='rbs'/'sine'/, band = [wlow,whigh] which specifies the lower and the upper bound of the passband frequencies(expressed as fractions of Nyquist frequency). Default is c(0,1) For type='prbs', band=[0,B] where B is such that the singal is constant over 1/B (clock period). Default is c(0,1) |
levels |
row vector defining the input level. It is of the form levels=c(minu, maxu) For 'rbs','prbs', 'sine', the generated signal always between minu and maxu. For 'rgs', minu=mean value of signal minus one standard deviation and maxu=mean value of signal plus one standard deviation Default value is levels=c(-1,1) |
Polynomial model with identifiable parameters
Description
Creates a polynomial model with identifiable coefficients
Usage
idpoly(A = 1, B = 1, C = 1, D = 1, F1 = 1, ioDelay = 0, Ts = 1,
noiseVar = 1, intNoise = F, unit = c("seconds", "minutes", "hours",
"days")[1])
Arguments
A |
autoregressive coefficients |
B, F1 |
coefficients of the numerator and denominator respectively of the deterministic model between the input and output |
C, D |
coefficients of the numerator and denominator respectively of the stochastic model |
ioDelay |
the delay in the input-output channel |
Ts |
sampling interval |
noiseVar |
variance of the white noise source (Default= |
intNoise |
Logical variable indicating presence or absence of integrator
in the noise channel (Default= |
unit |
time unit (Default= |
Details
Discrete-time polynomials are of the form
A(q^{-1}) y[k] = \frac{B(q^{-1})}{F1(q^{-1})} u[k] +
\frac{C(q^{-1})}{D(q^{-1})} e[k]
Examples
# define output-error model
mod_oe <- idpoly(B=c(0.6,-0.2),F1=c(1,-0.5),ioDelay = 2,Ts=0.1,
noiseVar = 0.1)
# define box-jenkins model with unit variance
B <- c(0.6,-0.2)
C <- c(1,-0.3)
D <- c(1,1.5,0.7)
F1 <- c(1,-0.5)
mod_bj <- idpoly(1,B,C,D,F1,ioDelay=1)
Estimate Impulse Response Coefficients
Description
impulseest is used to estimate impulse response coefficients from
the data
Usage
impulseest(x, M = 30, K = NULL, regul = F, lambda = 1)
Arguments
x |
an object of class |
M |
Order of the FIR Model (Default: |
K |
Transport delay in the estimated impulse response (Default:NULL) |
regul |
Parameter indicating whether regularization should be
used. (Default: |
lambda |
The value of the regularization parameter. Valid only if
|
Details
The IR Coefficients are estimated using linear least squares. Future Versions will provide support for multivariate data.
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Sections 17.4.11 and 20.2
See Also
Examples
uk <- rnorm(1000,1)
yk <- filter (uk,c(0.9,-0.4),method="recursive") + rnorm(1000,1)
data <- idframe(output=data.frame(yk),input=data.frame(uk))
fit <- impulseest(data)
impulseplot(fit)
Impulse Response Plots
Description
Plots the estimated IR coefficients along with the significance limits at each lag.
Usage
impulseplot(model, sd = 2)
Arguments
model |
an object of class |
sd |
standard deviation of the confidence region (Default: |
See Also
Output or Input-data
Description
Extract output-data or input-data in idframe objects
Usage
inputData(x, series)
Arguments
x |
|
series |
the indices to extract |
Extract or set series' names
Description
Extract or set names of series in input or output
Usage
inputNames(x) <- value
Arguments
x |
|
value |
vector of strings |
ARX model estimation using instrumental variable method
Description
Estimates an ARX model of the specified order from input-output data using the instrument variable method. If arbitrary instruments are not supplied by the user, the instruments are generated using the arx routine
Usage
iv(z, order = c(0, 1, 0), x = NULL)
Arguments
z |
an idframe object containing the data |
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 |
x |
instrument variable matrix. x must be of the same size as the output
data. (Default: |
Value
An object of class estpoly containing the following elements:
sys |
an |
fitted.values |
the predicted response |
residuals |
the residuals |
input |
the input data used |
call |
the matched call |
stats |
A list containing the following fields: |
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Sections 21.7.1, 21.7.2
Lennart Ljung (1999), System Identification: Theory for the User, 2nd Edition, Prentice Hall, New York. Section 7.6
See Also
Examples
data(arxsim)
mod_iv <- iv(arxsim,c(2,1,1))
ARX model estimation using four-stage instrumental variable method
Description
Estimates an ARX model of the specified order from input-output data using the instrument variable method. The estimation algorithm is insensitive to the color of the noise term.
Usage
iv4(z, order = c(0, 1, 0))
Arguments
z |
an idframe object containing the data |
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 |
Details
Estimation is performed in 4 stages. The first stage uses the arx function. The resulting model generates the instruments for a second-stage IV estimate. The residuals obtained from this model are modeled using a sufficently high-order AR model. At the fourth stage, the input-output data is filtered through this AR model and then subjected to the IV function with the same instrument filters as in the second stage.
Value
An object of class estpoly containing the following elements:
sys |
an |
fitted.values |
the predicted response |
residuals |
the residuals |
input |
the input data used |
call |
the matched call |
stats |
A list containing the following fields: |
References
Lennart Ljung (1999), System Identification: Theory for the User, 2nd Edition, Prentice Hall, New York. Section 15.3
See Also
Examples
mod_dgp <- idpoly(A=c(1,-0.5),B=c(0.6,-.2),C=c(1,0.6),ioDelay = 2,noiseVar = 0.1)
u <- idinput(400,"prbs")
y <- sim(mod_dgp,u,addNoise=TRUE)
z <- idframe(y,u)
mod_iv4 <- iv4(z,c(1,2,2))
Replace Missing Data by Interpolation
Description
Function for replacing missing values with interpolated ones. This is an
extension of the na.approx function from the zoo package.
The missing data is indicated using the value NA.
Usage
misdata(data)
Arguments
data |
an object of class |
Value
data (an idframe object) with missing data replaced.
See Also
Examples
data(cstr_mis)
summary(cstr_mis) # finding out the number of NAs
cstr <- misdata(cstr_mis)
Number of series in input or output
Description
Number of series in input or output in a idframe object
Usage
nInputSeries(data)
Arguments
data |
|
Estimate Output-Error Models
Description
Fit an output-error model of the specified order given the input-output data
Usage
oe(x, order = c(1, 1, 0), init_sys = NULL, options = optimOptions())
Arguments
x |
an object of class |
order |
Specification of the orders: the four integer components (nb,nf,nk) are order of polynomial B + 1, order of the polynomial F, and the input-output delay respectively |
init_sys |
Linear polynomial model that configures the initial parameterization.
Must be an OE model. Overrules the |
options |
Estimation Options, setup using
|
Details
SISO OE models are of the form
y[k] + f_1 y[k-1] + \ldots + f_{nf} y[k-nf] = b_{nk} u[k-nk] +
\ldots + b_{nk+nb} u[k-nk-nb] + f_{1} e[k-1] + \ldots f_{nf} e[k-nf]
+ e[k]
The function estimates the coefficients using non-linear least squares
(Levenberg-Marquardt Algorithm)
The data is expected to have no offsets or trends. They can be removed
using the detrend function.
Value
An object of class estpoly containing the following elements:
sys |
an |
fitted.values |
the predicted response |
residuals |
the residuals |
input |
the input data used |
call |
the matched call |
stats |
A list containing the following fields: |
options |
Option set used for estimation. If no custom options were configured, this is a set of default options |
termination |
Termination conditions for the iterative
search used for prediction error minimization:
|
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Sections 14.4.1, 17.5.2, 21.6.3
Examples
data(oesim)
z <- dataSlice(oesim,end=1533) # training set
mod_oe <- oe(z,c(2,1,2))
mod_oe
plot(mod_oe) # plot the predicted and actual responses
Data simulated from an OE model
Description
This dataset contains 2555 samples simulated from the following OE model:
y[k] = \frac{0.6q^{-2} - 0.2q^{-3}}{1 - 0.5q^{-1}} u[k] + e[k]
Usage
oesim
Format
an idframe object with 2555 samples, one input and one
output
Details
The model is simulated with a 2555 samples long full-band PRBS input. The noise variance is set to 0.1
Create optimization options
Description
Specify optimization options that are to be passed to the numerical estimation routines
Usage
optimOptions(tol = 0.01, maxIter = 20, LMinit = 0.01, LMstep = 2,
display = c("off", "on")[1])
Arguments
tol |
Minimum 2-norm of the gradient (Default: |
maxIter |
Maximum number of iterations to be performed |
LMinit |
Starting value of search-direction length
in the Levenberg-Marquardt method (Default: |
LMstep |
Size of the Levenberg-Marquardt step (Default: |
display |
Argument whether to display iteration details or not
(Default: |
Plotting idframe objects
Description
Plotting method for objects inherting from class idframe
Usage
## S3 method for class 'idframe'
plot(x, col = "steelblue", lwd = 1, main = NULL,
size = 12, ...)
Arguments
x |
an |
col |
line color, to be passed to plot.(Default= |
lwd |
line width, in millimeters(Default= |
main |
the plot title. (Default = |
size |
text size (Default = |
... |
additional arguments |
Examples
data(cstr)
plot(cstr,col="blue")
Plotting idfrd objects
Description
Generates the bode plot of the given frequency response data. It uses the ggplot2 plotting engine
Usage
## S3 method for class 'idfrd'
plot(x, col = "steelblue", lwd = 1, ...)
Arguments
x |
An object of class |
col |
a specification for the line colour (Default : |
lwd |
the line width, a positive number, defaulting to 1 |
... |
additional arguments |
See Also
Examples
data(frd)
plot(frd)
Predictions of identified model
Description
Predicts the output of an identified model (estpoly) object K steps ahead.
Usage
## S3 method for class 'estpoly'
predict(object, newdata = NULL, nahead = 1, ...)
Arguments
object |
|
newdata |
optional dataset to be used for predictions. If not supplied, predictions are made on the training set. |
nahead |
number of steps ahead at which to predict (Default:1). For infinite-
step ahead predictions or pure simulation, supply |
... |
other arguments |
Value
Time-series containing the predictions
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Chapter 18
Examples
data(arxsim)
mod1 <- oe(arxsim,c(2,1,1))
Yhat <- predict(mod1,arxsim) # 1-step ahead predictions
Yhat_2 <- predict(mod1,arxsim,nahead=2) # 2-step ahead predictions
Yhat_inf <- predict(mod1,arxsim,nahead=Inf) # Infinite-step ahead predictions
Estimate parameters of ARX recursively
Description
Estimates the parameters of a single-output ARX model of the specified order from data using the recursive weighted least-squares algorithm.
Usage
rarx(x, order = c(1, 1, 1), lambda = 0.95)
Arguments
x |
an object of class |
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 |
lambda |
Forgetting factor(Default= |
Value
A list containing the following objects
- theta
Estimated parameters of the model. The
k^{th}row contains the parameters associated with thek^{th}sample. Each row inthetahas the following format:
theta[i,:]=[a1,a2,...,ana,b1,...bnb]- yhat
Predicted value of the output, according to the current model - parameters based on all past data
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Section 25.1.3
Lennart Ljung (1999), System Identification: Theory for the User, 2nd Edition, Prentice Hall, New York. Section 11.2
Examples
Gp1 <- idpoly(c(1,-0.9,0.2),2,ioDelay=2,noiseVar = 0.1)
Gp2 <- idpoly(c(1,-1.2,0.35),2.5,ioDelay=2,noiseVar = 0.1)
uk = idinput(2044,'prbs',c(0,1/4)); N = length(uk);
N1 = round(0.35*N); N2 = round(0.4*N); N3 = N-N1-N2;
yk1 <- sim(Gp1,uk[1:N1],addNoise = TRUE)
yk2 <- sim(Gp2,uk[N1+1:N2],addNoise = TRUE)
yk3 <- sim(Gp1,uk[N1+N2+1:N3],addNoise = TRUE)
yk <- c(yk1,yk2,yk3)
z <- idframe(yk,uk,1)
g(theta,yhat) %=% rarx(z,c(2,1,2))
Data input into a idframe object
Description
Read the contents of a data.frame/matrix into a idframe object.
Usage
read.idframe(data, ninputs = NULL, Ts = 1, unit = c("seconds", "minutes",
"hours", "days")[1])
Arguments
data |
a |
ninputs |
the number of input columns. (Default: 0) |
Ts |
sampling interval (Default: 1) |
unit |
Time Unit (Default: "seconds") |
Value
an idframe object
Examples
data(cstrData)
data <- read.idframe(cstrData,ninputs=1,Ts= 1,unit="minutes")
Read the contents of a table-formatted file
Description
Read the contents of an file in table format into a idframe object.
Usage
read.table.idframe(file, header = TRUE, sep = ",", ninputs = 0, Ts = 1,
unit = c("seconds", "minutes", "hours", "days")[1], ...)
Arguments
file |
the path to the file to read |
header |
a logical value indicating whether the first row corresponding to
the first element of the rowIndex vector contains the names of the variables.
(Default: |
sep |
the field separator character. Values on each line of the file are
separated by this character. (Default: |
ninputs |
the number of input columns. (Default: 0) |
Ts |
sampling interval (Default: 1) |
unit |
Time Unit (Default: "seconds") |
... |
additional arguments to be passed to the |
Details
The read.table.idframe function uses the read.table function,
provided by the utils package, to read data from a table-formatted file and then calls the
read.idframe function to read the data into a idframe object
Value
an idframe object
See Also
Examples
dataMatrix <- data.frame(matrix(rnorm(1000),ncol=5))
colnames(dataMatrix) <- c("u1","u2","y1","y2","y3")
write.csv(dataMatrix,file="test.csv",row.names=FALSE)
data <- read.table.idframe("test.csv",ninputs=2,unit="minutes")
Plot residual characteristics
Description
Computes the 1-step ahead prediction errors (residuals) for an estimated polynomial model, and plots auto-correlation of the residuals and the cross-correlation of the residuals with the input signals.
Usage
residplot(model, newdata = NULL)
Arguments
model |
estimated polynomial model |
newdata |
an optional dataset on which predictions are to be computed. If not supplied, predictions are computed on the training dataset. |
Simulate response of dynamic system
Description
Simulate the response of a system to a given input
Usage
sim(model, input, addNoise = F, innov = NULL, seed = NULL)
Arguments
model |
the linear system to simulate |
input |
a vector/matrix containing the input |
addNoise |
logical variable indicating whether to add noise to the
response model. (Default: |
innov |
an optional times series of innovations. If not supplied (specified
as |
seed |
integer indicating the seed value of the random number generator. Useful for reproducibility purposes. |
Details
The routine is currently built only for SISO systems. Future versions will include support for MIMO systems.
Value
a vector containing the simulated output
Examples
# ARX Model
u <- idinput(300,"rgs")
model <- idpoly(A=c(1,-1.5,0.7),B=c(0.8,-0.25),ioDelay=1,
noiseVar=0.1)
y <- sim(model,u,addNoise=TRUE)
Estimate frequency response
Description
Estimates frequency response and noise spectrum from data with fixed resolution using spectral analysis
Usage
spa(x, winsize = NULL, freq = NULL)
Arguments
x |
an |
winsize |
lag size of the Hanning window (Default: |
freq |
frequency points at which the response is evaluated
(Default: |
Value
an idfrd object containing the estimated frequency response
and the noise spectrum
References
Arun K. Tangirala (2015), Principles of System Identification: Theory and Practice, CRC Press, Boca Raton. Sections 16.5 and 20.4
Examples
data(arxsim)
frf <- spa(arxsim)
Step Response Plots
Description
Plots the step response of a system, given the IR model
Usage
step(model)
Arguments
model |
an object of class |
See Also
Examples
uk <- rnorm(1000,1)
yk <- filter (uk,c(0.9,-0.4),method="recursive") + rnorm(1000,1)
data <- idframe(output=data.frame(yk),input=data.frame(uk))
fit <- impulseest(data)
step(fit)
Sampling times of IO data
time creates the vector of times at which data was sampled. frequency returns the number of damples per unit time and deltat the time-interval
between observations
Description
Sampling times of IO data
time creates the vector of times at which data was sampled. frequency returns the number of damples per unit time and deltat the time-interval
between observations
Usage
time(x)
Arguments
x |
a idframe object, or a univariate or multivariate time-series, or a vector or matrix |