Documentation

System Identification Toolbox Functions

Data Preparation

Represent Data

iddata Time- or frequency-domain data
idfrd Frequency-response data or model
idinput Generate input signals
sim Simulate response of identified models to arbitrary inputs
size Query output/input/array dimensions of input–output model and number of frequencies of FRD model

Select Data for Estimation

fselect Select frequency points or range in FRD model
getexp Specific experiments from multiple-experiment data set
merge (iddata) Merge data sets into iddata object
fcat Concatenate FRD models along frequency dimension

Analyze Data

bode Bode plot of frequency response, magnitude and phase of frequency response
bodemag Bode magnitude response of LTI models
plot Plot input-output data
advice Analysis and recommendations for data or estimated linear models
delayest Estimate time delay (dead time) from data
isreal Determine whether model parameters or data values are real
realdata Determine whether iddata is based on real-valued signals
feedback Identify possible feedback data
pexcit Level of excitation of input signals
impulseest Nonparameteric impulse response estimation
etfe Estimate empirical transfer functions and periodograms
spa Estimate frequency response with fixed frequency resolution using spectral analysis
spafdr Estimate frequency response and spectrum using spectral analysis with frequency-dependent resolution
iddataplotOptions Options set for iddata/plot

Preprocess Data

detrend Subtract offset or trend from data signals
retrend Add offsets or trends to data signals
diff Difference signals in iddata objects
idfilt Filter data using user-defined passbands, general filters, or Butterworth filters
misdata Reconstruct missing input and output data
nkshift Shift data sequences
idresamp Resample time-domain data by decimation or interpolation
resample Resample time-domain data by decimation or interpolation (requires Signal Processing Toolbox software)
getTrend Data offset and trend information
chgFreqUnit Change frequency units of frequency-response data model
fdel Delete specified data from frequency response data (FRD) models
TrendInfo Offset and linear trend slope values for detrending data

Transform Data

fft Transform iddata object to frequency domain data
ifft Transform iddata objects from frequency to time domain
etfe Estimate empirical transfer functions and periodograms
spa Estimate frequency response with fixed frequency resolution using spectral analysis
spafdr Estimate frequency response and spectrum using spectral analysis with frequency-dependent resolution

Linear Model Identification

Process Models

procest Estimate process model using time or frequency data
idproc Continuous-time process model with identifiable parameters
pem Prediction error estimate for linear and nonlinear model
idpar Create parameter for initial states and input level estimation
delayest Estimate time delay (dead time) from data
init Set or randomize initial parameter values
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
getpar Obtain attributes such as values and bounds of linear model parameters
setpar Set attributes such as values and bounds of linear model parameters
procestOptions Options set for procest

Input-Output Polynomial Models

arx Estimate parameters of ARX or AR model using least squares
armax Estimate parameters of ARMAX model using time-domain data
bj Estimate Box-Jenkins polynomial model using time domain data
iv4 ARX model estimation using four-stage instrumental variable method.
ivx ARX model estimation using instrumental variable method with arbitrary instruments
oe Estimate Output-Error polynomial model using time or frequency domain data
polyest Estimate polynomial model using time- or frequency-domain data
idpoly Polynomial model with identifiable parameters
pem Prediction error estimate for linear and nonlinear model
arxstruc Compute and compare loss functions for single-output ARX models
ivstruc Loss functions for sets of ARX model structures
selstruc Select model order for single-output ARX models
struc Generate model-order combinations for single-output ARX model estimation
arxRegul Determine regularization constants for ARX model estimation
delayest Estimate time delay (dead time) from data
init Set or randomize initial parameter values
polydata Access polynomial coefficients and uncertainties of identified model
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
getpar Obtain attributes such as values and bounds of linear model parameters
setpar Set attributes such as values and bounds of linear model parameters
setPolyFormat Specify format for B and F polynomials of multi-input polynomial model for backward compatibility
rarmax Estimate recursively parameters of ARMAX or ARMA models
rarx Estimate parameters of ARX or AR models recursively
rbj Estimate recursively parameters of Box-Jenkins models
roe Estimate recursively output-error models (IIR-filters)
rpem Estimate general input-output models using recursive prediction-error minimization method
rplr Estimate general input-output models using recursive pseudolinear regression method
segment Segment data and estimate models for each segment
armaxOptions Option set for armax
arxOptions Option set for arx
arxRegulOptions Option set for arxRegul
bjOptions Option set for bj
iv4Options Option set for iv4
oeOptions Option set for oe
polyestOptions Option set for polyest

State-Space Models

ssest Estimate state-space model using time or frequency domain data
ssregest Estimate state-space model by reduction of regularized ARX model
n4sid Estimate state-space model using a subspace method.
idss State-space model with identifiable parameters
pem Prediction error estimate for linear and nonlinear model
delayest Estimate time delay (dead time) from data
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
getpar Obtain attributes such as values and bounds of linear model parameters
setpar Set attributes such as values and bounds of linear model parameters
ssform Quick configuration of state-space model structure
init Set or randomize initial parameter values
idpar Create parameter for initial states and input level estimation
idssdata State-space data of identified system
findstates Estimate initial states of a model
ssestOptions Option set for ssest
ssregestOptions Option set for ssregest
n4sidOptions Option set for n4sid
findstatesOptions Option set for findstates

Transfer Function Models

tfest Transfer function estimation
idtf Transfer function model with identifiable parameters
pem Prediction error estimate for linear and nonlinear model
delayest Estimate time delay (dead time) from data
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
getpar Obtain attributes such as values and bounds of linear model parameters
setpar Set attributes such as values and bounds of linear model parameters
tfdata Access transfer function data
init Set or randomize initial parameter values
tfestOptions Options set for tfest

Linear Grey-Box Models

greyest Linear grey-box model estimation
idgrey Linear ODE (grey-box model) with identifiable parameters
pem Prediction error estimate for linear and nonlinear model
findstates Estimate initial states of a model
init Set or randomize initial parameter values
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
getpar Obtain attributes such as values and bounds of linear model parameters
setpar Set attributes such as values and bounds of linear model parameters
findstatesOptions Option set for findstates

Frequency-Response Models

etfe Estimate empirical transfer functions and periodograms
spa Estimate frequency response with fixed frequency resolution using spectral analysis
spafdr Estimate frequency response and spectrum using spectral analysis with frequency-dependent resolution
idfrd Frequency-response data or model
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
bode Bode plot of frequency response, magnitude and phase of frequency response
bodemag Bode magnitude response of LTI models
freqresp Frequency response over grid
chgFreqUnit Change frequency units of frequency-response data model

Correlation Models

cra Estimate impulse response using prewhitened-based correlation analysis
impulseest Nonparameteric impulse response estimation
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
impulseestOptions Options set for impulseest

Nonlinear Model Identification

Nonlinear ARX Models

nlarx Estimate parameters of a nonlinear ARX model
idnlarx Nonlinear ARX model
pem Prediction error estimate for linear and nonlinear model
isnlarx Detect nonlinearity in estimation data
customnet Custom nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
linear Class representing linear nonlinearity estimator for nonlinear ARX models
neuralnet Class representing neural network nonlinearity estimator for nonlinear ARX models
polyreg Powers and products of standard regressors
treepartition Class representing binary-tree nonlinearity estimator for nonlinear ARX models
wavenet Class representing wavelet network nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
customreg Custom regressor for nonlinear ARX models
sigmoidnet Class representing sigmoid network nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
addreg Add custom regressors to nonlinear ARX model
getreg Regressor expressions and numerical values in nonlinear ARX model
evaluate Value of nonlinearity estimator at given input
plot Plot nonlinearity of nonlinear ARX model
sim(idnlarx) Simulate nonlinear ARX model
findop Compute operating point for Nonlinear ARX model
operspec Construct operating point specification object for idnlarx model
linearize Linearize nonlinear ARX model
linapp Linear approximation of nonlinear ARX and Hammerstein-Wiener models for given input
findstates Estimate initial states of a model
data2state(idnlarx) Map past input/output data to current states of nonlinear ARX model
init Set or randomize initial parameter values
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
getDelayInfo Get input/output delay information for idnlarx model structure
nlarxOptions Option set for nlarx
findopOptions Option set for findop
findstatesOptions Option set for findstates

Hammerstein-Wiener Models

nlhw Estimate a Hammerstein-Wiener model
idnlhw Hammerstein-Wiener model
pem Prediction error estimate for linear and nonlinear model
customnet Custom nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
deadzone Class representing dead-zone nonlinearity estimator for Hammerstein-Wiener models
poly1d Class representing single-variable polynomial nonlinear estimator for Hammerstein-Wiener models
pwlinear Class representing piecewise-linear nonlinear estimator for Hammerstein-Wiener models
saturation Class representing saturation nonlinearity estimator for Hammerstein-Wiener models
sigmoidnet Class representing sigmoid network nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
unitgain Specify absence of nonlinearities for specific input or output channels in Hammerstein-Wiener models
wavenet Class representing wavelet network nonlinearity estimator for nonlinear ARX and Hammerstein-Wiener models
evaluate Value of nonlinearity estimator at given input
plot Plot input and output nonlinearity, and linear responses of Hammerstein-Wiener model
sim(idnlhw) Simulate Hammerstein-Wiener model
findop Compute operating point for Hammerstein-Wiener model
operspec Construct operating point specification object for idnlhw model
linearize Linearize Hammerstein-Wiener model
linapp Linear approximation of nonlinear ARX and Hammerstein-Wiener models for given input
findstates Estimate initial states of a model
init Set or randomize initial parameter values
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
nlhwOptions Option set for nlhw
findopOptions Option set for findop
findstatesOptions Option set for findstates

Nonlinear Grey-Box Models

nlgreyest Estimate the parameters of a nonlinear grey-box model
idnlgrey Nonlinear grey-box model
pem Prediction error estimate for linear and nonlinear model
findstates Estimate initial states of a model
init Set or randomize initial parameter values
getinit Values of idnlgrey model initial states
setinit Set initial states of idnlgrey model object
getpar Parameter values and properties of idnlgrey model parameters
setpar Set initial parameter values of idnlgrey model object
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
sim(idnlgrey) Simulate nonlinear ODE model
nlgreyestOptions Option set for nlgreyest
findstatesOptions Option set for findstates

Grey-Box Model Estimation

greyest Linear grey-box model estimation
nlgreyest Estimate the parameters of a nonlinear grey-box model
idgrey Linear ODE (grey-box model) with identifiable parameters
idnlgrey Nonlinear grey-box model
pem Prediction error estimate for linear and nonlinear model
findstates Estimate initial states of a model
init Set or randomize initial parameter values
getinit Values of idnlgrey model initial states
setinit Set initial states of idnlgrey model object
getpar Parameter values and properties of idnlgrey model parameters
setpar Set initial parameter values of idnlgrey model object
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
sim(idnlgrey) Simulate nonlinear ODE model
greyestOptions Option set for greyest
nlgreyestOptions Option set for nlgreyest
findstatesOptions Option set for findstates

Time-Series Model Identification

ar Estimate parameters of AR model for scalar time series
armax Estimate parameters of ARMAX model using time-domain data
arx Estimate parameters of ARX or AR model using least squares
etfe Estimate empirical transfer functions and periodograms
spa Estimate frequency response with fixed frequency resolution using spectral analysis
spafdr Estimate frequency response and spectrum using spectral analysis with frequency-dependent resolution
ivar AR model estimation using instrumental variable method
n4sid Estimate state-space model using a subspace method.
ssest Estimate state-space model using time or frequency domain data
pem Prediction error estimate for linear and nonlinear model
nlarx Estimate parameters of a nonlinear ARX model
idpoly Polynomial model with identifiable parameters
idss State-space model with identifiable parameters
idnlarx Nonlinear ARX model
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
init Set or randomize initial parameter values
noise2meas Noise component of model
spectrum Output power spectrum of time series models
forecast Forecast linear system response into future
arOptions Option set for ar
forecastOptions Option set for forecast
simOptions Option set for sim

Model Validation

Compare Output with Measured Data

compare Compare model output and measured output
goodnessOfFit Goodness of fit between test and reference data
findstates Estimate initial states of a model
idpar Create parameter for initial states and input level estimation
compareOptions Option set for compare
findstatesOptions Option set for findstates

Residual Analysis

resid Compute and test model residuals (prediction errors)
pe Prediction error for an identified model
fpe Akaike Final Prediction Error for estimated model
aic Akaike Information Criterion for estimated model
peOptions Option set for pe

Uncertainty Analysis

present Display model information, including estimated uncertainty
simsd Simulate linear models with uncertainty using Monte Carlo method
freqresp Frequency response over grid
rsample Random sampling of linear identified systems
showConfidence Display confidence regions on response plots for identified models
getcov Parameter covariance of linear identified parametric model
setcov Set parameter covariance data in identified model
translatecov Translate parameter covariance across model operations
step Step response plot of dynamic system
stepplot Plot step response and return plot handle
impulse Impulse response plot of dynamic system; impulse response data
bode Bode plot of frequency response, magnitude and phase of frequency response
bodemag Bode magnitude response of LTI models
nyquist Nyquist plot of frequency response
nyquistplot Nyquist plot with additional plot customization options
iopzmap Plot pole-zero map for I/O pairs of model
iopzplot Plot pole-zero map for I/O pairs and return plot handle
tfdata Access transfer function data
zpkdata Access zero-pole-gain data
simsdOptions Option set for simsd

Model Analysis

Continuous- and Discrete-Time Conversions

c2d Convert model from continuous to discrete time
d2c Convert model from discrete to continuous time
d2d Resample discrete-time model
translatecov Translate parameter covariance across model operations
c2dOptions Create option set for continuous- to discrete-time conversions
d2cOptions Create option set for discrete- to continuous-time conversions
d2dOptions Create option set for discrete-time resampling

Model Type and Other Transformations

idfrd Frequency-response data or model
idpoly Polynomial model with identifiable parameters
idtf Transfer function model with identifiable parameters
idss State-space model with identifiable parameters
canon State-space canonical realization
balred Model order reduction
noisecnv Transform identified linear model with noise channels to model with measured channels only
translatecov Translate parameter covariance across model operations
merge Merge estimated models
noise2meas Noise component of model
absorbDelay Replace time delays by poles at z = 0 or phase shift
chgTimeUnit Change time units of dynamic system
chgFreqUnit Change frequency units of frequency-response data model
fdel Delete specified data from frequency response data (FRD) models
stack Build model array by stacking models or model arrays along array dimensions
ss2ss State coordinate transformation for state-space model

Linearization of Nonlinear Models

linapp Linear approximation of nonlinear ARX and Hammerstein-Wiener models for given input
idnlarx/findop Compute operating point for Nonlinear ARX model
idnlarx/linearize Linearize nonlinear ARX model
idnlhw/findop Compute operating point for Hammerstein-Wiener model
idnlhw/linearize Linearize Hammerstein-Wiener model
findopOptions Option set for findop

Data Extraction

polydata Access polynomial coefficients and uncertainties of identified model
ssdata Access state-space model data
idssdata State-space data of identified system
tfdata Access transfer function data
zpkdata Access zero-pole-gain data
frdata Access data for frequency response data (FRD) object
freqresp Frequency response over grid
getpvec Model parameters and associated uncertainty data
setpvec Modify value of model parameters
getcov Parameter covariance of linear identified parametric model
setcov Set parameter covariance data in identified model
get Access model property values
set Set or modify model properties
nparams Number of model parameters
ndims Query number of dimensions of dynamic system model or model array
order Query model order
pole Compute poles of dynamic system
zero Zeros and gain of SISO dynamic system
size Query output/input/array dimensions of input–output model and number of frequencies of FRD model
damp Natural frequency and damping ratio
dcgain Low-frequency (DC) gain of LTI system
bandwidth Frequency response bandwidth

Simulation and Prediction

sim Simulate response of identified models to arbitrary inputs
sim(idnlarx) Simulate nonlinear ARX model
sim(idnlgrey) Simulate nonlinear ODE model
sim(idnlhw) Simulate Hammerstein-Wiener model
simsd Simulate linear models with uncertainty using Monte Carlo method
predict K-step ahead prediction
rsample Random sampling of linear identified systems
forecast Forecast linear system response into future
idinput Generate input signals
simOptions Option set for sim
simsdOptions Option set for simsd
forecastOptions Option set for forecast
predictOptions Option set for predict
forecastOptions Option set for forecast

Response Computation and Visualization

sim Simulate response of identified models to arbitrary inputs
sim(idnlarx) Simulate nonlinear ARX model
sim(idnlgrey) Simulate nonlinear ODE model
sim(idnlhw) Simulate Hammerstein-Wiener model
bode Bode plot of frequency response, magnitude and phase of frequency response
bodeplot Plot Bode frequency response with additional plot customization options
bodemag Bode magnitude response of LTI models
step Step response plot of dynamic system
stepplot Plot step response and return plot handle
stepinfo Rise time, settling time, and other step response characteristics
nyquist Nyquist plot of frequency response
nyquistplot Nyquist plot with additional plot customization options
impulse Impulse response plot of dynamic system; impulse response data
impulseplot Plot impulse response and return plot handle
pzmap Pole-zero plot of dynamic system
pzplot Pole-zero map of dynamic system model with plot customization options
iopzmap Plot pole-zero map for I/O pairs of model
iopzplot Plot pole-zero map for I/O pairs and return plot handle
spectrum Output power spectrum of time series models
spectrumplot Plot disturbance spectrum of linear identified models
lsim Simulate time response of dynamic system to arbitrary inputs
lsimplot Simulate response of dynamic system to arbitrary inputs and return plot handle
lsiminfo Compute linear response characteristics
showConfidence Display confidence regions on response plots for identified models
findstates Estimate initial states of a model
stepDataOptions Options set for step
bodeoptions Create list of Bode plot options
nyquistoptions List of Nyquist plot options
timeoptions Create list of time plot options
getoptions Return @PlotOptions handle or plot options property
setoptions Set plot options for response plot
pzoptions Create list of pole/zero plot options
spectrumoptions Option set for spectrumplot
identpref Set System Identification Toolbox preferences
findstatesOptions Option set for findstates
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