Appendix 1. Main Functions of the System Identification Toolbox

Main functions of the System Identification Toolbox

Func-

Description

tion

Main functions

idhelp is used to call up help on the toolbox's capabilities; iddemo is used to call up demonstration examples; ident is the command that invokes the graphical user interface; midprefs is the command that sets (changes) the directory for the mid-

prefs.mat file, which stores information about the initial parameters of the graphical user interface when it is opened

predict

the command produces a forecast of the plant's output based on its theta-

model, taking into account information about its previous actual

output values (recommended for computing the forecast

of time-series values)

pe

computes the model error for a given input and known

output of the plant

idsim

returns the output of a theta-format model

iddata

creates a data object file

detrend

removes the trend from a data set

idfilt

filters data using a Butterworth filter

idinput

generates input signals for identification

merge

merges several experiments

misdate

estimates and replaces missing input and output data in

a file created using the iddata command

resample restores the shape of a quantized data signal by deci-

mation and interpolation, and changes the sampling rate

Nonparametric estimation functions

covf

computes the auto- and cross-correlation func-

tions of a set of experimental data

cra

determines an estimate of the impulse response using the

correlation analysis method for a single-input, single-

output (SISO) plant

etfe

returns an estimate of the discrete transfer function for

a generalized linear model of a single-input, single-output plant in the fre-

quency form

impulse

displays the impulse response of the model

spa

returns the frequency-response characteristics of the plant and estimates

of the spectral densities of its signals for a generalized lin-

ear model of the plant (returns the plant model in fre-

quency format)

step

displays the step response of the model

of the plant

ar

estimates the parameters of an autoregressive (AR) model, i.e., the co-

efficients of the polynomial A(z), when modeling scalar

time series

armax

estimates the parameters of an ARMAX model

arx

estimates the parameters of ARX and AR models

bj

estimates the parameters of a Box-Jenkins model

ivar

estimates the parameters of a scalar AR model

iv4

estimates the parameters for ARX models using

the four-stage instrumental variable method

n4sid

used for estimating the parameters of state-space mod-

els in canonical form for an arbitrary

number of inputs and outputs

ivx

estimates the parameters of ARX models using the instrumen-

tal variable method

oe

estimates the parameters of an OE model

pem

estimates the parameters of a generalized multivariable linear

model

Model structure specification functions

idpoly

creates a plant model in polynomial form

idss

creates a plant model in state-space form

idarx

creates a multivariable ARX model of the plant

idgrey

creates a user-defined model of the plant

arx2th

creates a theta-format model matrix from the polynomials of an ARX

model of a multivariable plant

canform

creates the canonical form of a state-space model

for a multivariable plant

mf2th

converts a state-space model structure into

theta format

poly2th

creates a theta-format model from the original input–

output model

Model data extraction functions

arxdata

returns the coefficient matrices of the polynomials of ARX

models, as well as their standard deviations

polydata

returns the coefficient matrices of the polynomials

ssdata

returns the matrices (and the value of the sampling interval

in the discrete case) of ss models (state-

space models)

tfdata

returns the numerator and denominator of the transfer function

zpkdata

returns the zeros, poles, and generalized transfer

coefficients for each channel of a theta-format or LTI

model (if the Control System Toolbox is used, with

the name sys)

idfrd

creates a frequency-domain model of the plant in frd format

idmodred

reduces the order of the plant model

c2d, d2c

the first function converts a continuous-time model into a dis-

crete-time one, the second does the opposite

ss, tf, zpk,

functions for creating models of stationary systems in the form

frd

of a state-space model (ss), a transfer function

given its zeros and poles (zpk), a transfer

function written in operator form (tf), and in frequency

form (frd)

Model display functions

bode,

displays the logarithmic frequency response

bodeplot,

ffplot

plot

displays the input–output data for the plant's data

present

displays a view of the theta-format model with an estimate of the standard

deviation, the loss function, and an estimate of

model accuracy

pzmap

displays the zeros and poles of the model (with regions of uncer-

tainty)

nyquist

displays the Nyquist diagram (frequency-response locus) of the transfer

function

view

displays LTI models (when using the Control

System Toolbox)

Model adequacy verification functions

compare

allows comparison of the outputs of the model and the plant, with

comparative plots displayed and an indication of the

model's adequacy estimate

resid

computes the residual error for a given model and the corre-

sponding correlation functions

Model structure selection functions

aic, fpe

compute the AIC information criterion and the final

prediction error of the model

arxstruc

computes the loss functions for a number of different competing

single-output ARX models

selstruc

performs selection of the best model structure