The System Identification Toolbox lets you

build and evaluate linear models of dynamic

systems from measured input-output data.

You can use time- and frequency-domain

techniques to fit models to single- or multi-

channel data. It includes tools for modeling

dynamic systems that are not easily repre-

sented by first principles, including engine

subsystems, flight dynamics, thermofluid

processes, and electromechanical systems.

The toolbox supports virtually all polyno-

mial (transfer function) and state-space

model representations and model identi-

fication by nonparametric correlation and

spectral analysis. Toolbox functions can

identify continuous- or discrete-time models

with an arbitrary number of input and

output channels. You can import and pre-

process measured data, generate parametric

and nonparametric models, and validate esti-

mated models against measured data.

As with all MathWorks toolboxes, the System

Identification Toolbox is open and extensible,

letting you create custom algorithms for

your particular application. You can import

estimated models directly into MATLAB®,

Simulink®, and MATLAB toolboxes, for use in ®, and MATLAB toolboxes, for use in ®

simulation or control system development.

System Identification Toolbox 6Create linear dynamic models from measured input-output data

KEY FEATURES■ Parametric and nonparametric multi-input/multi-output

model identification using frequency- and time-domain data

■ Specialized tools for identification of first-, second-, and third-

order dynamic models

■ Advice functions for evaluating test data and identified models

■ Frequency- and time-domain data preprocessing tools,

including offset removal, detrending, prefiltering, and recon-

structing missing data

■ Tools for estimating time delays and detecting feedback loops

from the test data

■ Simulink blocks for identifying and handling estimated models

and transferring data to and from the MATLAB workspace

The System Identification Toolbox can use input-output data from a nonlinear Simulink model to estimate a linear model.

Nedge180

valve timing

throttle(deg)

-K-

rad/sto rpm

In1 Out1

Zero Initial Throttle Angle

Teng

Tload

N

VehicleDynamics

Throttle Ang.

Engine Speed, NMass Airflow Rate

Throttle & Manifold

1s

Intake

EngineModel

Estimated Engine Model fromSystem Identification Toolbox

In1 Out1

Engine Speed Offset

EngineSpeed(rpm)

Load

Drag Torque

mass(k+1)

mass(k)

trigger

Compression

Air Charge

N

Torque

Combustion

EngineSpeed(rpm)

Working with the System Identification Toolbox You can interact with the toolbox via a

graphical user interface or the MATLAB

command line and programming language.

Graphical User Interface The main graphical user interface (GUI)

lets you easily analyze test data and identify

models. You can use this GUI to step through

the identification process and apply advanced

estimation techniques on multiple data

sets and models. You access commands to

perform operations such as:

• Loading and saving test data and identifi-

cation sessions

• Preprocessing test data, including filtering,

offset removal, and detrending

• Managing data sets and identified models

graphically

• Comparing multiple estimated models

against validation data

MATLAB Command Line and Programming Language Like all MATLAB based tools, the System

Identification Toolbox has an extensive

command-line interface. You can:

• Work directly on data sets to

identify models

• Access additional MATLAB commands

and visualization capabilities

• Develop and share your own algorithms

using the MATLAB programming language

Assessing Identification ExperimentsThe System Identification Toolbox helps

you ensure that the observed test data you ensure that the observed test data

represents the dynamics of the system under

investigation.

Analyzing and Designing Test SignalsThe toolbox helps you analyze and design

test signals to ensure that the system dynam-

ics are properly excited about operating

points of interest. It can suggest options in

sampling methods, note unwanted offset in

the data, detect the presence of feedback in

the data, and give bounds on possible model

orders, based on the statistical properties of

the input signal.

Working with Observed DataA GUI helps you import time-domain,

frequency-domain, and frequency-response

data to estimate a model. You can import

You can examine the frequency content of the

measured data to ensure that it contains the

necessary ranges (left) or compare the input

and output signals in the measured data (below).

data from systems with multiple input and

output channels, assign channel names,

specify starting and sampling times, and

define variable units.

After the data has been imported, you can

transform it between frequency and time

domains to determine if the data needs to

be preprocessed before model identification.

The main GUI helps you import, analyze, and use data to identify and validate a model.

Preprocessing Measured Data Measured data often has offsets, out-

liers, periods of missing values, and other

anomalies. These anomalies may lead to an

improperly identified system. You can pre-

process the measured data to remove these

sources of error by:

• Detrending to remove data drift and offset

• Filtering to emphasize important frequency

ranges in the data and remove high-

frequency disturbances

• Resampling to increase estimation speed

and accuracy

Selecting Data Sets for Identification and ValidationThe toolbox lets you select two data sets

from the measured data, one for identifying

the model and one for validating it. You can

use frequency- and time-domain data inter-

changeably to identify and validate models.

Estimating and Validating ModelsYou can try different methods and model

structures to estimate the linear dynamics of

the system under investigation. The model

estimates can be validated by comparing their

simulated output against measured output data.

Estimating ModelsThe toolbox lets you estimate models using

several predefined structures. You can

estimate multiple models at one time and

then concentrate on a particular model for

additional refinement. You can focus the

estimation on model characteristics, such as

stability, the dominant frequency range of the

excitation signal, or specific frequency ranges.

The System Identification Toolbox provides

three methods for estimating models:

• Parametric estimation

• Process model estimation

• Nonparametric estimation

Parametric EstimationParametric estimation lets you select a

model structure from predefined polynomial

(transfer function) and state-space forms.

After selecting the structure, you can edit the

model order and choose a focus for the esti-

mation, such as model stability or dynamic

simulation. Certain model structures let

you generate multiple estimations by simply you generate multiple estimations by simply

defining a range of model orders.

You can select the best model and use it as

the starting point as you further refine your

model estimate.

The Filter dialog window lets you

select specific frequency ranges in

the measured data.

You can easily separate the measured data into

identification and validation sets.

The Parametric Model dialog window

provides the options for model structures

and orders and lets you specify the type

of estimation.

Process Model EstimationProcess model estimation focuses on lower-

order, continuous-time models that are

characterized by a main time constant, a

static gain, a possible dead time, and a pos-

sible process zero (nonconstant numerator).

The process modeling tool lets you customize

the structure of the estimated model based

on your knowledge of the system. You can

specify known parameters and initial guesses

or let the software make initial guesses.

Alternatively, you can implement multi-

input models and define the structure of an

optional disturbance model.

Nonparametric EstimationNonparametric estimation uses spectral and

correlation analysis methods to estimate

frequency functions directly. The toolbox

performs spectral analysis using data window

techniques to obtain estimates of the transfer

function and the noise spectrum. It performs

correlation analysis using automatic pre-

whitening of the input signal.

Validating ModelsToolbox functions let you compare the esti-

mated model output to an output data set to

ensure that the estimated model accurately

represents the system dynamics. The toolbox

contains an advice function that suggests

additional comparison tests and evaluates

the model order, indicating when the order

might be higher than needed. The toolbox

provides five analysis tools to determine the

fitness of the identified model:

• Model output – Indicates how well the model

dynamics were captured by comparing the

model output against the validation set

• Residual analysis – Compares the outputs of

the estimated models and the validation data

• Frequency response – Displays the model’s

frequency response to show damping levels

and resonance frequencies

• Transient response – Indicates the model’s

behavior when excited by a step or

impulse input

• Zeros and poles – Displays the poles and

zeros of estimated models

Required Products MATLAB

Related Products Simulink. Design and simulate continuous-

and discrete-time systems.

Control System Toolbox. Design and analyze

controllers for dynamic closed-loop systems.

For a complete list of related products, visit

www.mathworks.com/products/sysid

Platform and System RequirementsThe System Identification Toolbox is available

for Windows 98/ME/NT/2000/XP. For addi-

tional information and system requirements,

visit www.mathworks.com/products/sysid www.mathworks.com/products/sysid www.mathworks.com/products/sysid ■

Tel: 508.647.7000 info@mathworks.com www.mathworks.com 8000v05 10/03

© 2003 by The MathWorks, Inc. MATLAB, Simulink, Stateflow, Handle Graphics, and Real-Time Workshop are registered trademarks, and TargetBox is a trademark of The MathWorks, Inc. Other product or brand names are trademarks or registered trademarks of their respective holders.

For demos, application examples, tutorials, user stories, and pricing:

•Visit www.mathworks.com

•Contact The MathWorks directly

US & Canada 508-647-7000

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Visit www.mathworks.com to obtain contact information for authorized MathWorks representatives in countries throughout Asia Pacific, Latin America, the Middle East, Africa, and the rest of Europe.

The Process Model GUI lets you specify the order of the model, the time delay,

and the type of estimation.