Principles of System Identification

Process

(Unknown)

Input

u[k]

(Probe

signal)

Output

y[k]

(Observed

response)

Identification

Model

FIGURE 1.1

Identification is the task of using input-output data to build a model: a mathematical

abstraction of the proces s.

Disturbances

Measurable

Process

Actuators

System that is actually identied by the user

Output

Input

signals

Sensors

Measurements

of responses &

disturbances

Sensor Noise

FIGURE 1.6

The system being ide ntified consists of the true process and additional elements.

Model Development

Data Generation and Acquisition

Sensors

PROCESS

Inputs

Disturbances

Measurable

DATA

Select Candidate

Models

VISUALIZATION

PRE-PROCESSING

NON-PARAMETRIC

ANALYSIS

MODEL

ESTIMATION

Estimation

Criteria

MODEL QUALITY

ASSESSMENT

Satisfactory?

Prior

Knowledge

No

Yes

MODEL

Residual Analysis

Estimation Error Analysis

Cross-Validation

...

Actuators Outputs

FIGURE 1.7

A generic iterative procedure for system identification.

Linear

Non-linear

Time-varying

Time-invariant

Deterministic

Stochastic

MultiscaleSingle-Scale

Discrete

Continuous

Dynamic

Static

Distributed

Lumped

First-Principles

Models

Empirical

FIGURE 3.2

Types of models.

Empirical Models

Parametric

Non-parametric

Models do not possess

any specic structure

but usually described

by responses (responses

are not parametrized

Models possess a specic

structure and are

characterized by delay,

order and a set of

parameters

Models are developed

using minimal process

knowledge. Parameters

cannot be (easily) related

to physical properties.

A priori knowledge is used

in model development.

Model Parameters (full/

partial set) have physical

Meaning.

Black-box

Grey-box

FIGURE 3.3

Four broad categories of empirical models.

+

Time-series modelling concepts

are used to build these models

Shock wave

(ctitious, random)

Physical inputs

(Exogenous)

Process response

(Observed)

Stochastic

Deterministic

Contains eects of noise,

unmeasured disturbances, etc.

Contains the physics or

explicable part of the process

+

FIGURE 3.4

Composite model from identification.

0 0.5 1 1.5

2

−1

−0.8

−0.6

−0.4

−0.2

0

0.2

0.4

0.6

0.8

1

Time

Amplitude

(a) Two continuous-time signals with F

1

= 1 Hz and F

2

= 5 Hz

0 0.5 1 1.5 2

−1

0

1

Amplitude

Sampled Signals at F

s

= 4 Hz

0 0.5 1 1.5 2

−1

0

1

Time

Amplitude

(b) Sampled vers ions at F

s

= 4 Hz

FIGURE 6.4

Incorrect sampling rates can result in ambiguous disc rete-time signals.

Confounding

variable

Conditioning

Direct link

YX

Z

X.Z Y.Z

Z

FIGURE 7.3

Schematic illustrating confounding and conditioning.