DYNAMICS and CONTROL

Presented by

Pedro AlbertosProfessor of Systems Engineering and Control - UPV

MODULE 1I (1)

Models of

Systems & Signals

1

Representations

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DYNAMICS & CONTROL

Modules: Examples of systems and signals

Models of systems and signals

• Representations

• Analogies

• Formalism

Controlled systems: properties

Control systems design

Control benefits

Topics to study

SYSTEM

SIG

NA

LS

SIGNALS: Time variant magnitudes

What is common in all the examples?

SYSTEMS: Set of interconnected elements3

DYNAMICS & CONTROL

)(tT

How a signal can be represented?

Thermometer

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Equivalence of signals

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Signal components:

• information

• “noise”

What can you see in this image?

Misleading Information

A signal is composed of:

Basic signal

Some given information may have:

Different meaning

Multiple meaning

Noise/disturbances/harmonics

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DYNAMICS & CONTROL

6

Signal

Room Thermometer

MeasuredPeople

Heating

Ventilation

TemperatureO

uts

ide

Tem

p.

Win

d

Curt

ains

7

)(tT

Continuous Time

Discrete Time

Binary

Multivalue, discrete

Qualitative

…

Kind of signals

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DYNAMICS & CONTROL

Large

Regular

Small

Continuous Time

Discrete Time

Binary

Multivalue, discrete

Qualitative

…

Sinusoidals

Steps

Ramps

Random

…

Kind of signals

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DYNAMICS & CONTROL

Continuous Time

Discrete Time

Binary

Multivalue, discrete

Qualitative

…

Sinusoidals

Steps

Ramps

Random

…

Kind of signals

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DYNAMICS & CONTROL

Continuous Time

Discrete Time

Binary

Multivalue, discrete

Qualitative

…

Sinusoidals

Steps

Ramps

Random

…

Kind of signals

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DYNAMICS & CONTROL

Continuous Time

Discrete Time

Binary

Multivalue, discrete

Qualitative

…

Sinusoidals

Steps

Ramps

Random

…

Kind of signals

8

DYNAMICS & CONTROL

)(tT

Concept of System

• Set of components interacting among them and with the

environment:

GESTALT: The whole is more than the sum of the parts

Key Features: INTERACTION

DYNAMICS

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System’s Model

• Pilot plant (aero-modelism)

• Equivalent electric (mechanical) model

• Simulation model (training system)

• Mathematical model

• Hybrid models

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DYNAMICS & CONTROL

A D.C. Motor

MOTORaE

• Physical

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• Schematic

• Block diagram

u(t) y(t)G

Type of Systems (models)• Static

• Resistor

• Display

• Dynamic• Water tank

• DC motor

• Multivariable

• Concentrated/Distributed

• Linear

• Time invariant

• Uncertain

• Stochastic

• Fuzzy

• …

How to judge if a system is a dynamic one?

According to the signals:

u(t) y(t)

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DYNAMICS & CONTROL

G

• Binary

• Digital

• Continuous

System’s structure

• Series

• Parallel

• Loop (Feedback)

• General

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DYNAMICS & CONTROL

System’s structure

Process 2 Process nProcess 1

• Series

• Parallel

Process 2

Process 1

+

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DYNAMICS & CONTROL

System’s structure• Loop

Process 2Process 1

Process 3

+)(tr )(te )(tx )(ty

)(td

)(tm

• General

• Any combination of series/parallel/loop

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DYNAMICS & CONTROL

Representation of systems and signals

Information and noise

Representation:

• Graphics

• Table

• Mathematical Function

What have we seen today?

Physical systems:

• Variables relationships

• Analogies

• Mathematical models

• Systems’ structure

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DYNAMICS & CONTROL

What is next?

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DYNAMICS & CONTROL

Modules: Examples of systems and signals

Models of systems and signals

• Representations

• Analogies

• Formalism

Controlled systems: properties

Control systems design

Control benefits

Topics to study

Thank you!

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The sources of some of these figures are :

•Slide 8-1 http://commons.wikimedia.org/wiki/File%3AIndustrial_robot.jpg Por Jo Teichmann, Augsburg, Germany (KUKA Roboter GmbH) [Public domain], undefined

•Slide10 http://commons.wikimedia.org/wiki/File%3AIndustrial_robot.jpg Por Jo Teichmann, Augsburg, Germany (KUKA Roboter GmbH) [Public domain], undefined

DYNAMICS & CONTROL