v-sd e-1-wise14 [kompatibilitätsmodus]

Course System DynamicsD. SöffkerLU-1: Regularities, definitions, terms

Chair of Dynamics and Control

Course System Dynamics Fall/Winter 2014/2015ISE Bachelor in Mechanical Engineering

Univ.-Prof. Dr.-Ing. Dirk Söffker

Room: MB 143Time: Tue 11.00 am - 2.00 pm

Assistants: Ms. Dipl.-Ing. Sandra Rothe

Additional: TutoriumPractical exercise (Mandatory)

Url: http://www.uni-due.de/srs/v-sd_en.shtmlManuscriptNote 1: The collected material is prepared for the use only in connection with this lecture.It is not allowed to use this material outside the lecture of Prof. Söffker.

Note 2: The reprinted figures are coming – if nothing different is mentioned - from the textbook of Prof. Lunze and are free for use inconnection with this textbook-based course. Some material is taken from the (older) manuscript of Prof. Schwarz, who is the owner of the related rights.



0. Formal introduction► Hints / Organisation / Lecture and exercise dates► Organisation of the practical exercise

(New rules, moodle, enrollment NOW, see add. information)► Contents of the course► Consulting hours► WEBpages (Manuscript with password)► Officeboard (white): Entrance MB 34x

1. Definitions Technical Control / Control1.1a > Literature► O. Föllinger: Regelungstechnik► G. Ludyk: Theoretische Regelungstechnik► J. Lunze: Regelungstechnik (‚Textbook‘)► K. Ogata: Modern Control Engineering (Bachelor) ► G. Franklin et al.: Feedback Control of Dynamic Systems (Bachelor)► R. C. Dorf et al.: Modern Control Systems (Bachelor)1.1b > Journals► at-automatisierungstechnik► Automatica► IEEE Transact. on Automatic Control



1.1c > Standards (Normen)► DIN 19221f

> DIN 19226 Regelungs- und Steuerungstechnik1.1d > Societies► VDI/VDE

> Gesellschaft für Mess- und Automatisierungstechnik► IEEE – Institute of Electric and Electronics Engineers

> Control System Society► IFAC - International Federation of Automatic Control)

1.1d > Relations to other scientific disciplines► Measurement techniques

Dynamics and Control

Process Informatics

Automation systems / Automatic control

► Mechatronics (Mechanical Engineering + Electronics)



1.2 What is control?►►

► feedback > closed loop // no feed back > open loop, interaction (verbal)

► control (open / closed loop) > interaction

► causal mechanism

► Can the causal mechanism be graphically represented?> cause > effect ( directed information / signal flow)> causal mechanism > ‚flow of signals‘ >> causal representation



1.3 Definitions (see definition page of Chair SRS)

- System

- Physical variable

- Control variable

- Feedforward (‚Def.‘):

- Feedback control (‚Def.‘):

- Disturbance variable



- Input variable

- Control difference / control deviation

- Desired variable

- Plant / system to be controlled

- Controller

- Transfer element / Transfer system



Connections:

► Feedback – Connected systems - Control

► Dynamics – System Dynamics – Control technique - System Theory

Question:What is the idea of control technique / control?



1.4 Examples1.4.1 Heating

from: Rake, Regelungstechnik A (Skript), RWTH Aachen, 1984



1.4.1 Heating - 2. example

nach: Rake, Regelungstechnik A (Skript), RWTH Aachen, 1984



1.4 Examples1.4.2 Building automation



1.4 Examples1.4.3 Mechatronics / Robotic / Autonomous systems

Elastic robot ELROB,Chair of Dynamics and Control

Hydraulic research robot HYROB, Chair of Dynamics and Control




Robot arm of a concretepump machine,Fa. Schwing, Herne

Autonomous robot,UNLV, USA

Autonomous robot,Chair of Dynamics and Control



Example: Stabilization of an inverted, elastic pendulum



Example: Vibration control of elastic,hydraulically driven robot




examples from automotive engineering:- ABS- ESP- ASR- ...

1.4.4 From process controlto supervision



1.4 Examples1.4.4 Process control and supervision / ‚Human in the loop‘

Hist

ory

Mam

-Mac

hin

eIn

terf

ace

R11

A1

B1

C1

D1

E1

F1

Futu

re

E1

R11

A1

B1

C1

D1

E1

TerminalReal technical system:example Power Station

Inte

rfac

eInteracting Human

R11

A1

B1

C1

D1

F1

E1

R11

A1

B1

C1

D1

E1

F1

Learning

Mental modelof the reality

Planing

?

Function - orientedrepresentation of

causal mechanism of the technical system using a suitable

modeling technique

Interaction

(5)

(7)

(4)

(6)

(1)

(6)(2)

(3)

Reality



Human-Maschine-Interaction I

Example: DrivingSimulator(Chair SRS)



Human-Maschine-Interaction II

Example: Driver(Coop. with DLR,Braunschweig)



Human-Maschine-Interaction III

Example: Human operationat nuclear poweroperating center

Course System DynamicsD. SöffkerLU-2: Dynamical systems and description


2 Dynamical systems, system dynamics and description of dynamical systems

2.1 Modeling:

Importance of modeling in control

Real dynamical systems > systems and signals> Mapping of structures physical effects

Representation of the causal net / signal flow> Abstraction > time behavior

Abstraction: from the behavior of the real system to the formal representation of the behavior ( > math. eq.)

1/10



Modeling procedure:

1. Description of the modeling goal

2. Choice of modeling assumptions

3. Verbal description of the plant

4. Putting-up of the block diagram

5. Putting-up of the model equations

6. Model validation

2/10



2.2 Block diagram

Description element / structural behavior> Consideration of a single dynamical element/system

branch (‚arrows‘):

Block (dynamical system):

> causal direction / signal flow

3/10



Symbols:

2.3 Linearization of a nonlinear static I/O-behavior

> nonproportional transmittance

> Control technique is based on linear theory

4/10



Nonlinear block:

Linearization of the transmittance / signal transfer- graphically- analytical

Nonlinear transmittance / nonlinear static input/output behavior

Analytical linearizationUsing Taylor series approximation:

5/10



2.4 System description using differential equations

Goal:Fact:

> linear ODE n-th order

> Example: excited mass-damper-spring system

General scheme of the procedure:- Putting-up of single equations (> element equations)- Putting-up of coupled equations- Building up a system of ODEs

6/10



Example: From the physics using modeling principles tothe mathematical descriptions of transmission I: Spring-mass-damper system

Modeling usingprinciple of force balances

> Animation example (U GATECH)

Modeling gives:

Renaming of variables to control-oriented ones gives:

7/10



Example: From the physics using modeling principles tothe mathematical descriptions of transmission I: Spring-mass-damper system

8/10



9/10

General scheme of the procedure:- Putting-up of elementary equations (> element equations)- Putting-up/Combining elementary eq. to coupled equations- Building up a system of ODEs- Using control-oriented variables > Renaming of variables



2.5 Linearity / Causality / Time-invariance of dynamical systems

Def.: Linear transmittance is, if superposition can be used.Superposition principle:

Causality:

Time-invariance:

(Philosophical remark: 10/10

Uni

vers

ity o

f D

uisb

urg-

Esse

n Cha

ir o

f D

ynam

ics

and

Con

trol

U

niv.

-Pro

f. D

r.-I

ng.

Dirk

Söf

fker

C

ours

e S

yste

m D

ynam

ics

/ C

ontr

ol E

ng

inee

rin

g

S

prin

g/W

inte

r 20

14/1

5

Term

s an

d D

efin

itio

ns

Sys

tem

:

Purp

ose-

orie

nted

par

t of

the

rea

l w

orld

. Th

e sy

stem

is

in int

erac

tion

with

the

rea

l w

orld

, w

here

by f

rom

the

rea

l wor

ld in

puts

are

act

ing

to t

he s

yste

m a

nd o

utpu

ts a

re a

ctin

g fr

om

the

syst

em t

o th

e en

viro

nmen

t.

Ph

ysic

al v

aria

ble

s /

ph

ysic

al v

alu

es:

In

tera

ctio

n qu

aliti

es (

qual

ities

/ s

tate

s) w

ithin

a s

yste

m o

r fr

om t

he s

yste

m t

o th

e en

viro

nmen

t, in

tech

nica

l sy

stem

s us

ually

of

phys

ical

nat

ure.

Phy

sica

l va

lues

are

usu

ally

de

fined

in c

onne

ctio

n w

ith t

he p

urpo

se o

f re

late

d sy

stem

s to

be

cons

ider

ed.

The

variab

les

to b

e co

nsid

ered

in c

ontr

ol a

re u

sual

ly s

cala

rs o

r ve

ctor

s. T

he m

ain

prop

erty

of

variab

les

cons

ider

ed w

ithin

sys

tem

dyn

amic

s or

con

trol

is t

he t

ime

depe

ndin

g be

havi

or.

Con

tro

l var

iab

le /

Ou

tpu

t (s

ing

le in

pu

t –

sin

gle

ou

tpu

t sy

stem

):

Var

iabl

e of

the

sys

tem

to

be c

ontr

olle

d. T

he v

aria

ble

shou

ld b

e us

ually

fix

or

variab

le.

In

Sin

gle

Inpu

t -

Sin

gle

Out

put

(SIS

O)

syst

ems

the

outp

ut (

here

onl

y on

e ex

ists

) is

the

co

ntro

l var

iabl

e.

Op

en lo

op s

yste

m:

Ope

n lo

op s

yste

ms

are

wor

king

so

that

the

inp

uts

of t

he s

yste

ms

are

affe

ctin

g th

e ou

tput

s de

pend

ing

on t

he d

ynam

ic p

rope

rtie

s of

the

sys

tem

and

no

t vi

ce v

ersa

. Th

e ch

arac

terist

ic p

rope

rty

of a

n op

en l

oop

syst

em i

s th

e no

n cl

osed

beh

avio

r of

the

sig

nal

flow

. C

lose

d lo

op s

yste

m:

With

in

a cl

osed

lo

op

syst

em

the

cont

rol

variab

le

is

usua

lly

onlin

e m

easu

red

and

com

pare

d w

ith a

giv

en d

esired

/ r

efer

ence

var

iabl

e (w

hich

als

o ca

n be

zer

o).

The

resu

lt is

gi

ven

to t

he i

nput

in

the

way

tha

t it

is a

ctin

g so

tha

t th

e co

ntro

l va

riab

le t

ends

to

the

desi

red

valu

e. T

his

real

izes

the

fee

dbac

k an

d cl

oses

the

loop

. Th

e ch

arac

terist

ic p

rope

rty

of a

clo

sed

loop

sys

tem

is

the

clos

ed b

ehav

ior

of t

he s

igna

l flo

w.

This

cha

nges

the

dyn

amic

beh

avio

r of

the

ove

rall

syst

em a

nd a

llow

s th

e au

tom

atic

co

mpe

nsat

ion

of d

istu

rban

ces

actin

g to

the

sys

tem

and

affec

ting

the

cont

rol v

aria

ble.

D

istu

rban

ce (

vari

able

/ v

alu

e):

From

th

e en

viro

nmen

t to

th

e sy

stem

ac

ting

variab

le,

whi

ch

influ

ence

s th

e co

ntro

l va

riab

le in

an

unw

ante

d w

ay.

Inp

ut

(var

iab

le /

val

ue)

: Var

iabl

e ac

ting

dire

ct t

o th

e sy

stem

and

cha

nges

the

out

put

of t

he s

yste

m.

In o

pen

loop

sy

stem

the

inp

ut v

aria

ble

acts

fro

m t

he e

nviron

men

t to

the

sys

tem

, in

clo

sed

loop

sy

stem

s th

e in

put

is t

he o

utpu

t of

the

con

trol

ler

and

the

inpu

t of

the

sys

tem

to

be

cont

rolle

d.

Des

ired

var

iab

le /

valu

e /

ref

eren

ce v

aria

ble

/val

ue:

Var

iabl

e fr

om t

he e

nviron

men

t to

the

con

trol

ler,

whi

ch g

ives

the

ref

eren

ce f

or t

he o

utpu

t as

the

val

ue t

o be

con

trol

led.

C

ontr

ol d

evia

tion

/ c

ontr

ol d

iffe

ren

ce:

Var

iabl

e de

notin

g th

e di

ffer

ence

be

twee

n th

e de

sire

d an

d th

e co

ntro

l va

riab

le.

The

cont

rol d

evia

tion

is a

n in

tern

al v

aria

ble

insi

de t

he c

ontr

olle

r.

Pla

nt

(sys

tem

to

be

con

tro

lled

):

The

plan

t is

the

sys

tem

to

be c

ontr

olle

d (c

lose

d lo

op)

or t

he s

yste

m t

o be

affec

ted

by t

he

inpu

t (o

pen

loop

).

Con

tro

ller:

Th

e co

ntro

ller

is t

he p

art

of t

he s

yste

m,

whi

ch a

ffec

ts t

he p

lant

usi

ng a

n ac

tuat

or.

From

a

prac

tical

poi

nt o

f vi

ew c

ontr

olle

r an

d ac

tuat

or a

re d

istin

guis

hed,

fro

m a

the

oret

ical

poi

nt

the

cont

rol

unit

com

bine

s th

e co

ntro

l an

d th

e ac

tuat

or a

nd i

s ca

lled

cont

rolle

r. F

rom

a

prac

tical

poi

nt o

f vi

ew t

he t

echn

ical

con

trol

uni

t of

ten

also

con

sist

s of

the

uni

t fo

r co

mpa

riso

n of

des

ired

and

con

trol

var

iabl

e.

Tran

sfer

ele

men

t:

Abs

trac

t un

ders

tand

ing

of a

gen

eral

sys

tem

with

dyn

amic

pro

pert

ies,

whi

ch c

an b

e th

e sy

stem

to

be c

ontr

olle

d or

the

con

trol

ler

or a

noth

er e

lem

ent

of t

he t

rans

fer

chai

n. T

he

impo

rtan

t as

pect

is

th

at

the

tran

sfer

el

emen

t is

a

syst

em,

whe

reby

th

e dy

nam

ic

prop

ertie

s of

the

tra

nsm

ittan

ce f

rom

inp

ut t

o ou

tput

are

of

inte

rest

. Th

e re

leva

nt a

spec

t is

the

dyn

amic

cha

ract

eriz

atio

n of

the

tra

nsfe

r be

havi

or.

Plan

t an

d co

ntro

llers

are

in

this

w

ay n

othi

ng m

ore

than

tra

nsfe

r el

emen

ts,

the

deno

tatio

n pl

ant

or c

ontr

olle

r re

sults

fro

m

the

func

tion

of t

he t

rans

fer

elem

ent

with

in t

he lo

op.

Tran

sfer

sys

tem

: Abs

trac

t un

ders

tand

ing

of a

set

of el

emen

ts b

uild

ing

up a

new

ele

men

t >

sys

tem

. A

ctu

ator

: Act

uato

r is

the

phy

sica

l de

vice

in

fron

t of

the

pla

nt u

sed

for

phys

ical

exc

itatio

n of

the

pl

ant

to a

ffec

t th

e pl

ant.

In

the

theo

retic

al /

abs

trac

t co

nsid

erat

ion

the

actu

ator

is p

art

of

the

tran

sfer

ele

men

t co

ntro

ller.

M

easu

rem

ent

dev

ice:

Th

e ph

ysic

al d

evic

e us

ed f

or m

easu

ring

of

the

outp

ut /

the

con

trol

var

iabl

e is

cal

led

mea

sure

men

t de

vice

/ u

nit.

In

the

theo

retic

al /

abs

trac

t co

nsid

erat

ion

the

dyna

mic

al

prop

ertie

s of

usu

al n

egle

cted

, so

the

mea

sure

men

t de

vice

is

unde

rsta

nd i

s an

ide

al

tran

sfer

ele

men

t w

ithou

t an

y ki

nd o

f dy

nam

ic p

rope

rtie

s. F

or p

ract

ical

con

side

ratio

ns t

he

dyna

mic

s pr

oper

ties

of t

he m

easu

rem

ent

unit

as w

ell

as o

f th

e ac

tuat

or h

as t

o be

co

nsid

ered

. R

efer

ence

val

ue:

Pa

ram

eter

of

the

refe

renc

e va

riab

le

Con

tro

l val

ue:

Pa

ram

eter

of

the

cont

rol v

aria

ble

----

---

Rem

ark:

Th

e gi

ven

term

s an

d de

finiti

ons

are

used

fro

m d

iffer

ent

auth

ors

etc.

in a

diff

eren

t w

ay.

The

impo

rtan

t as

pect

is

the

verb

al/t

erm

-bas

ed s

epar

atio

n fr

om s

igna

ls a

nd p

hysi

cal

variab

les,

fro

m s

yste

ms

and

beha

vior

s, f

rom

the

phy

sica

l/te

chni

cal

real

izat

ion

and

from

th

e m

athe

mat

ical

abs

trac

t m

appi

ng.

For

exam

ple

equ

atio

ns a

re u

sed

to d

escr

ibed

the

be

havi

or o

f sy

stem

s, t

he o

utpu

t va

riab

les

of t

echn

ical

sys

tem

s sh

ow a

lso

this

beh

avio

r.

In o

lder

tex

t bo

oks

and

prac

tical

orien

ted

liter

atur

e th

is d

istin

ctio

n is

oft

en n

ot r

ealiz

ed.

It is

a go

od ide

a to

und

erst

and

the

clea

r se

para

tion

betw

een

real

ity,

the

map

ping

-bas

ed

mat

hem

atic

al r

epre

sent

atio

n to

be

open

for

fut

ure

adva

nced

info

rmat

ion

scie

nce

orie

nted

co

ntro

l and

inte

ract

ion

appr

oach

es.

v-sd e-1-wise14 [kompatibilitätsmodus]

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