Block Diagram Representation (Control)

5/28/2018 Block Diagram Representation (Control)

1/16

BlockDiagramRepresen

tation

BlockDiagramRepresen

tation

1)1)1)1)What

isablockd

iagram

?

What

isablockd

iagram

?

What

isablockd

iagram

?

What

isablockd

iagram

?

2)2)2)2)Howtoobtaintra

nsferfunct

ionfrom

Howtoobtaintra

nsferfunct

ionfrom

Howtoobtaintra

nsferfunct

ionfrom

Howtoobtaintra

nsferfunct

ionfrom

abloc

kdiagram

?

abloc

kdiagram

?

abloc

kdiagram

?

abloc

kdiagram

?

3)3)3)3)Howtosimplifya

blockdiag

ram

?

Howtosimplifya

blockdiag

ram

?

Howtosimplifya

blockdiag

ram

?

Howtosimplifya

blockdiag

ram

?

Block

Block

Block

Block

dia

grams

dia

grams

dia

grams

dia

grams

areareareare

used

used

used

used

asasasas

schematic

schematic

schematic

schematic

representa

tions

representa

tions

representa

tions

representa

tionsofofofofmat

hematical

mat

hematical

mat

hematical

mat

hematicalm

odels

m

odels

m

odels

m

odels....

W

hatisaB

lockdiagra

ms

B

lockdiagra

ms

B

lockdiagra

ms

B

lockdiagra

ms?

Consistof

avarietyofe

lementscorrespondto

Consistof

avarietyofe

lementscorrespondto

Consistof

avarietyofe

lementscorrespondto

Consistof

avarietyofe

lementscorrespondto

mathematicalentities




Canberea

rrangedtoh

elpsimplifytheequations

Canberea

rrangedtoh


Canberea

rrangedtoh


Canberea

rrangedtoh


usedtomodelthesystem





2/16

Processesa

rerepresent

edbytheblocksinblock

diagrams:

Proc

ess

variable

va

riable

Processesm

usthaveat

leastoneinputvariable

andatleastoneoutput

variable

Reclassifyp

rocesseswit

houtinputoroutput:

Input

variable

Output

variable

Exampleofunittran

sformation

processes

Engin

e

Engine

speed(rpm

)

Acce

lerator

depth(deg)

Speed

o-

mete

r

Measured

speed

Actual

spe

ed

xampeomeasure

menrocesses


3/16

Manysyste

msmeasure

theiroutput

andusethis

measurementtocontro

lsystembeh

avior

Thisisknownasfeedba

ckcontrol

theoutputis

fedback

intothesyst

em

Thesummingjunctionisaspecialp

rocessthat

com

aresthein

utand

thefeedbac

k

FeedbackControlSy

stems

FeedbackControlSy

stems

Inputstos

ummingjunctionmusthavesame

units!

proce

ss

sens

or

input

output

Inputisthe

outputwewantthesystem

tohave

Summingjunctionsubtrac

tsthemeasuredoutput

fromthedes

iredoutput,d

ifferenceiserrorsignal

Controllerac

tsbasedonm

agnitudeofe

rrorsignal

Actuatorpro

videsexterna

lpowertosys

temand

Generic

Feedbac

kContro

lSystem

Generic

Feedbac

kContro

lSystem

Plantistheprocesswearetryingtocon

trol

actuator

se

nsor

desired

outp

ut

output

c

ontroller

plan

t


4/16

Reminder:ComponentBloc

kDiagram

Reminder:ComponentBloc

kDiagram

BlockD

iagram

BlockD

iagram

Itrepresent

sthemathe

maticalrel

ationships

betweentheelementsofthesystem.

Thetransferfunctionofeachcomp

onentis

placedinbox,andtheinput-outpu

t

relationshipsbetween

components

are

indicatedby

linesandarrows.

)(

)(

)(

1

1

1

sY

s

Gs

U

=


5/16

BlockDiagramAlg

ebra

BlockDiagramAlg

ebra

Usingblockdiagram,w

ecansolve

the

equations

bygraphic

alsimplific

ation,

whichisofteneasieran

dmoreinfor

mative

thanalgebraicmanipulation,eventhoughthe

methodsareineveryw

ayequivalen

t.

Itisconvenienttothinkofeachblockas

representinganelectronicamplifierwith

thetransfe

rfunctionpr

intedinside.

Theinterco

nnectionsofblocksinclu

de

summingp

oints,where

anynumberofsignals

maybeaddedtogether.

Blockinseries:

Blocksinparallelwith

theiroutp

utsadded:

11stst&2&2ndnd

ElementaryBlock

Diagram

s

ElementaryBlock

Diagram

s

2

1

1 2

GG

)s(

U

)s(Y

=

2

1

1 2

G

G

)s(

U

)s(Y

+

=


6/16

Single

Single

Single

Single----loopne

gativefeedbac

k

loopne

gativefeedback

loopne

gativefeedbac

k

loopne

gativefeedback

Theo

veralltransfer

functionisgivenby:

33rdrdEle

mentar

yBlock

Diagram

Ele

mentar

yBlock

Diagram

1

G

)s(Y

Tw

oblocksareconn

ectedina

fe

edbackarrangem

entsothateach

fe

edsintotheother

:

2

1

1

GG

)s(R

+

FeedbackRule

FeedbackRule

1

1

GG G

s

R

)s(Y

+

=

Thegain

ofasingle

Thegain

ofasingle

Thegain

ofasingle

Thegain

ofasingle----lo

opnegativefeedback

lo

opnegativefeedback

lo

opnegativefeedback

lo

opnegativefeedback

system

is

givenbythe

forwardgaindividedby

system

is

givenbythe


system

is

givenbythe


system

is

givenbythe


th

esumof1p

lustheloopgain

th

esumof1p

lustheloopgain

th

esumof1p

lustheloopgain

th

esumof1p

lustheloopgain


7/16

Blockdiagra

mreduction

G2

+-

C((((

s))))

R(s)

H

G1

Closed-lo

opsystem

transferfunction:

R(s)

C((((s))))

CR

G

G

H

GG

=

+

1

21

2

1

G

GHG

G

1

21

2

1+

Blockdiag

ram

reduction

Blockdiag

ram

reduction

Blockdiag

ram

reduction

Blockdiag

ram

reduction

----

RRRR

GGGG1111RRRR----GGGG2222RRRR

RRRR

CCCC

GGGG2222

GGGG1111

++++

CCCC

GGGG1111----GGGG2222

++++

GGGGHHHH1111

HHHH2222

++++----

RRRR

CCCC

GGGG

++++----

RRRR

CCCC

HHHH1111----HHHH2222


8/16

Blockdiagram

manipulations

-

G1

+

+-

G1

G-11

+-

G1

G1

G1

-

+

Reductiono

fminorlo

ops

+-

G2

H2

+-

G1

R

G3

C

M

+-

G1

H1

G

C

M

R

CR

GG

G

G

G

H

GG

G

H

=

+

+

1

2

3

2

3

2

1

2

3

1

1

G

G

G

G

G

H

=

+

2

3

2

3

2

1


9/16

Example

+ -

G2

H2

+-

G1

R

H1

C+ -

G2

H2

+-

G

1

R

H1

C

G2-1

Signalflow

diagrams

variables

nodes

transfer

functions

a

rrows

G2

R

G1

C

M

R

M

C

G2

H

+

-

G1

R

C

1

2

M

E

R

M

C

G1

G2

-H

1

1

1


10/16

Example

G3

H2

+-

G

2

R

C

G4

G

1

+-

++

R

M

C

G1

G2-H1

1 1

1

G3

G

4

-H2

11ststElem

entaryP

rincipleofBlock

Elem

entaryP

rincipleofBlock

Diagram

Algebra

Diagram

Algebra


11/16

22ndnd

Elem

entaryPrinciple

of

Elem

entaryPrinciple

of

BlockDiagramA

lgebra

BlockDiagramA

lgebra

33rdrdElem

entaryP

rincipleofBlock

Elem

entaryP

rincipleofBlock

Diagram

Algebra

Diagram

Algebra


12/16

E

xample1:

E

xample1:

Transferfunctionfroma

SimpleBlo

ckDiagram

Transferfunctionfroma

SimpleBlo

ckDiagram

=

)s(R

)s(Y

)s(T

4

2

4

2

4

2

1

4

22

2

2

+

+

+

=

+

+

+

=

s

s

s

)s(T

s ss s

)s(T

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram


13/16

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram


14/16

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram


15/16

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram

Example2:TFfrom

theBlock

Diagram


16/16

Example2

:TFfrom

theBlock

Diagram

Example2

:TFfrom

theBlock

Diagram

4

2

1

3

1

6

1

5

2

1

1

G

GG

GG

GG

G

GG

)s(T

+

+

=

BlockDia

gram

BlockDia

gram

BlockDia

gram

BlockDia

gram

BlockDia

gram

BlockDia

gram

BlockDia

gram

BlockDia

gram

andits

andits

andits

andits

andits

andits

andits

anditscorrespond

ing

correspond

ing

correspond

ing

correspond

ing

correspond

ing

correspond

ing

correspond

ing

correspond

ingSignal

Signal

Signal

Signal

Signal

Signal

Signal

Signal

FlowGraph

FlowGraph

FlowGraph

FlowGraph

FlowGraph

FlowGraph

FlowGraph

FlowGraph

C

ompactalternativenotationtotheblockdiagram

notationtotheblockdiagram

notationtotheblockdiagram

notationtotheblockdiagram.

Itcharacterizes

thesystem

byanetworkofdirected

b

ranchesandassociatedtrans

ferfunctions.

T

hetwowaysofdepictingsignalareequivalent.

Block Diagram Representation (Control)

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