Block Diagram Representation (Control)
description
Transcript of Block Diagram Representation (Control)
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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
mathematicalentities
mathematicalentities
mathematicalentities
Canberea
rrangedtoh
elpsimplifytheequations
Canberea
rrangedtoh
elpsimplifytheequations
Canberea
rrangedtoh
elpsimplifytheequations
Canberea
rrangedtoh
elpsimplifytheequations
usedtomodelthesystem
usedtomodelthesystem
usedtomodelthesystem
usedtomodelthesystem
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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
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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
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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
=
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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
+
=
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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
forwardgaindividedby
system
is
givenbythe
forwardgaindividedby
system
is
givenbythe
forwardgaindividedby
th
esumof1p
lustheloopgain
th
esumof1p
lustheloopgain
th
esumof1p
lustheloopgain
th
esumof1p
lustheloopgain
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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
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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
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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
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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
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22ndnd
Elem
entaryPrinciple
of
Elem
entaryPrinciple
of
BlockDiagramA
lgebra
BlockDiagramA
lgebra
33rdrdElem
entaryP
rincipleofBlock
Elem
entaryP
rincipleofBlock
Diagram
Algebra
Diagram
Algebra
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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
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Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
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Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
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Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
Example2:TFfrom
theBlock
Diagram
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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.