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Block Diagram Reduction Abhishek Vaghela
Electronics & Communication Engg Dept.
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• Pictorial Representation of functions performed by each
component of a system and that of flo of signals.
Block Diagram
!ingle block diagram representation
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Components of a system
!ignals
"ake off Point
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Terminology
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• Plant: Physical object to be controlled. G!"#
• Control $lement: G%!s# & also called the controllerre'uired to generate the appropriate control signalapplied to the plant.
• (eedback $lement: )!"# is the componentre'uired to establish the functional relationshipbet*een the primary feedback signal B !s # andthe controlled output C!s#.
• Reference +nput: R !s# is an e,ternal signal appliedto a feedback control system in order to commanda speci-ed action of the plant.
• The Controlled utput C!s# is that 'uantity or
condition of the plant *hich is controlled.
Terminology
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• /ctuating "ignal $!s# & also called the error orcontrol action& is the algebraic sum consisting ofthe reference input R !s # plus or minus !usuallyminus# the primary feedback B !s # .
• 0anipulated 1ariable 0!s# !control signal# is that'uantity or condition *hich the control elements G%!s# apply to the plant G!s# .
• Disturbance 2 !s# is an undesired input signal
*hich a3ects the 4alue of the controlled outputC!s#. +t may enter the plant by summation *ith 0!s # & or 4ia an intermediate point& as sho*n in theblock diagram.
Terminology
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• (or*ard Path is the transmission path from theactuating signal $!s# to the output C!s#.
• (eedback Path is the transmission path from theoutput C!s# to the feedback signal B !s #.
• "umming Point: / circle *ith a cross is the symbolthat indicates a summing point. The !5# or !6# signat each arro*head indicates *hether that signal isto be added or subtracted.
Terminology
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• G(s) = Direct transfer function = Forward transfer function.
• H (s ) = Feedback transfer function.
• C(s) / R(s) = Closed loop transfer function = Control ratio‐
De-nitions
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• the output C(s) and input R(s)
are related as follows
Closed loop transfer function
C(s) =G(s)E(s)
here
E (s)=R(s)−(s)=R(s)−H(s)C(s)
Eliminating E(s) fro! t"ese e#uations $i%es
C(s)=G(s) &R(s)−H(s)C(s)'
"his can be ritten in the form
#$%G(s)H (s)'C(s)=G(s)R(s)
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• Cascade Connections
Block diagram and
"impli-cations
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Parallel Connections
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0o4ing a summing point after a
block
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0o4ing a summing point ahead
of block
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0o4ing a take of point after a
block
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0o4ing a take of point before a
block
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$,ample 7 %
To reduce the block diagram to simple form.
234122411411
)341241(
H GGG H GGG H GG
GGGGGG
R
C
++−
+=
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$,ample 7
%
%1G 2G 3G
1 H
2 H
%%
C R
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/ns*er
R
321232121
321
1 GGG H GG H GG
GGG
++−
C
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$,ample 7 8
2G 3G1G
4G
1 H
2 H
)( sY '(sR
)ind the transfer function of the folloing block diagram
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)( s R
I
1G
2 H
)( sY
4G
2G
1 H
A B
3G
2G
$. *o+ing pickoff point A ahead of block2G
,. Eliminate loop - & simplify
324 GGG + B
!olution
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/. *o+ing pickoff point 0 behind block324 GGG +
1G B
)( s R
21G H 2 H
)( sY
)/(1 324 GGG +
II
1G B
)( s RC
324 GGG +
2 H
)( sY
21G H
4G
2G A
3G 324 GGG +
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1. Eliminate loop ---
)( s R
)(1
)(
3242121
3241
GGG H H GG
GGGG
+++
+ )( sY
)()(1
)(
)(
)()(
32413242121
3241
GGGGGGG H H GG
GGGG
s R
sY sT
+++++
+==
)( s R
1G
C
324
12
GGG
H G
+
)( sY
324 GGG +
2 H
C
)(1 3242324
GGG H
GGG
++
+
sin$ rule
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)ind the transfer function of the folloing block diagram
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E2ample 3 1
)ind the transfer function of the folloing block diagram
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4$ 4,
5,
5$
4/
R C
21321121221
3121
H H GGG H GG H G
GGGG
R
C
−++
+=
E2ample 36
%
3
%
3
%
%