Block Diagram Reduction Technique.pptx

8/17/2019 Block Diagram Reduction Technique.pptx

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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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E2ample 3 1



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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

%

%

Block Diagram Reduction Technique.pptx

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