Post on 13-Jan-2017
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BLOCK DIAGRAMyash
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BLOCK DIAGRAM:
o Defination:
1. A block diagram is a pictorial representation of the entire system.
2. The block diagram represents the relationship between the input and the output of the entire system.
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Different terms: Block diagram:
Output:
-Output= Gain*Input• The value of the input is multiplied to the value
of block gain to get the output.
Block diagram of physical system
OutputInput
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G R(s)input output
C(s)
Summing point
More than one signal can be added or subtracted at summing point
x
y
z=x+y orZ=x-y
+
_
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Take off point• The point from which a signal is taken for the
feedback purpose is called as take-off point• This means from the take-off point , the output
signal is fed back at the input side.
Forward path• The direction of flow of signal is from input to
output.
Take off point
G1 G2R(s) C(s)
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Feedback path
• The direction of flow of signal is from output to input. It is shown in figure.
GR(S)
+_
C(S)
Feed back path
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Advantages of block diagram
• The functional operation of the system can be observed from block diagram.
• Block diagram gives the information about performance of system.
• Block diagram is used for analysis and design of control system.
• It is very simple to construct the block diagram for big and complicated system.
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Disadvantages of block diagram
• Block diagram for a given system is not unique.• Source of energy in the system is not shown in
the diagram.• In the procedure of reduction of block diagram
algebra, some important functions may be omitted or hidden.
• The block diagram does not give any information about the physical construction of the system.
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Reduction techniques
2G1G 21GG
1. Combining blocks in cascade
1G
2G21 GG
2. Combining blocks in parallel
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3. Eliminating a feedback loop
G
HGHG
1
4. Swap with two neighboring summing points
A B AB
G
1H
GG1
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Reduction techniques
5. Moving a summing point behind a block
G G
G
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8. Moving a pickoff point ahead of a block
G G
G G
G1
G
6. Moving a summing point ahead of a block
G G
G1
7. Moving a pickoff point behind a block
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A Feedback Control System
G=direct transfer function = forward transfer function H=feedback transfer function GH=loop transfer function=open-loop transfer function C/R=closed –loop transfer function= control ratio C
E/R=actuating signal ratio =error ratio
B/R=primary feedback ratio
R
R= G
1+_ GHE 1
1+_ GHB
R
=
= GH1+_ GH
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Characteristic Equation
• The control ratio is the closed loop transfer function of the system.
• The denominator of closed loop transfer function determines the characteristic equation of the system.
• Which is usually determined as:
)()()(
)()(
sHsGsG
sRsC
1
01 )()( sHsG
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Example-1
1. Open loop transfer function
2. Feed Forward Transfer function
3. control ratio
4. feedback ratio
5. error ratio
6. closed loop transfer function
7. characteristic equation
)()()()( sHsGsEsB
)()()( sGsEsC
)()()(
)()(
sHsGsG
sRsC
1
)()()()(
)()(
sHsGsHsG
sRsB
1
)()()()(
sHsGsRsE
1
1
)()()(
)()(
sHsGsG
sRsC
1
01 )()( sHsG
)(sG
)(sH
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Example-2:Reduction of block diagram
Step 1: Combine all cascade blocks using transformation 1.
Step 2: Combine all parallel blocks using transformation 2.
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Step 3: Eliminate all minor feedback loops using transformation 4.
Step 4: Shift summing points to the left and takeoff points to the right of the major loop, using transformation 7,10 and 12. However in this example step-4 does not apply.Step 5: Repeat steps 1 to 4 until the canonical form has been achieved for a particular input
Step 6: Repeat steps 1 to 5 for each input, as required.
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Example-3
• For the system represented by the following block diagram determine:1. Open loop transfer function2. Feed Forward Transfer function3. control ratio4. feedback ratio5. error ratio6. closed loop transfer function7. characteristic equation
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– First we will reduce the given block diagram to canonical form
1sK
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1sK
ssK
sK
GHG
11
11
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1. Open loop transfer function
2. Feed Forward Transfer function
3. control ratio
4. feedback ratio
5. error ratio
6. closed loop transfer function
7. characteristic equation
)()()()( sHsGsEsB
)()()( sGsEsC
)()()(
)()(
sHsGsG
sRsC
1
)()()()(
)()(
sHsGsHsG
sRsB
1
)()()()(
sHsGsRsE
1
1
)()()(
)()(
sHsGsG
sRsC
1
0)()(1 sHsG
)(sG
)(sH
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Example-4
R_+
_+1G 2G 3G
1H
2H
+ +
C
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R_+
_+
1G 2G 3G
1H
1
2
GH
+ +
C
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R_+
_+
21GG 3G
1H
1
2
GH
+ +
C
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R_+
_+ 21GG 3G
1H
1
2
GH
+ +
C
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R_+
_+
121
21
1 HGGGG
3G
1
2
GH
C
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R_+
_+
121
321
1 HGGGGG
1
2
GH
C
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R_+
232121
321
1 HGGHGGGGG
C
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R
321232121
321
1 GGGHGGHGGGGG
C
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Example 5Find the transfer function of the following block diagrams
2G 3G1G
4G
1H
2H
)(sY)(sR
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1. Moving pickoff point A ahead of block2G
2. Eliminate loop I & simplify
324 GGG B
1G
2H
)(sY4G
2G
1H
AB3G
2G
)(sR
I
Solution:
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3. Moving pickoff point B behind block324 GGG
1GB)(sR
21GH 2H
)(sY
)/(1 324 GGG
II
1GB)(sR C
324 GGG
2H
)(sY
21GH
4G
2GA
3G 324 GGG
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4. Eliminate loop III
)(sR)(1
)(
3242121
3241
GGGHHGGGGGG
)(sY
)()(1)(
)()()(
32413242121
3241
GGGGGGGHHGGGGGG
sRsYsT
)(sR1G
C
324
12
GGGHG
)(sY324 GGG
2H
C
)(1 3242
324
GGGHGGG
Using rule 6
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……THANK YOU……