1. Salman Bin Abdulaziz University
EE3511: Automatic Control Systems
Block Diagram
Dr. Ahmed Nassef
EE3511_L8
Salman Bin Abdulaziz University

2. Salman Bin Abdulaziz University
Learning Objective
To understand the concept of Block diagrams and their assumptions
To be able to reduce complex block diagrams to a simple (one block) diagram
EE3511_L8
Salman Bin Abdulaziz University

3. Block Diagram of Electrical Communication System
channel
Input
signal
Transmitter
Receiver
Output
signal
The block diagram illustrates the functional parts of the communication system but many details are hidden
More details can be added by drawing detailed block diagram for each the shown subsystems.
EE3511_L8
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4. Salman Bin Abdulaziz University
Block Diagrams X Y G G H
A block diagram is pictorial representation of systems.
It shows different components (subsystems) that make a system and shows their interactions.
Each rectangular block represents a subsystem.
Inputs are represented by arrows entering the block.
Outputs are represented by arrows leaving the block.
EE3511_L8
Salman Bin Abdulaziz University

5. Salman Bin Abdulaziz University
Block diagrams
A block diagram is used to represent linear relationship between the input and the output of a subsystem.
Let the input and the output be U and Y,
the relationship between U and Y is represented by a rectangular block having a transfer function G G U
Y = G U
EE3511_L8
Salman Bin Abdulaziz University

6. Block Diagram Notation
Transfer function block
V=GX
Summing point
The output of the sum point is the algebraic sum of the entering signals
E=V-W X V Y E G P
Pickoff point
Variables connected at pickoff point have identical values
Y=Z Z W H
The signal entering the sum point is multiplied by -1
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Voltage Divider
Input
Output
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8. Two-input-two-output systems
inputs
outputs
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9. Main Objective of This Lesson
Given a block diagram with input X and output Y, find a single block that represent the transfer function between X and Y X Y G P H X
T=? Y
EE3511_L8
Salman Bin Abdulaziz University

10. Rules of Block Diagram Manipulation
Blocks in Series G H
H G G
Blocks in parallel
H + G H
Blocks in Feedback G
G .
1+H G _ H X
Moving a sum point X G Y Y G G X
Moving a pickoff point X Y G G V V Y G
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Salman Bin Abdulaziz University

11. Block Diagram Manipulation Blocks in Cascade (Series)Y X HG Y X V G H
Two blocks in cascade are replaced by a single block whose transfer function is the product of transfer functions
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12. Block Diagram Manipulations Parallel CombinationY X G Y
G+H X H
Two blocks that are in parallel can be replaced by a single block whose transfer function is the sum of transfer functions
EE3511_L8
Salman Bin Abdulaziz University

13. Block Diagram Manipulations Moving a pickoff point (#1)
Z=V G
Z=V G V Y G Y V
You can move a pickoff point behind a block (Backward movement).
EE3511_L8
Salman Bin Abdulaziz University

14. Block Diagram Manipulations Moving a pickoff point (#2)
Z=X
Z=X
G─1 X G Y G Y X
You can move a pickoff point ahead of a block (Forward movement).
EE3511_L8
Salman Bin Abdulaziz University

15. Block Diagram Manipulations Moving a summing point (#1)Y X X Y G G
G─1 U U
You can move a summing point behind a block (Backward movement).
EE3511_L8
Salman Bin Abdulaziz University

16. Block Diagram Manipulations Moving a summing point (#2)Y X X G G Y U U G
You can move a summing point ahead of a block (Forward movement).
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Salman Bin Abdulaziz University

17. Block Diagram Manipulations Eliminating a Feedback LoopX Y G X Y H
The feedback loop is replaced by the ratio of:
forward path gain over (1 - the loop gain)
EE3511_L8
Salman Bin Abdulaziz University

18. Example 1 Pressure Measurement System
The pressure measurement system consists of
A pressure sensor
Signal conditioner
Pressure Sensor
Generates electric
current proportional
to the pressure
G=0.1 mA/Pa
Signal
Conditioner
(Amplifier)
K=20 U Y
EE3511_L8
Salman Bin Abdulaziz University

19. Example 1(solution) Pressure Measurement System
Pressure Sensor
Generates electric
current proportional
to the pressure
G=0.1 mA/Pa
Signal
Conditioner
(Amplifier)
K=20 P V
T.F=20*0.1= 2 mA/Pa V P
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Salman Bin Abdulaziz University

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Example 2
Find the transfer function of the following system G H K ?
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Example 2(solution)
Find the transfer function of the following system U V W Y G H K
Y = KW = K (HV) = K H (GU) = KHG U
KHG
The transfer function of three blocks in series is the product of the three transfer functions
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More Rules G G H H K K L L
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23. Salman Bin Abdulaziz University
Example 3
Find the transfer function of the following system G H K ?
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24. Example 3 (solution)
Find the transfer function of the following system
Replace by a single block GH G H K
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25. Salman Bin Abdulaziz University
Example 4
Reduce the block diagram to a single block F X Y A B D E C ? Y X
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26. Salman Bin Abdulaziz University
Example 4
Reduce the block diagram to a single block F X Y A B D E C
Loop replaced by
AB/(1-ABC)
Parallel paths
D+E F X
AB .
1-ABC Y
D+E
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27. Example 4 Reduce the block diagram to a single block X Y X X Y F AB .
1-ABC Y
D+E
Two processes in series F X
AB (D+E)
1-ABC X
AB(D+E) .
1-ABC+FAB(D+E) Y
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Salman Bin Abdulaziz University

28. Example 5 Alternative way to solve Example 4
Reduce the block diagram to a single block F X Y A B D E C
This is the same block diagram in Example 4 ? Y X
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Salman Bin Abdulaziz University

29. Example 5 Alternative way to solve Example 4
Reduce the block diagram to a single block F X Y A B D E C
Replacing the parallel blocks F X Y A B
D+E
Move the pickoff point in front of D+E block C
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Salman Bin Abdulaziz University

30. Example 5 Reduce the block diagram to a single block X Y X Y F A B D+E
Replacing the cascade blocks
D+E C F X Y
AB(D+E)
. C .
D+E
Replacing the parallel blocks
EE3511_L8
Salman Bin Abdulaziz University

31. Example 5 Reduce the block diagram to a single block X Y X Y AB(D+E)
─ F
Replacing the cascade blocks then the feedback loop X
AB(D+E) .
1-ABC+FAB(D+E) Y
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Salman Bin Abdulaziz University

32. Salman Bin Abdulaziz University
Homework
Find the transfer function relating X and Y K X Y G M H
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33. Salman Bin Abdulaziz University
Summary
Block diagrams are for linear systems
Apply the rules of block manipulation to simplify the block diagrams
Alternative approaches can be done in reduction
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Salman Bin Abdulaziz University

34. Salman Bin Abdulaziz University
Keywords
Summing point
Pickoff point
Transfer function
Cascade combination
Parallel combination
Feedback combination
Block diagram
Block diagram reduction
EE3511_L8
Salman Bin Abdulaziz University