SIGNIFICANCE OF BLOCK DIAGRAM AND SIGNAL FLOW GRAPH IN CONTROL SYSTEM

1. SIGNIFICANCE OF BLOCK DIAGRAM AND SIGNAL FLOW GRAPH IN
CONTROL SYSTEM

2. CONTENT
 BLOCK DIAGRAM
 BLOCK DIAGRAM REDUCTION
 WHY SIGNAL FLOW GRAFH
 MANSON’S GAIN FORMULA
 SIGNIFICANCE OF B.D. &SFG
 CONCLUSION
 REFERENCES

3. BLOCK DIAGRAMS
 A block diagram of a system is a pictorial
representation of the functions performed by
each component and of the flow of signals.
 Such diagram depicts the interrelationships
that exist among the various components.
 Differing from a purely abstract mathematical
representation, a block diagram has the
advantage of indicating more realistically the
signal flows of the actual system.

4. • In a block diagram all system variables are linked to
each other through functional blocks.
• The functional block or simply block is a symbol for the
mathematical operation on the input signal to the block
that produces the output.
• The transfer functions of the components are usually
entered in the corresponding blocks, which are
connected by arrows to indicate the direction of the flow
of signals.
The arrowhead pointing toward the block indicates the input.
the arrowhead leading away from the block represents the output.
Such arrows are referred to as signals.

5. Summing point and branch (pickoff) point
Summing Point. A circle with a cross is the symbol that indicates a summing
operation. The plus or minus sign at each arrowhead indicates whether that
signal is to be added or subtracted.
Branch Point. A branch point is a point from which the signal from a block
goes concurrently to other blocks or summing points.
Summing point
Block diagram of a
Closed-loop system

6. Three basic forms
G1 G2
G2
G1
G1
H1
G1 G2 G1 G2 G1
G1
H11+
cascade parallel feedback

7. 2 block diagram reduction
2 block diagram transformations
behind a block
x1 y
G
±
x2
±
x1
x2
y
G
G
Ahead a block
±
x1
x2
y
G
x1
y
G
±
x21/G
1. Moving a summing point to be:

8. 2. block diagram reduction
2. Moving a pickoff point to be:
behind a block
G
x1
x2
y
G
x1
x2
y
1/G
ahead a block
G
x1
x2
y
G
G
x1
x2
y

9. 2. block diagram reduction
3. Interchanging the neighboring—
Summing points
x3
x1
x2
y＋
－
x1
x3
y＋
－
x2
Pickoff points
y
x1
x2
y
x1 x2

10. 2. block diagram reduction
4. Combining the blocks according to three basic forms.
Notes:
1. Neighboring summing point and pickoff point can not be
interchanged！
2. The summing point or pickoff point should be moved to the
same kind！
3. Reduce the blocks according to three basic forms！
Examples:

11. Moving pickoff point
G1 G2 G3 G4
H3
H2
H1
a b
G4
1
G1 G2
G3 G4
H3
H2
H1
Example 2.1

12. G2
H1
G1
G3
Moving summing point Move to the same kind
G1 G2
G3
H1
G1
Example 2.2

13. G1
G4
H3
G2 G3
H1
Disassembling the
actions
H1
H3
G1
G4
G2 G3
H3H1
Example 2.19

14. SIGNAL FLOW GRAPHS (SFG)
Why SFG?
Block Diagrams are adequate for representation,
but cumbersome.
The “flow graph gain formula” (Mason) allows the system
transfer function to be directly computed without
manipulation or reduction of the diagram.
SFG looks compact

15. 3. Signal-Flow Graph
Block diagram reduction ——is not convenient to a complicated
system.
Signal-Flow graph —is a very available approach to determine
the relationship between the input and output variables of a sys-
tem, only needing a Mason’s formula without the complex reduc-
tion procedures.
3.1 Signal-Flow Graph
only utilize two graphical symbols for describing the relation-
ship between system variables。
Nodes, representing the signals or variables.
Branches, representing the relationship and gain
Between two variables.
G

16. b
3. Signal-Flow Graph
Example 3.1
34
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gxfxx
exdxx
cxbxaxx

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3.2 some terms of Signal-Flow Graph
Path — a branch or a continuous sequence of branches traversing
from one node to another node.
Path gain — the product of all branch gains along the path.

17. Signal-Flow Graph
Loop —— a closed path that originates and terminates on the
same node, and along the path no node is met twice.
3.2.3 Mason’s gain formula
Loop gain —— the product of all branch gains along the loop.
Touching loops —— more than one loops sharing one or more
common nodes.
Non-touching loops — more than one loops they do not have a
common node.
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18. Manson’s gain formula

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19. Signal-Flow Graph
Example 3.3
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22
11
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x
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20. 1.SIMPLE AMPLIFIER
2.containing a two-port network

21. • Position servo and signal flow graph

22. CONCLUSION
• The B.D. & SFG modeling may provide control
engineers with a better understanding of the
composition and interconnection of
component of system
• It can be used together with transfer function,
to describe the cause-effect relationships
throughout the system

23. TEXT BOOK CONTROL SYSTEM:- by
I.J.NAGARATH
 LINEAR CONTROL SYSTEM:- D. Roy Choudhury
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