Digital

1. Block diagrams
&
Signal flow graphs
Dr.Ziad Saeed Mohammed
2019-2020

2. Automatic Control by Meiling CHEN 2
block
summer
pickoff point
Automatic control

3. Automatic Control by Meiling CHEN 3
)
(
)
(
)
( s
E
s
G
s
Y 
)
(
)
(
)
(
)
( s
Y
s
H
s
R
s
E 

)
(
)
(
)
(
)
(
)
(
)]
(
)
(
)
(
)[
(
)
( s
Y
s
H
s
G
s
R
s
G
s
Y
s
H
s
R
s
G
s
Y 



)
(
)
(
1
)
(
)
(
)
(
)
(
s
H
s
G
s
G
s
R
s
Y
s
T



Automatic control

4. Automatic Control by Meiling CHEN 4
Automatic control

5. Automatic Control by Meiling CHEN 5
Automatic control

6. Automatic Control by Meiling CHEN 6
original equivalent
A
B C
B
A  C
B
A 





A
B
C
C
A B
C
A 





A
B
C
B
A 




C
A
B C
B
A  C
B
A 






7. Automatic Control by Meiling CHEN 7
original equivalent
A
B
B
AG


G
AG
A
B
B
AG


G
G
B
A 
G
1
A
B
G
B
A )
( 


G
B
A 
A
B


G
G
G
B
A )
( 

8. Automatic Control by Meiling CHEN 8
original equivalent
A
G
G
AG
AG
A
G
AG
AG
A
G
AG
A
A
G
AG
A
G
1

9. Automatic Control by Meiling CHEN 9
Example 1
Automatic control

10. Automatic Control by Meiling CHEN 10
Example 2
Automatic control

11. Automatic Control by Meiling CHEN 11
Signal flow graphs Automatic control

12. Automatic Control by Meiling CHEN 12
Automatic control

13. Automatic Control by Meiling CHEN 13
Mason’s Rule
Mason’s gain rule is as follows: the transfer function of a
system with signal-input, signal-output flow graphs is









3
3
2
2
1
1
)
(
p
p
p
s
T
Δ=1-(sum of all loop gains)+(sum of products of gains of all combinations if 2
nontouching loops)- (sum of products of gains of all combinations if 3
nontouching loops)+…
A path is any succession of branches, from input to output, in the direction of the
arrows, that does not pass any node more than once.
A loop is any closed succession of branches in the direction of the arrows that
does not pass any node more than once.
Automatic control

14. 14
Example 3
Automatic control

15. 15
a b
c
d
e
f
g
1 1
h

i

j

1
y 2
y 5
y
3
y
Example 4
3
5
y
y
find