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
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
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
