Basic elements of Block Diagram and
their representation of signal flow:
Series(cascade):
)(sX
)(1 sH
)(sH 2
)(sY
( )X s
)(
sHsHsH
)(
)(
2
1
Parallel:
)(1 sH
)(sX
)(2 sH
1
2
)(
)(
)(
sHsHsH
Feed-back:
)(sX
)(1 sH
)(2 sH
)(1 sH
)(2 sH
)(sY
( )
Y s H s H s X s
( )
( )
( )
1
2
( )X s
)(sY
( )
Y s
( )X s
[
1
)(1 sH
)(sY
)(2 sH
( )
1
( )]
( )
H s H s X s
( )Y s
1( )H s
2
)(sY
+
1
)(
sH
=
2( )H s
)(
sH
1
)(
)(
sHsH
2
1
Rule of the node:
1E
2E
1T
2T
4E
3T
2
3E
T E T E
1
1
T E
5
4
T E
6
4
4
E
E
5
E
6
5T
6T
5E
6E
T E
3
3
2
Block Diagram and the Signal Diagram
( )X s
1s
a
K
)(sY
1
( )X s
1s
a
K
)(sY
4
)(sY
0b
( )X s
1s
0a
1
1
( )X s
1s
0a
0b
)(sY
1
Mason Rule(梅森规则)
sH )(
k
kG
LLL
k
i
j
系统的总增益
k
式中
1
j
i
,
j
i
,
+
L
i
LL
i
i
所有不同回路
,
kj
所有三个互不接触
回路的增益 之和
的增益之和
积
= 1 -
-
所有两个互不接触
回路的增益积之和
+ ...
Gk 由输入节点到输出节点的第K条前向通路增益。
k 不与第K条前向通路相接触的那一部分值。即
把第K条前向通路去掉后的值。
)(sX
)(sE
1
s
1
s
)(sF
3
)(sY
2
( )X s
1
)(sE
1s
)(sF
1s
1
)(sY
3
2
( )
H s
(1/ ) 1/
s
s
( )
1 [( 3/ )
( 2 /
s
1
3
s
2
2
s
2
s
)]
)(sX
)(1 sE
1
s
1-
)(1 sY
)(2 sE
)(sY
1
s
2-
( )X s
1
1( )E s
1s
2( )E s
1s
1
)(sY
1( )Y s
1
1
( )
H s
1 [( 1/ )
s
1
3
s
2
2
s
(1/ ) 1/
)]
( 2 /
2
s
s
( )
[( 1/ )( 2 / )]
s
1
1)(
2)
(
s
s
s
s