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SIGNAL FLOW GRAPHS. SUBMITTED BY: Mrs. RAMANDEEP KAUR ASSOT. PROFESSOR-EEE. Automatic control. block. pickoff point. summer. Automatic control. Automatic control. Automatic control. original. equivalent. G. G. G. original. equivalent. G. G. G. G. G. original. equivalent. G. - PowerPoint PPT Presentation
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SIGNAL FLOW GRAPHS
SUBMITTED BY:Mrs. RAMANDEEP KAURASSOT. PROFESSOR-EEE
Automatic Control by Meiling CHEN 2
blocksummer
pickoff point
Automatic control
(c) 3
)()()( sEsGsY
)()()()( sYsHsRsE
)()()()()()]()()()[()( sYsHsGsRsGsYsHsRsGsY
)()(1
)(
)(
)()(
sHsG
sG
sR
sYsT
Automatic control
4
Automatic control
5
Automatic control
6
original equivalent
A
B C
BA CBA
A
BC
CA BCA
A
B
CBA
C
A
B C
BA CBA
7
original equivalent
A
B
BAG
G
AG A
B
BAG
GG
BA
G
1
A
B
GBA )(
G
BA A
B
G
G
GBA )(
8
original equivalent
AG
G
AG
AG
AG
AG
AG
AG
AG
A
AG
AG
AG
1
9
Example 1 Automatic control
10
Example 2 Automatic control
11
Signal flow graphs Automatic control
12
Automatic control
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
332211)(
pppsT
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
Example 3 Automatic control
15
a b
cd
e
f
g1 1
h
ij
1y 2y 5y3y
Example 4
3
5
y
yfind
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