lesson 5
DESCRIPTION
Automatic control 1. modeling. Lesson 5. Block diagrams & Signal flow graphs. 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. - PowerPoint PPT PresentationTRANSCRIPT
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Lesson 5
Block diagrams
&
Signal flow graphs
Automatic control1. modeling
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Automatic Control by Meiling CHEN 2
blocksummer
pickoff point
Automatic control
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Automatic Control by Meiling CHEN 3
)()()( sEsGsY
)()()()( sYsHsRsE
)()()()()()]()()()[()( sYsHsGsRsGsYsHsRsGsY
)()(1
)(
)(
)()(
sHsG
sG
sR
sYsT
Automatic control
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Automatic Control by Meiling CHEN 4
Automatic control
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Automatic Control by Meiling CHEN 5
Automatic control
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Automatic Control by Meiling CHEN 6
original equivalent
A
B C
BA CBA
A
BC
CA BCA
A
B
CBA
C
A
B C
BA CBA
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Automatic Control by Meiling CHEN 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 )(
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Automatic Control by Meiling CHEN 8
original equivalent
AG
G
AG
AG
AG
AG
AG
AG
AG
A
AG
AG
AG
1
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Automatic Control by Meiling CHEN 9
Example 1 Automatic control
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Automatic Control by Meiling CHEN 10
Example 2 Automatic control
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Automatic Control by Meiling CHEN 11
Signal flow graphs Automatic control
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Automatic Control by Meiling CHEN 12
Automatic control
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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
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
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Automatic Control by Meiling CHEN 14
Example 3 Automatic control
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Automatic Control by Meiling CHEN 15
a b
cd
e
f
g1 1
h
ij
1y 2y 5y3y
Example 4
3
5
y
yfind