Lesson 5

Block diagrams

&

Signal flow graphs

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blocksummer

pickoff point

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)()()( sEsGsY

)()()()( sYsHsRsE

)()()()()()]()()()[()( sYsHsGsRsGsYsHsRsGsY

)()(1

)(

)(

)()(

sHsG

sG

sR

sYsT

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Automatic control

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Automatic control

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original equivalent

A

B C

BA CBA

A

BC

CA BCA

A

B

CBA

C

A

B C

BA CBA

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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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original equivalent

AG

G

AG

AG

AG

AG

AG

AG

AG

A

AG

AG

AG

1

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Example 1 Automatic control

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Example 2 Automatic control

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Signal flow graphs Automatic control

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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.

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Example 3 Automatic control

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a b

cd

e

f

g1 1

h

ij

1y 2y 5y3y

Example 4

3

5

y

yfind