lesson 5

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Lesson 5 Block diagrams & Signal flow graphs Automatic control 1. modeling

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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 Presentation

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Page 1: Lesson 5

Lesson 5

Block diagrams

&

Signal flow graphs

Automatic control1. modeling

Page 2: Lesson 5

Automatic Control by Meiling CHEN 2

blocksummer

pickoff point

Automatic control

Page 3: Lesson 5

Automatic Control by Meiling CHEN 3

)()()( sEsGsY

)()()()( sYsHsRsE

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

)()(1

)(

)(

)()(

sHsG

sG

sR

sYsT

Automatic control

Page 4: Lesson 5

Automatic Control by Meiling CHEN 4

Automatic control

Page 5: Lesson 5

Automatic Control by Meiling CHEN 5

Automatic control

Page 6: Lesson 5

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

Page 7: Lesson 5

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 )(

Page 8: Lesson 5

Automatic Control by Meiling CHEN 8

original equivalent

AG

G

AG

AG

AG

AG

AG

AG

AG

A

AG

AG

AG

1

Page 9: Lesson 5

Automatic Control by Meiling CHEN 9

Example 1 Automatic control

Page 10: Lesson 5

Automatic Control by Meiling CHEN 10

Example 2 Automatic control

Page 11: Lesson 5

Automatic Control by Meiling CHEN 11

Signal flow graphs Automatic control

Page 12: Lesson 5

Automatic Control by Meiling CHEN 12

Automatic control

Page 13: Lesson 5

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

Page 14: Lesson 5

Automatic Control by Meiling CHEN 14

Example 3 Automatic control

Page 15: Lesson 5

Automatic Control by Meiling CHEN 15

a b

cd

e

f

g1 1

h

ij

1y 2y 5y3y

Example 4

3

5

y

yfind