Name :- Smit Shah -140410109096

T.Y Electrical 2 Sem 5

Subject:-Control System Engineering..

Topic :-Block Reduction Method… 1

2

Block diagram

Transfer Function

Consists of Blocks

Can be reduced

)(sR2G 3G1G

4G

1H

2H

)(sY

G )(sY)(sR

3

Reduction techniques

2G1G 21GG

2. Moving a summing point behind a block

G G

G

1G

2G21 GG

1. Combining blocks in cascade or in parallel

4

5. Moving a pickoff point ahead of a block

G G

G G

G1

G

3. Moving a summing point ahead of a block

G G

G1

4. Moving a pickoff point behind a block

5

6. Eliminating a feedback loop

G

HGHG

1

7. Swap with two neighboring summing points

A B AB

G

1H

GG1

6

Example 1

Find the transfer function of the following block diagrams

2G 3G1G

4G

1H

2H

)(sY)(sR

(A)

7

1. Moving pickoff point A ahead of block 2G

2. Eliminate loop I & simplify

324 GGG B

1G

2H

)(sY4G

2G

1H

AB3G

2G

)(sR

I

Solution:

8

3. Moving pickoff point B behind block 324 GGG

1GB)(sR

21GH 2H

)(sY

)/(1 324 GGG

II

1GB)(sR C

324 GGG

2H

)(sY

21GH

4G

2G A3G 324 GGG

9

4. Eliminate loop III

)(sR)(1

)(

3242121

3241

GGGHHGGGGGG

)(sY

)()(1)(

)()()(

32413242121

3241

GGGGGGGHHGGGGGG

sRsYsT

)(sR1G

C

324

12

GGGHG

)(sY324 GGG

2H

C

)(1 3242

324

GGGHGGG

Using rule 6

10

2G1G

1H 2H

)(sR )(sY

3H

(B)

11

Solution:

1. Eliminate loop I

2. Moving pickoff point A behind block22

2

1 HGG

1G

1H

)(sR )(sY

3H

BA

22

2

1 HGG

2

221G

HG

1G

1H

)(sR )(sY

3H

2G

2H

BA

II

I

22

2

1 HGG

Not a feedback loop

)1(2

2213 G

HGHH

12

3. Eliminate loop II

)(sR )(sY22

21

1 HGGG

2

2213

)1(G

HGHH

21211132122

21

1)()()(

HHGGHGHGGHGGG

sRsYsT

Using rule 6

13

2G 4G1G

4H

2H

3H

)(sY)(sR

3G

1H

(C)

14

Solution:

2G 4G1G

4H)(sY

3G

1H

2H

)(sRA B

3H4

1G

4

1G

I1. Moving pickoff point A behind block 4G

4

3

GH

4

2

GH

15

2. Eliminate loop I and Simplify

II

III

443

432

1 HGGGGG

1G)(sY

1H

B

4

2

GH

)(sR

4

3

GH

II

332443

432

1 HGGHGGGGG

III

4

142

GHGH

Not feedbackfeedback

16

)(sR )(sY

4

142

GHGH

332443

4321

1 HGGHGGGGGG

3. Eliminate loop II & IIII

143212321443332

4321

1)()()(

HGGGGHGGGHGGHGGGGGG

sRsYsT

Using rule 6

17

3G1G

1H

2H

)(sR )(sY

4G

2G AB

(D)

18

Solution:

1. Moving pickoff point A behind block 3G I

1H3

1G

)(sY1G

1H

2H

)(sR

4G

2G A B

3

1G

3G

19

2. Eliminate loop I & Simplify

3G

1H

2G B

3

1G

2H

32GG B

23

1 HGH

1G)(sR )(sY

4G3

1

GH

23212

32

1 HGGHGGG

II

20

)(sR )(sY12123212

321

1 HGGHGGHGGGG

3. Eliminate loop II

12123212

3214 1)(

)()(HGGHGGHG

GGGGsRsYsT

4G

21