Control SystemsBlock Diagram

Dr. Juma Yousuf Alaydi

Block Diagram Reduction

Figure 1: Single block diagram representation

Figure 2: Components of Linear Time Invariant Systems (LTIS)

Figure 3: Block diagram components

Figure 4: Block diagram of a closed-loop system with a feedback element

BLOCK DIAGRAM SIMPLIFICATIONS

Figure 5: Cascade (Series) Connections

Figure 6: Parallel Connections

Block Diagram Algebra for Summing Junctions

Figure 7: Summing Junctions

Block Diagram Algebra for Branch Point

Figure 8: Branch Points

Block Diagram Reduction Rules

Table 1: Block Diagram Reduction Rules

Table 2: Basic rules with block diagram transformation

Example 1

R

_+

_

+1G 2G 3G

1H

2H

++

C

Example

R

_+

_

+1G 2G 3G

1H

1

2

G

H

++

C

Example

R

_+

_

+21GG 3G

1H

1

2

G

H

++

C

Example

R

_+

_

+21GG 3G

1H

1

2

G

H

++

C

Example

R

_+

_

+121

21

1 HGG

GG

3G

1

2

G

H

C

Example

R

_+

_

+121

321

1 HGG

GGG

1

2

G

H

C

Example

R

_+232121

321

1 HGGHGG

GGG

C

Example

R

321232121

321

1 GGGHGGHGG

GGG

C

Example 2

Find the transfer function of the following block diagrams

2G3G1G

4G

1H

2H

)(sY)(sR

1. Moving pickoff point A ahead of block2G

2. Eliminate loop I & simplify

324 GGG B

1G

2H

)(sY4G

2G

1H

AB

3G

2G

)(sR

I

Solution:

3. Moving pickoff point B behind block324 GGG

1GB

)(sR

21GH 2H

)(sY

)/(1 324 GGG

II

1GB

)(sRC

324 GGG

2H

)(sY

21GH

4G

2G A3G 324 GGG

4. Eliminate loop III

)(sR

)(1

)(

3242121

3241

GGGHHGG

GGGG

)(sY

)()(1

)(

)(

)()(

32413242121

3241

GGGGGGGHHGG

GGGG

sR

sYsT

)(sR

1GC

324

12

GGG

HG

)(sY324 GGG

2H

C

)(1 3242

324

GGGH

GGG