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BLOCK DIAGRAMyash


BLOCK DIAGRAM:

o Defination:

1. A block diagram is a pictorial representation of the entire system.

2. The block diagram represents the relationship between the input and the output of the entire system.


Different terms: Block diagram:

Output:

-Output= Gain*Input• The value of the input is multiplied to the value

of block gain to get the output.

Block diagram of physical system

OutputInput


G R(s)input output

C(s)

Summing point

More than one signal can be added or subtracted at summing point

x

y

z=x+y orZ=x-y

+

_


Take off point• The point from which a signal is taken for the

feedback purpose is called as take-off point• This means from the take-off point , the output

signal is fed back at the input side.

Forward path• The direction of flow of signal is from input to

output.

Take off point

G1 G2R(s) C(s)


Feedback path

• The direction of flow of signal is from output to input. It is shown in figure.

GR(S)

+_

C(S)

Feed back path


Advantages of block diagram

• The functional operation of the system can be observed from block diagram.

• Block diagram gives the information about performance of system.

• Block diagram is used for analysis and design of control system.

• It is very simple to construct the block diagram for big and complicated system.


Disadvantages of block diagram

• Block diagram for a given system is not unique.• Source of energy in the system is not shown in

the diagram.• In the procedure of reduction of block diagram

algebra, some important functions may be omitted or hidden.

• The block diagram does not give any information about the physical construction of the system.


Reduction techniques

2G1G 21GG

1. Combining blocks in cascade

1G

2G21 GG

2. Combining blocks in parallel


3. Eliminating a feedback loop

G

HGHG

1

4. Swap with two neighboring summing points

A B AB

G

1H

GG1


Reduction techniques

5. Moving a summing point behind a block

G G

G


8. Moving a pickoff point ahead of a block

G G

G G

G1

G

6. Moving a summing point ahead of a block

G G

G1

7. Moving a pickoff point behind a block


A Feedback Control System

G=direct transfer function = forward transfer function H=feedback transfer function GH=loop transfer function=open-loop transfer function C/R=closed –loop transfer function= control ratio C

E/R=actuating signal ratio =error ratio

B/R=primary feedback ratio

R

R= G

1+_ GHE 1

1+_ GHB

R

=

= GH1+_ GH


Characteristic Equation

• The control ratio is the closed loop transfer function of the system.

• The denominator of closed loop transfer function determines the characteristic equation of the system.

• Which is usually determined as:

)()()(

)()(

sHsGsG

sRsC

1

01 )()( sHsG


Example-1

1. Open loop transfer function

2. Feed Forward Transfer function

3. control ratio

4. feedback ratio

5. error ratio

6. closed loop transfer function

7. characteristic equation

)()()()( sHsGsEsB

)()()( sGsEsC

)()()(

)()(

sHsGsG

sRsC

1

)()()()(

)()(

sHsGsHsG

sRsB

1

)()()()(

sHsGsRsE

1

1

)()()(

)()(

sHsGsG

sRsC

1

01 )()( sHsG

)(sG

)(sH


Example-2:Reduction of block diagram

Step 1: Combine all cascade blocks using transformation 1.

Step 2: Combine all parallel blocks using transformation 2.

http://alltypeim.blogspot.in/However in this example step-6 does not apply.

Step 3: Eliminate all minor feedback loops using transformation 4.

Step 4: Shift summing points to the left and takeoff points to the right of the major loop, using transformation 7,10 and 12. However in this example step-4 does not apply.Step 5: Repeat steps 1 to 4 until the canonical form has been achieved for a particular input

Step 6: Repeat steps 1 to 5 for each input, as required.


Example-3

• For the system represented by the following block diagram determine:1. Open loop transfer function2. Feed Forward Transfer function3. control ratio4. feedback ratio5. error ratio6. closed loop transfer function7. characteristic equation


– First we will reduce the given block diagram to canonical form

1sK


1sK

ssK

sK

GHG

11

11


1. Open loop transfer function

2. Feed Forward Transfer function

3. control ratio

4. feedback ratio

5. error ratio

6. closed loop transfer function

7. characteristic equation

)()()()( sHsGsEsB

)()()( sGsEsC

)()()(

)()(

sHsGsG

sRsC

1

)()()()(

)()(

sHsGsHsG

sRsB

1

)()()()(

sHsGsRsE

1

1

)()()(

)()(

sHsGsG

sRsC

1

0)()(1 sHsG

)(sG

)(sH


Example-4

R_+

_+1G 2G 3G

1H

2H

+ +

C


R_+

_+

1G 2G 3G

1H

1

2

GH

+ +

C


R_+

_+

21GG 3G

1H

1

2

GH

+ +

C


R_+

_+ 21GG 3G

1H

1

2

GH

+ +

C


R_+

_+

121

21

1 HGGGG

3G

1

2

GH

C


R_+

_+

121

321

1 HGGGGG

1

2

GH

C


R_+

232121

321

1 HGGHGGGGG

C


R

321232121

321

1 GGGHGGHGGGGG

C


Example 5Find the transfer function of the following block diagrams

2G 3G1G

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

AB3G

2G

)(sR

I

Solution:


3. Moving pickoff point B behind block324 GGG

1GB)(sR

21GH 2H

)(sY

)/(1 324 GGG

II

1GB)(sR C

324 GGG

2H

)(sY

21GH

4G

2GA

3G 324 GGG


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


……THANK YOU……