02 Block Diagram Signal Flow

7/23/2019 02 Block Diagram Signal Flow

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Block Diagram & Signal Flow

Specially

preparedforthefo

llowingcourses:

ProcessControl&Instrumentation

Chemical

ProcessControl

FacultyofChemicalEngineering,UniversitiTeknolo

giMARAMalaysia


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Fundamentals of Block Diagram

Rectangular block:Represents the cause-and-effect

relationship between the input and

output of a physical system.

Control

Element

Input Output

Control element:

Represents any of the system

components such as controller,

process, sensor, transmitter,

transducer, control valve, metering

pump, solenoid valve, etc.

Arrow:

Represent the direction of signal

flow.

Controller

Control valve

%TO

%CO

%CO

%PV


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Fundamentals of Signal Flow

Take off point:A point where the signal is

channeled to various operators or

control elements.

Circle:

Represents the signals operation. A

negative or positive sign is placed

inside the circle to represent

deduction or addition of the

respective signals, respectively.

yxx+-

y

x x

x


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Examples of Block Diagram & Signal Flow

Example No. 1:Draw a block diagram for the

following equation:

x3= a1x1+ a2x25

where, a and x are the controlelements and signals, respectively.

1x

+-

2x

5

3x+

1a

2a

Example No. 2:

Draw a block diagram for the

following equation:

where, the integrator and

differentiator are the control

elements; while x is the control

signal.

dt

dxdtxx 214

1x dt

4x

2xdt

d

+

+


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Example No. 3:Draw a block diagram for the

following equation:

where, the integrator, differentiatorand square root extractor are the

control elements; while x is the

control signal.

121

2

14 xdt

xddtxx

1x dt

4xdtd +

+dt

d+


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Example No. 4:

Find Xn/X1for the following system.

)1(

10

s

Answer:

)1(

1

s1x

2x

nx

12)1(

10x

sx

2

)1(

1x

s

xn

. (1)

Put (1) into (2):

. (2)

1212 )1(

10

)1(

10

)1(

1

)1(

1x

sx

ssx

sxn


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Tutorial of Block Diagram & Signal Flow

Question No. 1:


)1(

1

s )1(

10

s1x

2x

Question No. 2:


)1(

10

s )1(

1

s1x

2x

nx

s

23x

nx

1212 )1(

10

)1(

1

)1(

10

)1(

10x

sx

ssx

sxn

Answer:

1)1()1(

20x

sssxn

Answer:


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Feed back Loop in Block Diagram

Feed back loop:A signal splits from a stream and

goes to a control element which

later added to the original stream.

Question:

What are the relationship betweenthese variables: r, e, b & c.

er

b

Answer:Perform balance at summing junction:

e = r + b (1)Perform balance at G block:

c = e G . (2)Perform balance at H block:

b = c H . (3)Solving (1), (2) and (3) simultaneously:

GH

G

r

c

1


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Feed back loop:A signal splits from a stream and

goes to a control element which

later added to the original stream.

Question:

What are the relationship betweenthese variables: r, e, b & c.

Answer:Perform balance at summing junction:

e = r - b (1)Perform balance at G block:

c = e G . (2)Perform balance at H block:

b = c H . (3)Solving (1), (2) and (3) simultaneously:

GH

G

r

c

1

er

b

cG

H


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GHG

rc

1

er

b

cG

H

r cGH

G

1

(i) Closed loop

(ii) Open loop

Mathematical equivalent. Block diagram.


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Rules for Block Diagram

1. Summing junction

2. Associative and commutative properties

3. Distributive property

4. Blocks in parallel

5. Positive feed back

6. Negative feed back


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Examples of Mathematical Equivalent of Block

Diagrams


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Diagrams


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Diagrams


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Diagrams


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Tutorials

Question:Calculate C/R of the following system.


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Tutorials



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Tutorials



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Tutorials

1


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02 Block Diagram Signal Flow

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