Block Diagram & Signal Flow

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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

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

Examples of Block Diagram & Signal Flow

Example No. 1: Draw a block diagram for the following equation:

x3 = a1 x1 + a2x2 – 5

where, a and x are the control elements 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 2

14

1x dt

4x

2xdt

d

+

+

Examples of Block Diagram & Signal Flow

Example No. 3: Draw a block diagram for the following equation:

where, the integrator, differentiator and square root extractor are the control elements; while x is the control signal.

12

12

14 xdt

xddtxx

1x dt

4xdt

d + + dt

d+

Examples of Block Diagram & Signal Flow

Example No. 4: Find Xn/X1 for the following system.

)1(

10

s

Answer:

)1(

1

s1x

2x

nx

12)1(

10x

sx

2)1(

1x

sxn

………. (1)

Put (1) into (2):

………. (2)

1212)1(

10

)1(

10

)1(

1

)1(

1x

sx

ssx

sxn

Tutorial of Block Diagram & Signal Flow

Question No. 1: Find Xn/X1 for the following system.

)1(

1

s )1(

10

s1x

2x

Question No. 2: Find Xn/X1 for the following system.

)1(

10

s )1(

1

s1x

2x

nxs

23x

nx

1212)1(

10

)1(

1

)1(

10

)1(

10x

sx

ssx

sxn

Answer:

1)1()1(

20x

sssxn

Answer:

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 between these variables: r, e, b & c.

er

b

cG

H

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

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 between these 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

Feed back Loop in Block Diagram

GH

G

r

c

1

er

b

cG

H

r cGH

G

1

(i) Closed loop

(ii) Open loop

Mathematical equivalent. Block diagram.

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

Examples of Mathematical Equivalent of Block Diagrams

Examples of Mathematical Equivalent of Block Diagrams

Examples of Mathematical Equivalent of Block Diagrams

Examples of Mathematical Equivalent of Block Diagrams

Tutorials

Question: Calculate C/R of the following system.

Tutorials

Question: Calculate C/R of the following system.

Tutorials

Question: Calculate C/R of the following system.

Tutorials

1

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