Block Diagram & Signal Flow Specially prepared for the following courses: • Process Control & Instrumentation • Chemical Process Control Faculty of Chemical Engineering, Universiti Teknologi MARA Malaysia
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Block Diagram & Signal Flow
Spec
ially
pre
par
ed f
or
the
follo
win
g co
urs
es:
• P
roce
ss C
on
tro
l & In
stru
men
tati
on
•
Ch
emic
al P
roce
ss C
on
tro
l
Facu
lty
of
Ch
emic
al E
ngi
nee
rin
g, U
niv
ersi
ti T
ekn
olo
gi M
AR
A M
alay
sia
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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