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Lesson 1: Introduction to Control
Systems Technology
ET 438a
Automatic Control Systems Technology
1
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Learning Objectives
After this presentation you will be able to:





2
Explain the function of an automatic control
system.
Identify a block diagram representation of a
physical system
Explain the difference between an open loop and
closed loop control system
Define a transfer function and compute the gain
for sinusoidal input/output cases.
Reduce block diagram systems using algebra.
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The Control Problem
Fundamental Control Concepts
Maintain a variable of process at a desired value
while rejecting the effects of outside
disturbances by manipulating another system
variable.
Examples:
Heating and Cooling homes and offices
Automobile cruise control
Hold the position of a mechanical linkage
Maintain level in a tank
Qout depends on h
If Qout = Qin, h constant
Qout > Qin, tank empties
Qout < Qin, tank overflows
h
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Basic Subsystems of Control
Feedback Control Subsystems
Measurement
Control decision
System modification
Measurementsight glass
Control Decision
Human adjusts Qout to
maintain h =H
Reference
(setpoint)
h = control
variable
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ProcessMaintain tank
level
Final Control
Element
Valve
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Automatic Control Systems
Use sensors and analog or digital electronics to monitor and adjust system
Level
Measurement
Sensor
Controller
Final control
element
Elements of Automatic Control
Process – single or multiple variables
Measurement – sensors
Error Detection – compare H to h
Controller – generate corrections
Final Control Element – modify
process
Maintain level
5
Valve Position
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Block Diagrams
Automatic control systems use mathematical descriptions of
subsystems to reduce complex components to inputs and outputs
Input signal
Control System
Component
Output signal
Energy
Source
(Optional)
Signals flow between components in system based on arrow direction
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Typical Component Block Diagrams
T (°C)
Temperature
Sensor
Vin (V)
Vout (V)
Valve Position
(% Open)
Dc Motor
n (rpm)
Armature V
Va (V)
L (ft)
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Level
Transmitter
Amplifier
Vout (mV)
Error
E (V)
Control
Valve
Liquid Flow
(m3/s)
Controller
Correction
V (V)
Current
(mA)
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Transfer Functions
Transfer function - ratio of the output to the input of a control system
component. Generally a function of frequency and time.
A∙sin(wt+a)
G
B∙sin(wt+b)
Block
Gain
Convert to phasors and
divide
G
B OutputSignal Bb B


 b  a
Input Signal
Aa A
A
Phase shift related to time
delay
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Transfer Functions
Examples
Example 1-1: Find transfer function of temperature sensor in block diagram
T (°C)
Temperature
Sensor
G
OutputSignal Vout

mV/C 
Input Signal
T
Vout (mV)
Example 1-2: a current-to-voltage converter takes an input of 17.530° mA and produces
an output of 8.3537° V Determine the transfer function gain and sketch the block diagram.
Iin  17.530 mA
G
I-to-V
Converter
G
Iin (mA)
Vo  8.3537  V
OutputSignal V o
8.3537  V


 V/ mA
Input Signal
Iin 17.530 mA
Vout (V)
G  0.4777  V/ mA
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Open-Loop Control
Open loop control modifies output based on predetermined control
values. There is no actual measurement of controlled quantity.
Tank level may vary
with outside
disturbances and
system changes
Controller
Final control
element
Valve
setting
Controller
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Control
Valve
Output
flow
Tank
Level
Tank
Disturbances
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Closed Loop Control
Closed loop control modifies output based on measured values of the
control variable. Measured value compared to desired value and used
to maintain desired value when disturbances occur. Closed loop
control uses feedback of output to input.
Desired
Value
+
Controller
-
Valve
setting
Output
flow
Control
Valve
Tank
Tank
Level
Level
Measurement
Measured
level
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Closed Loop Control
Example: Auto Cruise Control
Disturbances
Fuel
flow
Set Speed
+
Controller
-
Mechanical
Power
Fuel
Injectors
Engine
Actual
Speed
Auto
Error
Speed Sensor
Disturbances: Up hill/ down hill
Head wind/ tail wind
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Generalized Closed Loop Control
Block Diagram of Servo Control-Example Positioning Systems
R
+
E=R-Cm
-
Cm
Measurement
H=Cm/C
Reference = R
Error = E
Controlled Variable = C
13
C
Controller
G=C/E
Measured Variable = Cm
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Generalized Closed Loop Control
Find overall transfer function using signal flow algebra
(Input)(Gain)=(Output)
For servo control
1
E  R Cm
2
G
14
Find
C
R
C
 EG  C
E
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H
3
1
3
Cm
C
 C  H  Cm
E  R C
CmH
E
(R  C  H)  G  C
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Overall Transfer Function-Servo Control
C
R
(R  C  H)  G  C
Find
1
2
3
R G -CHG  C
Multiply through by G
R G  C  CHG
R  G  C  (1  G  H)
Add CHG to both sides
Factor C out of right hand side
R G
C
(1  G  H)
G
C

(1  G  H) R
Divide both sides by (1+GH)
Divide both sides by R
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Generalized Closed Loop Control
Block Diagram of Process Control-Example Chemical Reactors
E=R-Cm
SP
+
-
Control
Modes
Gc=V/E
Cm
Setpoint = SP
Error = E
Controlled Variable = C
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V
Manipulated
Variable
Gm=M/V
Measurement
H=Cm/C
M
Process
Gp=C/M
C
D=Disturbances
Measured Variable = Cm
Manipulated Variable = M
Controller Output = V
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Overall Transfer Function- Process
Control
Find overall transfer function of process control using signal flow algebra
Gc 
Series blocks multiple
V
E
Gm 
M
V
Gp 
C
M
V  M  C 
G  Gc  Gm  Gp         
 E   V  M
C 
G  
E 
Find overall transfer function Cm/SP C not directly measurable in
process control
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Overall Transfer Function- Process
Control
As before
E  SP  Cm
Cm  H  C 
GE  C
G  (SP  C m )  C
Cm
H
G  H  (SP  C m )  C m
G  (SP  C m ) 
G  H  SP  G  H  C m  C m
G  H  SP  C m  G  H  C m
G  H  SP  C m  (1  G  H)
G  H  SP
 Cm
1 G  H
GH
C
 m
1  G  H SP
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Cm
C
H
Substitute in for E
Substitute in for C eliminate it
Multiple both sides by H
Multiple L.H. side by GH
Add GHCm to both sides
Factor Cm from right side
Divide both sides by (1+GH)
Divide both sides by SP
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Control System Drawings
Industrial system standard ANSI/ISA-S5.1-1984 Uniform designation for
Instruments, instrument systems and control.
Functional
Identifier
Instrument Line Symbols
Loop
Identifier
3-15 psi
pneumatic
line
First ID Letter
Following ID Letter
4-20 mA
electric
current
A = Analysis
C= Controller
L = Level
I=Indicator
T = Temperature
R=Recorder
General Instrument
Symbol
Filled System
Capillary
T= Transmitter
V = Valve
Y = Relay/Converter
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Control System Drawings
Water
Supply
Syrup
Supply
101 =level control
102 = temperature control
103 = concentration control
LV
101
I/P
Current to
Pneumatic
Converter
4-20 mA
current
LY
101
AV
103
LT
101
LIC
101
Concentration
Valve
Heating Fluid
Supply
ARC
103
TV
102
Concentration
Recorder/Control
TIC
102
TT
102
Heating Fluid
Return
AT
103
Syrup
Concentration
Heated Product
Concentration
Transmitter
Temperature Transmitter
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Temperature Indicator/Control
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Linear and Non-linear Response
Linear R esponse
Output
2
2
Output
0
2
1
0.5
0
Input
0.5
0
1
2
Linear transfer functions give proportional
outputs. In this case the factor is 2
15
10
5
0
Time
5
10
15
Input
Output
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Non-linear Response
Saturation Non-Linearity
1
Input Signal
Saturation Non-Linearity
Output
10
0
0
1
15
10
5
0
Time
5
10
15
10
15
Input Signal
10
2
1
0
Input
1
2
Saturation Non-Linearity
3
Saturation non-linearity typical of practical systems
that have physical limits. Amplifiers, control valves
1
Output Signal
3
0
1
15
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10
5
0
Time
5
Output Signal
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Other Non-Linearities
Hystersis Non-Linearity
2
20
Output
Output
1
0
0
1
2
20
4
2
0
Input
2
4
40
Typical in magnetic circuit and in
instrumentation transducers
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General Non-Linearity
40
3
2
1
0
Input
1
2
3
Non-linearities cause distortion in sine waves
response that is not proportional to inputs value
for all signal values.
lesson1et438a.pptx
Block Diagram Simplifications
R +
G
-
R
C
H
C
G

R 1 G  H
C
Block diagram at left simplifies to the above.
Can use this to reduce multiple loops into one
Block.
Also remember that blocks in series multiply
G  G1  G 2  G 3
G1
G2
G3
G1G2G3
Equivalent Block
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Block Diagram Simplification Example
R +
G1
-
C
+
R1
G2
-
C1
G3
H1
H3
H2
H
C1
G2

R1 1  G 2  H1
Reduce the inner loop
H  H 2  H3
Combine outer feedback block
Combine reduced inner loop with remaining forward gain blocks
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Block Diagram Simplification Example (1)
R +
-
G1
G2
1  G 2  H1
C
G3
H=H2H3
 G2

 G1  G 2  G 3 
G  G1  
  G3  

1  G 2  H1 
 1  G 2  H1 
 G1  G 2  G 3 
 1 G  H 
C
G
2
1 



R 1 G  H
 G1  G 2  G 3 
1 
  H 2  H3
 1  G 2  H1 
26
Compute the value of G
Substitute the values of G and H into formula
and simplify
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Block Diagram Simplification Example (2)
C
G


R 1 G  H
 G1  G 2  G 3 
 1 G  H 
2
1 

G G G 
1   1 2 3   H 2  H3
 1  G 2  H1 
Multiply top and bottom of ratio by (1+G2H1) and simplify
 G1  G 2  G 3 
 1  G  H   1  G 2  H1 
G1  G 2  G 3
C
2
1 



R   G1  G 2  G 3 

 G1  G 2  G 3  H 2  H 3 
1  

  H 2  H 3   1  G 2  H1  1  G 2  H1   1  G 2  H1   

1  G 2  H1


  1  G 2  H1 

G1  G 2  G 3
C

R 1  G 2  H1  G1  G 2  G 3  H 2  H 3
Reduced
block
27
R
G1  G 2  G 3
1  G 2  H1  G1  G 2  G 3  H 2  H 3
Answer
C
lesson1et438a.pptx
End Lesson 1: Introduction to
Control Systems Technology
ET 438a
Automatic Control Systems Technology
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