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Continuous Control Systems
California State University,
Fullerton
Certificate Award
Industrial Controls Technology
Instructor: Victor Wegelin
PMA ConceptsPhone: (562) 434-6728
E-Mail: pmaconcept@aol.com
Web: http://www.pmaconcepts.com
Continuous Control Systems Agenda
• Week 1
Sec. 1 Introduction to Industrial Controls
Sec. 2 Block Diagrams, Transfer
Functions
Sec. 3 Properties of Physical Systems
Lab #1 Process Dynamics: Sections 1-3
Continuous Control Systems Agenda
• Week 2
Sec. 4 Control Strategies
On-Off Control
Open Loop, Feed Forward,
Feedback
Modes of Control
Sec. 5 Proportional Control
Continuous Control Systems Agenda
• Week 3
Sec. 6 Two Mode Control
Sec. 7 Three Mode Control
Modifications to PID Control
• Week 4
Sec. 8 Controller Tuning Methods
Continuous Control Systems Agenda
• Week 5
Lab #9 Open Loop Tuning
Lab #10 Closed Loop Tuning
Continuous Control Systems Agenda
• Week 6
Sec. 9 Advanced Regulatory Control
Sec. 10 Ratio Control
Sec. 11 Cascade Control
Sec. 12 Feed Forward Control
Continuous Control Systems Agenda
• Week 7
Sec. 13 Override Control
Sec. 14 Multiple Input-Multiple Output
Processes
Sec. 15 Summary of All Methods
Continuous Control Systems Agenda
• Week 8
Lab #16 Feedforward Control
Extra Credit
Lab #1 Process Dynamics: Sections 4, 5
Lab #15 Cascade Control
Overview
• This course will explore the cause and
effect relationship of properties of physical
systems and their control.
• Topics include modeling of physical
systems, feedback control characteristics,
stability, digital control, tuning of control
loops, and basics of proportional, integral,
and derivative (PID) control.
At the end of this course you should be
able to:
• Describe process characteristics relevant to
analysis and design of selected industrial
applications
• Relate to mathematical fundamentals
• Describe the behavior of the three modes of
control of a classical PID controller
• Identify several methods for tuning feedback
control loops
• Understand the use of advanced control strategies
Section 1
INTRODUCTION TO
INDUSTRIAL CONTROLS
TECHNOLOGY
What is Automatic Control?
• Application of feedback theory to the
control of various physical processes
• Expressed and applied through the language
of mathematics
• Involved with transient or dynamic
behavior, rather than static or equilibrium
state
Examples of Automatic Control
Aviation
Power Generation
Communication
Building
Energy Management
Space
Automotive
Factory Automation
History of Automatic Control
EARLY: Add more or less wood to keep the water boiling
FERTILE
CRESCENT: Measurement of water to irrigate fields
SAMURAI: Product Quality introduced - Sword Making
1788: James Watt - Flywheel Governor
1866: Whitehead - Torpedo Control
1880: Fisher - Pressure Activated Pump Governor
1920’s: Petrochemicals - Pneumatic Feedback Control
1930’s: Formal Feedback Theory developed - Electronics,
Communications, Servomechanisms
History of Automatic Control
1940’s: Autopilots, Radar Control Rooms emerge
1950’s: Aircraft, Power Generation Electronic Controllers,
Supervisory and Digitally Directed Analog Control
1960’s: Direct Digital Control (DDC)
1970’s: LSI Technology improves reliability, Distributed
Control Systems (DCS)
1980’s: Plant-Wide Control, Networks, Global Standards
1990’s: Integration of Plant Information Systems, Quality
Control as a Mechanism, Vision Recognition
1990’s: Internet Access and Integration
What is an Industrial Control System?
• Distributed Process Control System?
(e.g. Honeywell TDC 3000)
• PLC Network?
• Personal Computers, connected to a Local
Network, with Process I/O?
• Any Control System that comes in two or
more pieces?
• Any or all of the above?
Integrated Control SystemBlock Diagram
(SGS)
Safety Shutdown
System PLC’s
FIE
LD
DE
VIC
ES
Dedicated PLC’s
Process Analyzer
Systems
Tank Gauging
System
Blending System
SCADA Systems
MIS COMPUTERS
DISTRIBUTED
CONTROL SYSTEM
Process Control
Computers
Engineering
Workstations
Lab Analysis
Computers
Machinery
Monitoring
HC/H2S/GAS
Monitoring
FIE
LD
DE
VIC
ES
Hierarchical Control
MARKET DEMAND
DELIVERY DATES
RAW MATERIALS
MFG. RESOURCES
MIS
PROCESS / MFG
CONTROL
MANAGEMENT
INFO
SYSTEM
PLANNING/
SCHEDULING
UNIT/PLANT
OPTIMIZATION
MES
EXPERT SYSTEMS
CONTINUOUSFEED FORWARD
INTERACTING
BATCHSEQUENCE
RECIPES
BANG/BANG CONTROL
ADVANCED CONTROL
BASIC CONTROL
DATA FOR
EXECUTIVE
MANAGEMENT
DATA FOR
PLANT
MANAGEMENT
MAXIMIZE PROFIT
EFFICIENT
OPERATION
PROCESS
Why Automatic Control?
Direct Benefits:
• Increase Productivity
– Throughput, Yield
• Reduce Costs
– Materials, Manpower, Energy
• Environmental Compliance
– Waste Minimization
Why Automatic Control?
Indirect Benefits:
• Improve Safety
– Plant, Personnel
• Better Information
– Production, Management, Engineering
– Predictive Maintenance
• Improve Customer Response
– Order Scheduling, JIT (Just In Time)
The Purpose of Automation is to
Eliminate Product Variation
Normal Control
90
92
94
96
98
100
Product Quality Spec
Average Quality
The Purpose of Automation is to
Eliminate Product Variation
Improved Control
90
92
94
96
98
100
The Purpose of Automation is to
Eliminate Product Variation
92
94
96
98
100
Reduction in Quality Giveaway
90
Old Target
New Target
Section 2
BLOCK DIAGRAMS,
TRANSFER FUNCTIONS
Piping & Instrumentation Diagram
(P&ID)
LT
Supply
Outlet
X sp
SetpointDESIRED VALUE
LC
ControlValve
LevelController
LevelTransmitter Demand
MANIPULATED
VARIABLE
PROCESS
VARIABLE(LOAD)
PROCESS
CONTROLLINGSYSTEM
CONTROLLEDSYSTEM
X
Block Diagram
(MEASURED)
Xsp
X
++
+
eX
m
_
SETPOINTERROR
CONTROLLER
MANIPULATED
VARIABLE
PROCESS
PROCESS
VARIABLE
PROCESS(MEASURED)
VARIABLE
FEEDBACKELEMENTS
CONTROLLINGSYSTEM
CONTROLLEDSYSTEM
BIAS
LOAD (DEMAND)
DISTURBANCES
Σ ΣGC GP
GF
Some Definitions
• Process Variable (PV):
– Measured Variable: such as Pressure, Level Temperature, Flow, Concentration, Time
– Controlled Variable (C)
• Setpoint (SP):
– Desired setting of the Process Variable (PV)
• Error (E):
– Difference between SP and PV (E=SP-PV)
» Relationship indicates a negative feedback control system
Some Definitions
• Controlled Output (CO):
– Manipulated Variable (MV)
– Result of the mathematical relationship which
causes the PV to move toward the SP.
– Direct Action: An increase in process
measurement causes the controlled output to
increase (e.g. open gas valve to increase
temperature).
– Reverse Action: An increase in process
measurement causes the controlled output to
decrease (e.g. increase fan speed to decrease
temperature).
Controller Action
ReverseNoIncrease-CloseReverse
DirectNoIncrease-CloseDirect
DirectYesIncrease-CloseReverse
ReverseYesIncrease-CloseDirect
DirectNoIncrease-OpenReverse
ReverseNoIncrease-OpenDirect
Controller
Action
Signal ReversalActuator
(Valve) Action
Process Action
Types of Disturbances
• Change in Setpoint
• Change in Supply
• Change in Demand
• Change in Environment
Typical Heat Exchanger
T
TIC
TT
Steam
Supply
Insulation
Cold Waterin, Qw
Hot Water toProcess
Condensate
to Trap
Shell
Tube
sP
uP
Tout
Tin
m1
X
X 1
m
TE
sp
(e)
Block Diagram of Heat Exchanger
and Transmitter
Controller Valve top and
PositionerProcess
Sensing Element
Load Changes
Inlet Water
TemperatureSteam Supply
Pressure
Water Flow
RateQ
w
m1
x2
Pu
m
Tin
ToutX sp e
x 1
2
+ _Σ
Dynamic Systems
• Dynamic System Representation
– Dynamic systems are represented as a function
of time by differential equations - f(t)
– f(t) consists of terms in integral and differential
calculus (differential equations)
– Represents systems in the time domain
– Continuous functions with no discontinuities
– Difficult to solve
LaPlace Transforms
• The LaPlace Transform Method:
– Used to simplify the problem to an algebraic
representation in the frequency domain
– Should be unique
– Function must exist over the whole region of
interest in either domain
– Continuous and no discontinuities
F(s) = ,f(t)
F(s) = 4kf(t)e-st dtI
0
Z Transforms
• The Z Transform Method:
– All computers used today are digital (sampled data)
– The Z Transform is the digital equivalent of the LaPlace Transform
– z-n is the delay operator of n samples
– Time series generating current output value
• Current input value xn
• Previous input values xn-1, xn-2, … xn-i
• Previous output values yn-1, yn-2, … yn-i
– Transfer function
• g(z) = y(z) / x(z) = a0 + (1 + a1z-1)
– Time series
• yn = a0xn + a1yn-1
Section 3
PROPERTIES OF PHYSICAL
SYSTEMS
4 Characteristics
• If you wish to control the process, you must first understand
the process
• All Processes exhibit these 4 Characteristics:• Gain
• Direction
• Deadtime
• Time Constant
Static Gain
Input Change
Output Change
Static Gain
Case A B C
10%
10%
10%
20%
10%
5%
1010
2010
510= = =1 2 2
1
Input Output
GAIN =% inputªªªªªªªª% output
Dynamic Gain
Input Output
Amplifier
Output Output
InputInput
1 sec.
0.5AA
= 1 Hz
Frequency (Log Scale)
Gain
,
am
plit
ude
ratio
0.75
1.00
0.50
0.00
0.25
Bode Plot
GAIN of temperature control loop is product of the
gains of the individual elements in the loop
∆
HEATED PRODUCT OUT
Loop gain =
Loop gain =
Gain transmitter Gain controller Gain valve operator Gain valve plug Gain process
psi out
mA inTemp. of Product, F
mA
opsi
Inches Travel Steam Pressure, psi
Valve-plug Travel, in
Temperature, Fo
Steam Pressure, psi
x
x
x
x
x
x
x
x∆
∆
∆∆
∆
∆∆
∆ ∆
∆
Temperature of Product, F
COLD PRODUCT IN
PROCESS
CONTROLLER
PRIMARYELEMENT
TEMPERATURETRANSMITTER
mAo
psi
Temperature, Fo
Steam Pressure. psiin. Travel
Steam Pressure, psi
Valve Plug Travel, in
STEAM
∆
∆
∆
∆
∆∆
∆mA out
mA in
∆
∆
I/Ppsi out
mA in∆∆
Time Constants
• Deadtime - td:
– The time that elapses from the moment a
change is introduced into an element of the
control loop and the moment the output begins
to change
» Also called transport lag or distance/velocity lag
DEADTIME occurs in a weight-belt system
Hopper
Point A Point B
WeightTransmitter
GateAdjustment
Pro
cess
Time
Input,
(Poin
t A
)
Pro
cess
Outp
ut,
(Poin
t B
)
td
td
Time Constants
• RC Time Constant - τ:
– Capacitance: Response dominated by system
capacity.
– Resistance: Response dominated by system
resistance
First order system: g(t) = e-t/τ, τ = RC
The time it takes for the controlled variable to
reach 63.2% of its final value (First Order).R
C
Time Constants
Time e-t/ττττ 1st Order 2nd Order 3rd Order
5.000 5.000 5.000
0.0 1.000 0.000 0.000 0.000
0.1 0.980 0.020 0.000 0.000
0.2 0.961 0.039 0.002 0.000
0.5 0.905 0.095 0.009 0.001
1.0 0.819 0.181 0.033 0.006
2.0 0.670 0.330 0.109 0.036
3.0 0.549 0.451 0.204 0.092
4.0 0.449 0.551 0.303 0.167
5.0 0.368 0.632 0.400 0.253
6.0 0.301 0.699 0.488 0.341
7.0 0.247 0.753 0.568 0.428
8.0 0.202 0.798 0.637 0.508
9.0 0.165 0.835 0.697 0.582
10.0 0.135 0.865 0.748 0.646
11.0 0.111 0.889 0.791 0.703
12.0 0.091 0.909 0.827 0.752
13.0 0.074 0.926 0.857 0.793
14.0 0.061 0.939 0.882 0.828
15.0 0.050 0.950 0.903 0.858
16.0 0.041 0.959 0.920 0.883
17.0 0.033 0.967 0.934 0.903
18.0 0.027 0.973 0.946 0.920
19.0 0.022 0.978 0.956 0.934
20.0 0.018 0.982 0.964 0.946
21.0 0.015 0.985 0.970 0.956
22.0 0.012 0.988 0.976 0.964
23.0 0.010 0.990 0.980 0.970
24.0 0.008 0.992 0.984 0.976
25.0 0.007 0.993 0.987 0.980
Cascaded Lags - Step Response
0.0
0.2
0.4
0.6
0.8
1.0
0 5 10 15 20 25
Time (sec)
un
its
1st Order 2nd Order 3rd Order
CAPACITANCE dominates level control in
tank
F
Pro
cess
Time
Outp
ut,
Le
vel
Pro
cess
Input, F
i
i
LT FO
DisplacementPositive
Pump
Most Processes have both resistance (R) and
capacitance (C)
TI
Heat Input
Thermowell
TemperatureElement
Agitator
Total Time Constant of temperature control loop is
sum of the Time Constants and Deadtimes of the
individual elements in the loop
Temperature of Product, F.
HEATED PRODUCT OUTCOLD PRODUCT IN
PROCESS
CONTROLLER
PRIMARYELEMENT
TEMPERATURETRANSMITTER
mA0
psi
Temperature, F0
Steam Pressure. psiin. Travel
Steam Pressure, psi
Valve Plug Travel, in
STEAM
I/Ppsi out
mA in
mA out
mA in
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
∆
Effect of time lag on input and output
ProcessInput, A Output, B
45o
Input, A
360o
Output, B
Output, B
Input, A
Frequency (Log Scale)
-270
-180
-90
0
Phase A
ng
le,
Deg.
Bode Plot
Relation of Input and Output Sine Waves
SINE
INPUT
SINE
OUTPUT
360 DEGREESPERIOD - ONE CYCLE
INPUTAMPLITUDE
TIMEINPUTMAGNITUDE
PHASE ANGLEOR LAG
OUTPUTAMPLITUDE
TIME
OUTPUT MAGNITUDE
INPUT MAGNITUDE= MAGNITUDE RATIO OR GAIN
Ai
Ao
Mo OUTPUT
MAGNITUDE
P
Mi
Open Loop Step Response Graph
OUT
Pseudo
Dead Time
Pseudo
Time
Constant
Time
PVΔ
Δ
Kp =ΔPV
ΔOUT
63.2%
Td Tp
T0 T2T1
(Δout)
Kp =ΔOUT
(Δin)
Δout
Δin=
Open Loop Response Testing
Lag 1: First order system (1 lag)
Lag 2: Second order system (2 lags)
FOL+DT: First order lag + dead time approximation of second order system
Lab Exercise 1
How to determine the 4 Characteristics of Process Behavior:
• Gain
• Direction
• Deadtime
• Time Constant
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