chen 403 process dynamics & control introduction
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ChENChEN 403403
Process Dynamics & ControlProcess Dynamics & Control
IntroductionIntroduction
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Course TopicsCourse Topics• Math Modeling of Chemical Processes
• Solution of ODEs
» Laplace Transforms – Primary Emphasis
» General Analytical Techniques
» Numerical Methods
• Transfer Functions
• Behavior of 1st, 2nd, & Higher Order Systems
• Fitting Model Parameters to Data
• Feedback Control - Behavior & Stability
• Design & Tuning of Controllers
• Advanced Control Schemes
• Case Study
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Mathematical NomenclatureMathematical Nomenclature
• The nomenclature isn't what's important, it’s the concepts!
» Pretty much any symbols could be (and probably are) used
» Understand what's going on rather than memorizing symbols
• Will strive for consistency in the notes, homework, exams, etc.
» May be different from the text books, however
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Typical SymbolsTypical Symbols
Valve coefficient
Heat capacity (molar basis)
Heat capacity (mass basis)
Steady state value
Laplace transform of deviation variable
Deviation variable
Volumetric flow rateF
′F
′F
*F
p̂C
ɶpC
vC
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Importance of Process ControlImportance of Process Control
• Directly affects the safety and reliability of a process
» Control system must provide safe operation
» Control system must be able to “absorb” a variety of disturbances & keep the process in a good operating region
• Determines the quality of the products produced by a process
• Can affect how efficient a process is operated
• Bottom Line: process control has a major impact on the profitability of a company.
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Benefits of Improved ControlBenefits of Improved Control
Time
Impurity
Concentration
Limit
Old Controller
Improved PerformanceTime
Impurity
Concentration
Limit
New Controller
Improved Performance
Time
Time
Impurity
Concentration
Limit
Improved Performance
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LetLet’’s think about a simple s think about a simple household examplehousehold example
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The Dynamics of theThe Dynamics of theHousehold ShowerHousehold Shower
• What are the controlled or manipulated inputs?(What part of the system can be directly changed?)
• What are the set points?(What end result is desired?)
• What are the uncontrolled inputs?(What disturbances can happen outside of the shower stall?)
• Why might the set points change?(Do you want to run the shower the same way, morning or night, summer or winter, …?)
• What are the benefits of controlling this process?
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Design Aspects of Process Design Aspects of Process Control SystemsControl Systems
• Manipulated variables
» Variables that can be adjusted by the operator or controller
• Disturbances
» Uncontrolled changes, such as weather or feed composition
• Measured variables
» Values can be directly measured
• Unmeasured variables
» Values cannot be directly measured
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Control ObjectivesControl Objectives
• Operational objectives
» Stability of process
» Suppress influence of disturbances
» Optimize performance of plant
• What variables should be measured?
• What variables should be manipulated?
• What is the best control configuration?
• How should measurements be used to adjust the manipulated variables?
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Process Control GoalsProcess Control Goals
• Suppress the influence of external disturbances
• Ensure the stability of a chemical process
time time
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Process Control & OptimizationProcess Control & Optimization
• Control & optimization are terms that are many times erroneously interchanged
» Control: adjusting manipulated variables to maintain the controlled variables of the process at specified setpoints
» Optimization: chooses the values for key setpointssuch that the process operates at the “best”economic conditions
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Process Control HardwareProcess Control Hardware
• Measurement element
» Orifice meter
» Thermocouple
• Transmitter
• Control Valve (with actuator, positioner, & I/P)
• DCS Controller & I/O cards
• DCS Communication Network (a LAN)
• DCS Operator Console
• Advanced Control Computer
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CrossCross--section of a Globe Valvesection of a Globe Valve
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Process Flow DiagramProcess Flow Diagram
TC
F0, T0, 0
F1, T1, 1
Fs, Ts
V, T,
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Information Flow DiagramInformation Flow Diagram
T'1m
C' T's
T'sp
Gc
T'1
T'0
Ga
Gp
Gm
Gd
εεεε'+-
++
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Recognize Standard FormsRecognize Standard Forms
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
2.0
0 2 4 6 8 10 12
t/ττττ
y/ααααKp
ζ = 0.1
ζ = 0.5
ζ = 0.9ζ = 1.1
ζ = 5
ζ = 10
ζ = 1
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Recognize Standard FormsRecognize Standard Forms
Time Time Time
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Rate of Mass & Energy Rate of Mass & Energy AccumulationAccumulation
• Material Balance Equation
( )ρ= ρ − ρ ⇒ =0 0 1 0 1
d VF F F F
dt
• Heat Balance Equation
( )( )
( ) ( ) ( ) ( )
ρ= ρ − ρ + − ⇒
ρ + ρ + = ρ +
0 0 0 1 1 1
10 1 0 0
ˆˆ ˆ
ˆ ˆ ˆ
s
p p p s
d VHF H F H UA T T
dt
dTVC F C UA T F C T UA T
dt
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Transfer FunctionsTransfer Functions
• Laplace transforms create a transfer function
( ) ( ) ( ) ( )′′ ′ ′ρ + ρ + = ρ +1
0 1 0 0ˆ ˆ ˆp p p s
dTVC F C UA T F C T UA T
dt
ρ ρ′′ ′ ′ + = +
ρ + ρ + ρ +
011 0
0 0 0
ˆ ˆ
ˆ ˆ ˆp p
s
p p p
VC F CdT UAT T T
dtF C UA F C UA F C UA
′′ ′ ′τ + = ⋅ + ⋅11 0 0 s s
dTT K T K T
dt
′ ′ ′ ′τ + = ⋅ + ⋅1 1 0 0 s ssT T K T K T
′ ′ ′= ⋅ + ⋅τ + τ +
01 01 1
ss
K KT T T
s s
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Uncontrolled Tank TemperatureUncontrolled Tank Temperature
89
90
91
92
93
94
95
96
97
98
0 5 10 15 20 25 30 35 40
Time, t (min)
Outlet Temperature, T1 (°C)
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Control Loop Transfer FunctionsControl Loop Transfer Functions
• Uncontrolled response to disturbance
′= =
′ + τ + +1 0
00 1 1d
c a p m c
T G K
G G G G s G KT
• Closed loop response
′ ′ ′ ′ ′= + ⇒ = − − τ + τ + τ 0
1 0 1 0 0 1 exp1 1
ss
K K tT T T T T K
s s
′ + ′ ′= ⇒ = − − ′ τ + + + τ 1 0 0 0
1 0
0 00
11 exp
1 1c
c c
T K K K KT T t
s K K K KT
P Control:
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Tank Temperature Under P Tank Temperature Under P ControlControl
89
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97
98
0 5 10 15 20 25 30 35 40
Time, t (min)
Outlet Temperature, T1 (°C)
Uncontrolled
P Control
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Control Loop Transfer FunctionsControl Loop Transfer Functions
• Closed loop responsePI Control:
′=
′ τ + + + τ
τ =
ττ+ τ + +
1 0
00
I
I
2II
0 0
11 1
11 1
c
c
c c
T K
Ts K K
s
sK
s sK K K K
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Tank Temperature Under PI Tank Temperature Under PI ControlControl
89
90
91
92
93
94
95
96
97
98
0 5 10 15 20 25 30 35 40
Time, t (min)
Outlet Temperature, T1 (°C)
Uncontrolled
P Control
PI Control
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In SummaryIn Summary……
• Introduction to the course material
» Why is process control important?
» Some typical control problems
» Process & information flow diagrams