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ChENChEN 403403

Process Dynamics & ControlProcess Dynamics & Control

IntroductionIntroduction

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

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

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

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.

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

LetLet’’s think about a simple s think about a simple household examplehousehold example

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?

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

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?

Process Control GoalsProcess Control Goals

• Suppress the influence of external disturbances

• Ensure the stability of a chemical process

time time

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

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

CrossCross--section of a Globe Valvesection of a Globe Valve

Process Flow DiagramProcess Flow Diagram

TC

F0, T0, 0

F1, T1, 1

Fs, Ts

V, T,

Information Flow DiagramInformation Flow Diagram

T'1m

C' T's

T'sp

Gc

T'1

T'0

Ga

Gp

Gm

Gd

εεεε'+-

++

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

Recognize Standard FormsRecognize Standard Forms

Time Time Time

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

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

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)

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:

Tank Temperature Under P Tank Temperature Under P 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

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

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

In SummaryIn Summary……

• Introduction to the course material

» Why is process control important?

» Some typical control problems

» Process & information flow diagrams