Notes On Chemical Process Control And Chemical Modeling (Stephanopulos)

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TABLE OF CONTENTS '
PART I: THE CONTROL OF A CHEMICAL PROCESS: ITS CHARACTERISTICS AND THE
ASSOCIATED PROBLEMS . . . . . . . . . . , . . . . . . . . . . . .
Chapter 1. INCENTIVES FOR CHEMICAL PROCESS CONTROL . . . . . . . . . .
1.1 Suppress the Influence of External Disturbances . . . . . .
1.2 Ensure the Stability of a Process . . . . . . . . . . . . .
1.3 Optimize the Performance of a Chemical Process . . ,. . . . .
Chapter 2. DESIGN ASPECTS OF A PROCESS CONTROL SYSTEM . . . . . . . . .
2.1 Classification of the Variables in a Chemical Process . . .
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2.2 Elements of the Design of a Control System . . . . . . . . .
2.3 The Control Aspects of a Complete Chemical Plant . . . . . .
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Chapter 3: HARDWARE FOR A PROCESS CONTROL SYSTEM . . . . . . . . . . .
'3.1 Hardware Elements of a Control System . . . . . . . . . . .
3.2 The Use of Digital Computers in Process Control . . . . . .
SUMMARY AND CONCLUDING REMARKS ON PART I . . . . , . . . . . . . . . . . I/t,
THINGS TO THINK ABOUT ,. . . . . . . . . . . . . . . . . . . . . . . . . ,-
R E F E R E N C E S . . . . . . . . . . , . . . . . . . . . . . . . . . . . . . .
P R O B L E M S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PART II: MODELING THE DYNAMIC AND STATIC BEHAVIOR OF CHEMICAL PROCESSES .
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Chapter 4. THE DEVELOPMENT OF A MATHEMATICAL MODEL . . . . . . . . . .
4.1 Why Do We Need Mathematical Modelign for Process Control? .
4.2 State Variables and State Equations for a Chemical Process .
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4.3 Additional Elements of the Mathematical Models . . . . . . .
4.4 Dead-Time . . . . . . . . . . . . . . . . . . . . . . . . .
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4.5 Additional Examples of Mathematical Modeling . . . . . . .
4.6 Modeling Difficulties . . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . . .
Chapter 5. MODELING CONSIDERATIONS FOR CONTROL PURPOSES . . . . . . .
5.1 The Input-Output Model . . . . . . . . . . . . . . . . . .
5.2 Degrees of Freedom . . . . . . . . . . . . . . . . . . . .
5.3 Degrees of Freedom and Process Controllers . . . . . . . .
5.4 Formulating the Scope of Modeling for Process Control . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
/ THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
P R O B L E M S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PART III: ANALYSIS OF THE DYNAMIC BEHAVIOR OF CHEMICAL PROCESSES . . .
Chapter 6. COMPUTER SIMULATION AND THE LINEARIZATION OF NONLINEAR
SYSTEMS . . . . . . . . . . . . . . . . . . . . . . . . .
6.1 Computer Simulation of Process Dynamics . . . . . . . . .
6.2 Linearization of Systems With One Variable . . . . . . . .
6.3 Deviation Variables . . . , . . . . . . . . . . . . . . .
6.4 Linearization of Systems With Many Variables . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . : . . . . . . . . . .
Chapter 7. LAPLACE TRANSFORMS . . . . . . . . . . . . . . . . . . . .
7.1 Definition of the Laplace Transform . . . . . . . . . . . .
7.2 The Laplace Transforms of Some Basic Functions . . . . . .
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7.3 Laplace Transforms of Derivatives . . . . . . . . . . . .
7.4 Laplace Transforms of Integrals . . . . . . . . . . . . .
7.5 The Final-Value Theorem . . . . . . . . . . . . . . . . .
7.6 The Initial-Value Theorem . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 8. SOLUTION OF LINEAR DIFFERENTIAL EQUATIONS USING LAPLACE
T R A N S F O R M S . . . . . . . . . . . . . . . . . . . . . . . .
8.1 A Characteristic Example and the Solution Procedure . . .
8.2 Inversion of Laplace Transforms. Heaviside Expansion . . .
8.3 Examples on the Soiution of Linear Differentiation
Equations Using Laplace Transforms . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Appendix 8.A. The General Solution of an n-th Order
Differential
Appendix 8.B. The Solution
Differential
Equation . . . . . . . . . . . . .
of a General System of Linear
Equations . . . . . . . . . . . . .
Chapter 9. TRANSFER FUNCTIONS AND THE INPUT-OUTPUT MODELS . . . . . '.
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9.1 The Transfer Function of a Process with a Single Output .
9.2 The Transfer Function Matrix of a Process with Multiple
outputs ., . . . . . . . . . . . . . . . . . . . . . . .
9.3 The Poles and the Zeros of a Transfer Function . . . . . .
9.4 Qualitative Analysis of the Response of a System . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 10. THE DYNAMIC BEHAVIOR OF FIRST-ORDER SYSTEMS . . . . . . .
10.1 What is a First-Order System? . . . . . . . . . . . . . .
10.2 Processes Modeled as First-Order Systems . . . . . . . . .
10.3 The Dynamic Response of a Pure Capacitive Process . . . .
10.4 The Dynamic Response of a First-Order Lag System . . . .
10.5 First-Order Systems with Variable Time Constant and
Gain . . . . . . . . . . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . . 17 :
Chapter 11. THE DYNAMIC BEHAVIOR OF SECOND-ORDER SYSTEMS . . . . . .
11.1 What is a Second-Order System? . . . . . . . . . . . . .
11.2 The Dynamic Response of
11.3 Multicapacity Processes
11.4 Inherently Second-Order
a Second-Order System . . . . . .
as Second-Order Systems . . . . .
Processes . . . . . . . . . . . .
11.5 Second-Order Systems Caused by the Presence of
Controllers . . . . . . . . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . .., . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . : . . .
Appendix ll.A. Examples of Physical Systems with Inherent
Second-Order Dynamics . . . . . . . . . . . . .
Chapter 12. THE DYNAMIC BEHAVIOR OF HIGHER-ORDER SYSTEMS . . . . . .
12.1 N Capacities in Series . . . . . . . . . . . . . . . . .
12.2 Dynamic Systems with Dead Time . . . . . . . . . . . . .
12.3 Dynamic Systems with Inverse Response . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . ; . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . . .
R E F E R E N C E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PROBLEMS............... i...............
PART IV: ANALYSIS AND DESIGN OF FEEDBACK CONTROL SYSTEMS . . . . . . .
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Chapter 13. INTRODUCTION TO FEEDBACK CONTROL . . . . . . . . . . . .
13.1 The Concept of Feedback Control . . . . . . . . . . . . .
13.2 Types of Feedback Controllers . . . . . . . . . . . . . .
13.3 Measuring Devices (Sensors) . . . . . . . . . . . . . . .
13.4 Transmission Lines . . . . . . . . . . . . . . . . . . .
13.5 Final Control Elements . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 14. THE DYNAMIC BEHAVIOR OF FEEDBACK CONTROLLED PROCESSES . .
14.1 Block Diagram and the Closed-Loop Response . . . . . . .
14.2 The Effect of Proportional Control on the Response of a
Controlled Process . . . . . . . . . . . . . . . . . . .
14.3 The Effect of Integral Control Action . . . . . . . . . .
14.4 The Effect of Derivative Control Action. . . . . . . . .
14.5 The Effect of Composite Control Actions . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 15. STABILITY ANALYSIS OF FEEDBACK SYSTEMS . . . . . . . . .
15.1 The Notion of Stability . . . . . . . . . . . . . . . . .
15.2 The Characteristic Equation . . . . . . . . . . . . . . .
15.3 The Routh-Hurwitz Criterion for Stability . . . . . . . .
15.4 The Root-Locus Analysis . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Appendix 15.A. Rules for the Construction of Root-Locus
Diagrams . . . . . . . . . . . . . . . . . . .
Chapter 16. DESIGN OF FEEDBACK CONTROLLERS . . . . . . . . . . . . .
16.1 Outline of the Design Problems . . . . . . . . . . . . .
16.2 Simple Performance Criteria . . . . . . . . . . . . . . .
16.3 Select the Type of Feedback Controllers . . . . . . . . .
16.4 Controller Tuning Techniques . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 17. THE FREQUENCY RESPONSE ANALYSIS OF LINEAR PROCESSES . . .
17.1 The Response of a First-Order System to a.Sinusoidal
I n p u t . . . . . . . . . . . . . . . . . . . . . . . . . .
17.2 The Frequency Response Characteristics of a General
Linear System . . . . . . . . . . . . . . . . . . . . . .
17.3 Bode Diagrams . . . . . . . . . . . . . . . . . . . . . .
17.4 Nyquist Plots . . . . . . . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter lg. DESIGN OF FEEDBACK CONTROL SYSTEMS USING FREQUENCY
RESPONSE TECHNIQUES . . . . . . . . . . . . . . . . . . .
18.1 The Bode Stability Criterion . . . . . . . . . . . . . .
lg.2 Gain and Phase Margins . . . . . . . . . . . . . . . . .
lg.3 The Ziegler-Nichols Tuning Technique . . . . . . . . . .
18.4 The Nyquist Stability Criterion . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . , . . , . . . . . . . . . . . . .
Appendix 18.A. Complex Mapping and the Nyquist Criterion for
Stability . . . . . . . . . . . . . . . . . . .
R E F E R E N C E S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
P R O B L E M S . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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PART V: ANALYSIS AND DESIGN OF ADVANCED CONTROL SYSTEMS . . . . . . . .
Chapter 19. FEEDBACK CONTROL OF SYSTEMS WITH LARGE DEAD-TIME OR
INVERSE RESPONSE . . . . . . . . . . . . . . . . . . . .
19.1 Processes with Large Dead-Time . . . . . . . . . . . . .
19.2 Dead-Time Compensation i . . . . . t . . . . . . . . . . .
19.3 Control of Systems with Inverse Response . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 20. CONTROL SYSTEMS WITH MULTIPLE LOOPS . . . . . . . . . . .
20.1 Cascade Control . . . . . . . . . . . . . . . . . . . . .
20.2 Selective Control Systems . . . . . . . . . . . . . . . .
20.3 Split-Range Control . . . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 21. FEEDFORWARD AND RATIO CONTROL . . . . . . . . . . . . . .
21.1 The Logic of Feedforward Control . . . . . . . . . . . .
21.2 The Problem of Designing Feedforward Controllers . . . .
21.3 Practical Aspects on the Design of Feedforward
Controllers . . . . . , . . . . . . . . . . . . . . . . .
21.4 Feedforward-Feedback Control . . . . . . . . . . , . . .
21.5 Ratio Control . . . . . . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 22. ADAPTIVE AND INFERENTIAL CONTROL SYSTEMS . . . . . . . .
22.1 The Concept of Adaptive Control . . . . . . ., . . . . . .
22.2 Self-Tuning Controller . . . . . . . . . . . . . , . . .
22.3 The Concept of Inferential Control . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 23. EXPERIMENTAL MODELING OF CHEMICAL PROCESSES . . . . . . .
23.1 Why Do We Need Experimental Identification of Process
Dynamics? . . . . . . . . . . . . . . . . . . . . . . . .
23.2 Least-Squares Regression for Linear and Nonlinear
Systems ................. . . . . . . . .
23.3 Pulse Testing . . . . . . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . ;. .
PROBLEMS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PART VI: MULTIVARIABLE CONTROL SYSTEMS
Chapter 24. THE CONTROL OF PROCESSES
FOR COMPLEX PROCESSES . . . . .
WITH MULTIPLE INPUTS, MULTIPLE
OUTPUTS (MIMO) . . . . . . . . . . . . . . . . . . . . .
24.1 Formulation of the Control Problems . . . . . . . . . . .
24.2 Degrees of Freedom . . . . . . . . . . . . . . . . . . .
24.3 Generation of Alternative Control Systems . . . . . . . .
24.4 Practical Guides for Screening the Alternatives . . . . .
SUMMARY AND CONCLUDINGREMARKS : . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT
Chapter 25. INTERACTION AND
25.1 The Interaction
. . . . . . . . . . . . . . . . . . . . .
DECOUPLING . . . . . . . . . . . . . . .
of Control Loops . . . . . . . . . . . .
25.2 Selecting the Loops. The Relative-Gain Array Method . .
25.3 Design of Non-Interacting Control Loops . . . . . . . . .
SUMMARY.AND CONCLUDINGREMARKS . . . . . . . . . . . . . . . .
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Chapter 26. CONTROL OF CHEMICAL PLANTS . . . . . . . . . .
26.1 The Characteristics of the Problem . . . . . .
26.2 Selecting Control Objectives and Manipulations
26.3 The Cause-and-Effect Diagram . . . . . . . . .
26.4 A Decomposition Strategy . . . . . . . . . . .
26.5 An Example . . . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . .
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REFERENCES . . . . . : . . . . . . . . . . . . . .'. . . . . . . . . .
PROBLEMS.......: . . . . . . . . . . . . . . . . . . . . . . .
PART VII: PROCESS CONTROL USING DIGITAL COMPUTERS . . . . . . . . . . .
Chapter 27. THE DIGITAL COMPUTER CONTROL LOOP . . . . . . . . . . . .
27.1 The Hardware Elements . . . . . . . . . . . . . . . . . .
27.2 The Design Characteristics . . . . . . . . . . . . . . .
27.3 A Physical Example . . . . . . . . . . . . . . . . . . ;
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 28. SAMPLING AND RECONSTRUCTING CONTINUOUS SIGNALS . . . . .
28.1 Sampling Continuous Signals. The Impulse Sampler . . . .
28.2 The Reconstruction of Continuous Signals . . . . , . . .
28.3 Types of Hold-Elements and Their Characteristics . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 29. DISCRETE-TIME SYSTEMS AND THE Z-TRANSFORMS . . . . . . .
29.1 Converting Continuous to Discrete-Time Systems.The
Difference Equation . . . . . . . . . . . . . . . . . . .
29.2 The z-Transform and Its Properties . . . . . . . . . . .
29.3 The z-Transform of Some Basic Functions . . . . . . ; . .
29.4 The Inversion of z-Transforms . . . . . . . . . . . . . . .
29.5 The Relationship Between Laplace and z-Transforms . . . .
SUMMARY AND CONCLUDING REMARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . , . . . . , . . . . .
Chapter 30. THE DYNAMIC RESPONSE OF SAMPLED-DATA SYSTEMS . . . . . .
30.1 The Pulse Transfer Function of a Continuous Dynamic
System . . . . . . . . . . . . . . . . . . . . . . . . .
30.2 The Transfer Function of Discrete-Time Dynamic Systems .
30.3 The Equivalence Relationship between Continuous and
Discrete Time Dynamic Systems . . . . . . , . . . . . . .
SLWARY AND CONCLUDING REMARKS . . . . . . . . . . . . . , . .
THINGS TO THINK ABOUT . . . . . . . . , . . . . . . . . . . . .
Chapter 31. FEEDBACK CONTROL USING DIGITAL CO>fPUTERS . . . . . . . .
31.1 The Block Diagram and the Transfer Function of a
Closed-Loop System . . . . . . . . . . . . . . . . . . .
31.2 The Response of a Closed-Loop System and Its
Characteristics . . . . . . . . . . . , . . . . . . . . . .
SUWARY AND CONCLUDIXG REXARKS . . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
Chapter 32. THE DESIGN OF SAMPLED-DATA, FEEDBACK CONTROL SYSTEMS . .
32.1 Conditions for Stability of Sampled-Data Systems . . . .
32.2 The Effect of Sampling on the Closed-Loop Response of
of Sampled-Data Systems . . , . . . . . . . . . . . . . .
32.3 The Design of Sampled-Data, Feedback Loops Using
Frequency Response Techniques . . . . . . . . . . . . . .
EXJNNARY AND CONCLUDING REMARKS , . . . . . . . . . . . . . . .
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THINGS TO THINK ABOUT . . . . . . . . . , . . . . . . . . . . .
Chapter 33.
33.1
33.2
33.3
33.4
THE DESIGN OF ADDITIONAL SAMPLED-DATA, CONTROL
CONFIGURATIONS . . . . . . . . . . . . . . . . . . . . .
Feedforward Control and Ratio Control . . . . . . . . . .
Cascade Control . . . . . . . . . . . . . . . . . . . . .
Adaptive Control . . . . . . . . . . . . . . . . . . . .
Supervisory Control . . ,. . . . . . . . . . . . . . . . .
SUMMARY AND CONCLUDING REMARKS , . . . . . . . . . . . . . . .
THINGS TO THINK ABOUT . . . . . . . . . . . . . . . . . . . . .
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
PROBLEMS : . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
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PART I
THE CONTROL OF A CHEMICAL PROCESS: ITS CHARACTERISTICS AND THE
ASSOCIATED PROBLEMS
The purpose of the following three introductory chapters is:
- to define what we mean by chemical process control,
- to describe the needs and the incentives for controlling a
chemical process,
- to analyse the characteristics of a control system and to for-
mulate the problems that must be solved during the design of a
control system, and finally
- to provide the rationale for studying the material that follows
in the subsequent chapters.
In order to achieve the above objectives we will use a series
of examples taken from the chemical industry. ,These examples are
usually simplified and serve only to demonstrate the various
tlualit.i3tive points made.
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CHAPTER 1
INCENTIVES FOR CHEMICAL PROCESS CONTROL
A chemical plant is an arrangement of processing units (reactors, heat
exchangers, pumps, distillation columns, absorbers, evaporators, tanks, etc.),
integrated with each other in a systematic and rational manner. The plant's
overall objective is to convert certain raw materials (input feedstock) into
desired products using available sources of energy, in the most economic,way.
During its operation, a chemical plant must satisfy several requirements
imposed by its designers and the general technical, economic and social con-
ditions in the presence of ever-changing external influences (disturbances).
Among such requirements are the following:
- Safety: The safe operation of a chemical process is a primary requirement,
for the well being of the people in the plant and its continued contri-
bution to the economic development. Thus, the operating pressures,
temperatures, concentration of chemicals, etc. should always be within
allowable limits. For example, if a reactor has been designed to operate
at a pressure up to 100 psig, we should have a control system that will
maintain the pressure below
to avoid the development of
plant.
this value. As another example, we should try
explosive mixtures during the operation of a
- Production specifications: The plant should produce the desired amounts
and quality of the final products. For example, we may require the pro-
duction of two million pounds of ethylene per day, of 99.5% purity, from
an ethylene plant. Therefore, a control system is needed to ensure that
the production level (2 million pounds per day) and the purity specifi-
cations (99.5% ethylene) are satisfied.
- Environmental regulations: Various federal and state laws may specify
that the temperatures, concentrations of chemicals and flowrates of the
effluents from a plant be within certain limits. Such regulations for
example exist on the amounts of SO2 that a plant can eject to the atmos-
phere, and the quality of water returned to a river or a lake.
- Operational constraints: The various types of equipments used in a chemical
plant have constraints inherent to their operation. Such constraints should
be satisfied throughout the operation of a plant. For example, pumps must
maintain a certain net positive suction head; tanks should not overflow or
go dry; distillation columns should not be flooded: the temperature in a
catalytic reactor should not exceed an upper limit since the catalyst will
be destroyed. Control systems are needed to satisfy all these operational
constraints.
- Economics: The operation of a plant must conform with the market con-
ditions, i.e. the availability of raw materials and the demand of the
final products. Furthermore, it should be as economic as possible in its
utilization of raw materials, energy, capital and human labor. Thus, it
is required that the operating conditions are controlled at given optimum
levels of minimum operating cost, or maximum profit; etc.
All the above requirements dictate the need for a continuous monitoring
of the operation of a chemical plant and an external intervention (control) to
guarantee the satisfaction of the operational objectives. This is accomplished
through a rational arrangement of various equipment (measuring devices, valves,
controllers, computers) and human intervention (plant designers, plant
operators), which constitutes the control system.
There are three general classes of needs that a control system is called
to satisfy:
- Suppress the influence of external disturbances,
! - ensure the 'stability of a chemical process, and
- optimize the performance of a chemical process.
Let us examine these needs using various examples.
1.1 SUPPRESS THE INFLUENCE OF EXTERNAL DISTURBANCES.
Suppressing the influence of the external disturbances on a process is
the most common objective of a controller in a chemical plant. Such dis-
1_
turbances denote the effect that the surroundings (external world) have on a
reactor,
I
separator, heat exchanger, compressor, etc., and usually they are out
of the reach of the human operator.- Consequently, we need to introduce a
I
control mechanism that will make the proper changes on the process to cancel
the negative impact that such disturbances may have on the desired operation
p
of a chemical plant.
Example 1.1 - Controlling the Operation of a StirredTank Heater
Consider the tank heater system shown in Figure 1.1. A liquid enters the
tank with a flowrate Fi (ft3/min), and a temperature Ti (OF), where it is
heated with steam (having a flowrate Fs, lb/min). Let F and T be the
flowrate and temperature of the stream leaving the tank. The tank is con-
sidered to be well stirred, which implies that the temperature of the effluent
is equal to the temperature of the liquid in the tank.
The operational objectives of this heater are:
- Keep the effluent temperature T at a desired value Ts.
- Keep the volume of the liquid in the tank at a desired value Vs.
The operation of the heater is disturbed by external factors like changes in
the feed flowrate and temperature Fi and Ti' If nothing changed, then
after attaining T = Ts and V=Vs, we could leave the system alone without
any supervision and control. It is clear though that this cannot be true
since T i and Fi are subject to frequent changes. Consequently, some form
of control action is needed to alleviate the impact of the changing disturbances
and keep T and V at the desired values.
In Figure 1.2 we see such a control action to keep T = Ts when Ti or
Fi changes. A thermocouple measures the temperature T of the liquid in the
tank. Then T is compared with the desired value Ts yielding a deviation
e=T -T. The value of the deviation E is sent to a control mechanism
S
which decides what must be done in order for the temperature T to return
back to the desired value Ts. If E > 0 which implies T < Ts, the con-
troller opens the steam valve so that more heat can be supplied. O n t h e
contrary, the controller closes the steam valve when e-c0 or T>Ts. It
is clear that when T = Ts, i.e. E. = 0 the controller does nothing. This
control system that measures the variable'of direct importance (T in this
case) after a disturbance had its effect on it, is called Feedback control
system. The desired value Ts is called the Set Point and is supplied
externally by the person in charge of production.
A similar configuration can be used if we want to keep the volume V, or
equivalently the liquid level h, at its set point hs when Fi changes. In'.
this case we measure the level of the liquid in the tank and we.open or close
the valve that affects theaeffluent flowrate F or Fi (see Figure. 1.3). It is
clear that the control systems shown in Figure 1.3 are also feedback control
systems. All feedback systems shown in Figures 1.2 and 1.3 act post facto
(after the fact), i.e. after the effect of the disturbances has been felt by
the process.
Returning back to the tank heater example, we realize that we can use a
different control arrangement to maintain T = Ts when Ti changes. Measure'
I7
the temperature of the.inlet stream T i and open or close the steam valve to
provide more or less steam. Such control configuration is called Feedforward
control and is shown in Figure 1.4. We notice that the'feedforward control
does not wait until the effect of the disturbances has been felt by the sys-
tem, but acts appropriately before the external disturbance affects the system,
anticipating what its effect will be. The characteristics of the feedback and
feedforward control systems will be studied in detail in subsequent chapters.
The suppression of the impact that disturbances have on the operating
behavior of processing units is one of the main reasons for the usage of con-
trol in the chemical industry.
1.2 ENSURE THE STABILITY OF A PROCESS.
Consider the behavior of the variable x shown in Figure 1.5. Notice
that at time t = to the constant value of x is disturbed by some external
factors, but that as the time progresses the value of x returns to its
initial value to stay. If x is a process variable like temperature,
pressure, concentration, flowrate, etc., we say that the process is stable
self-regulating and needs no external intervention for its stabilization.
is clear that no control mechanism is needed to force x to return to its
initial value.
o r
It
In contrast to the above behavior, the variable y shown in Figure 1.6
does not return to,its initial value after it is disturbed by external
incluences. Processes whose variables follow the pattern indicated by y
in Figure 1.6 (curves a,b,c) are called unstable processes and require
external control for the stabilization of their behavior. The explosion of a
hydrocarbon duel with air is such an unstable system. Riding a bicycle is an
attempt to stabilize an unstable system and we attain that by pedaling,
steering and leaning our body right or left.
Example 1.2 - Controlling the Operation of an Unstable Reactor
i
-’
4
Consider a continuous stirred tank reactor (CSTR) where an irreversible
exothermic reaction A+B takes place. The reaction mixture is cooled by a
coolant medium that flows through a jacket around the reactor (Figure 1.7).
As it is known from the analysis of a CSTR system, the curve that describes
the amount of heat released by the exothermic reaction is a sigmoidal function
of the temperature T in the reactor (curve A in Figure 1.8). On the other
hand, the heat removed by the coolant is a linear function of the temperature
T (curve B in Figure 1.8). Consequently, when the CSTR is at steady state,
i.e. nothing is changing, the heat produced by the reaction should be equal to
5
I.
the heat removed by the coolant, thus yielding the steady states Pl, P2, Pg
at the'intersection of the curves A and B (Figure 1.8). The steady states
p1 and Pg are called stable while the P2 is unstable. To understand the
concept of stability let us consider the steady state P2.
Assume that we are able to start the reactor at the temperature T2, and
the concentration cA that corresponds to this temperature. Consider that
2
the temperature of the feed Ti increases. This will cause an increase in
the temperature of the reacting mixture, say T;. At, T; the heat released
by the reaction (Q;) is mqre than the heat removed by the coolant, ,Q; (see
Figure 1.8) thus leading to higher temperatures in the reactor and consequently
to increased rates of reaction. Increased rates of reaction produce larger 1I
amounts of heat released by the exothermic reaction which in turn lead to
higher temperatures and so on. Therefore, we see that an increase in Ti
.?::E:i.j
takes the reactor temperature away from the steady state P2 and that the tem-
I
:. . .
- -
perature will eventually reach the value of the steady state P3 (Figure 1.9a).
1:
Similarly, if Ti were to decrease, the temperature of the reactor would take
.:ti off from P 2 and end up at Pl (Figure 1.9b). By contrast, if we were
operating at the steady state P3 or Pl. and we perturbed the operation of
the reactor, it would return naturally back to the point P3 or Pl where
it started from (see Figures 1.5c,d). Note: The reader should verify this
assertion.
Sometimes we would like to operate the CSTR at the middle unstable steady
state for the following reasons: (i) the low temperature steady state P1
causes very low yields because the temperature Tl is very low. (ii) the
high temperature steady state P3 may be very high causing unsafe conditions,
destroying the catalyst for a catalytic reactor, or degrading the product B,
etc.
In such cases we need a controller which will ensure the stability of the
operation at the middle steady state. Question: The reader should suggest a
control mechanism to stabilize the operation of the reactor at the unstable
steady state P2. This example demonstrates very vividly the need for
stabilizing the operation of a system using some type of control in the
presence of external disturbances that tend to take the system away from the
desired point.,\
Bi.
:*: 1.3 OPTIMIZE THE PERFORMANCE OF A CHEMICAL PROCESS.,:4.:;- Safety and the satisfaction of the production specifications are the main
1
/ ::t/ ::! Once these are achieved, the
12
two operational objectives for a chemical plant.
. .
Given the
I
next goal is how to make the operation of the plant more profitable.
: :.,!.
1
','i.:
1, ,
$ :\ '.,
fact that the conditions that affect the operation of the plant do not remain
the same, it is clear that we would like to be able to change the operation of
the plant (flowrates, pressures, concentrations, temperatures) in such a way
that an economic objective (profit) is always maximized. This task is under-
taken by the automatic controllers of the plant and its human operators.
Let us now see an example from the chemical processing industry where the
controller is used to optimize the economic performance of a single unit.
Example 1.3 - Optimizing the Performance of a Batch Reactor
Consider a batch reactor where the following two consecutive reactions
take place:
A +B -t C
1 2
Both reactions are assumed to be endothermic with first order kinetics. The
heat required for the reactions is supplied by steam which flows through the
jacket around the reactor (Figure 1.10). The desired product is B while C
is an undesired waste. The economic objective for the operation of the batch
reactor is to maximize the profit @ over a period of time tR, i.e.
tR
,Maximize @=
I
{[Revenue from the sales of product B]- [cost of purchasing
0 A + cost of steam]] dt (1.1)
where .'
revenue from product B = p cB(t)
cost of raw material A = crcA(0)
cost of steam = Ch Q(t)
P = price per lb-mole of product B
C r = price per lb-mole of raw material A
8
8
8
8
8
8
8. .
8
I
8
8
8
8
8
8
8
'h = cost per lb of steam
cA (0) = concentration of A at the beginning of the batch reaction
and
tR = the period of reaction.
The only variable that we can change freely to maximize the profit is the
steam flowrate Q(t) which can vary with time. The steam flowrate will
affect the temperature in the batch reactor and the temperature in turn will
affect the rates of the desired and undesired reactions, The question is how
should we vary Q(t) with time so that the profit @ is maximized. Let us
examine some special policies with respect to Q(t).
a. If Q(t) is given the largest value that we can for the whole reaction
period tR, then the temperature of the reacting mixture will take the
largest value that is possible. Initially, when CA is large, we will
have high yields of B but we will also pay more for the steam. As
time goes on and the concentration of B increases the yield of C
also increases. Consequently, towards the end of the reaction period
the temperature must decrease, necessitating decrease in the steam
flowrate.
b. If the steam flowrate is kept at its lowest value, i.e. Q(t) = 0,
for the entire reaction period tR, we will not have any steam cost,
but also we will not have any production of B.
We see clearly from the above two extreme cases that Q(t) will vary between
its lowest and highest values during the reaction period tRa How should it
vary in order to maximize the profit is not trivial and requires the
solution of the above optimization problem.
In Figure 1.11 we see a general trend that the steam flowrate must
follow in order to optimize the profit a. Therefore, a control system is
needed which will: (a) compute the best steam flowrate for every time during
the reaction period and (b) will adjust the valve (inserted in the steam line)
so that the steam flowrate takes its best value (computed above in (a)). Such
problems as the above are known as optimal control problems.
This example indicates that the control of the steam flowrate is
not used to ensure the stability of the reactor or to eliminate the effect of
external disturbances on the reactor but to optimize its economic performance.
CHAPTER 2
DESIGN ASPECTS OF A PROCESS CONTROL SYSTEM
2.1 CLASSIFICATION OF THE VARIABLES IN A CHEMICAL PROCESS.
The variables (flowrates, temperatures, pressures, concentrations, etc.)
associated with a chemical process are classified into:
a. Input variables, which denote the effect of the surroundings on a
chemical process, and
b. output variables, which denote the effect of the process on the
surroundings.
Example 2.1
For the CSTR reactor discussed in Example 1.2 (Figure 1.7) we have:
input variables: cA , Ti, Ti, Tc , Fe(F)
i i
output variables: cA, T, F, Tc , V
0
Notice that the effluent flowrate F can be considered either as input or
output. If there is a control valve on the effluent stream so that its flow-
rate can be manipulated by a controller, the variable F is an input, since
the opening of the valve is adjusted externally, otherwise F is an output
variable.
Example 2.2-.
For the tank heater discussed in Example 1.1 (Figure 1.1) we have:
input variables: Fi, Ti, Fs(F)
output variables: F, V, T
The input variables can be further classified into the following
categories:
.1. Manipulated (or adjustable) variables, if their values
:can be adjusted freely by the human operator or a con-
&rol mechanism and
ii. disturbances, if their values are not the result of
adjustment by an operator or a control system.
The output variables are also classified into the following categories:
i. Measured output variables, if their values are known
by directly measuring them, and
ii. unmeasured output variables,- if they are not or cannot
be measured directly.
Example 2.3-
Suppose that the inlet stream in the CSTK system (Figure 1.7) comes from
an upstream unit over which we have no control. Then, CA , Fi, Ti are
i
1 disturbances. If the coolant flow-rate is controlled by a control valve,
then
F
C
is a manipulated variable, while
T is a disturbance.
ci
Also, if the flowrate of the effluent stream is controlled by a valve, then
F is a manipulated variable, otherwise it is an output variable.
With respect to the output variables we have the following: T, F, Tc ,
0
V are measured outputs since their values can be known easily using thermo-
couples (T, Tc ), a venturi meter (F), and a differential pressure cell (V).
0
The concentration CA can be's measured variable if an analyzer (gas
chromatograph, infrared spectrometer, etc.) is attached to the effluent
stream. In many industrial plants such analyzers are not available because
they are expensive and/or have low reliability (give poor measurements or
break down easily). Consequently, in such cases cA is an unmeasured output
variable.
Example 2.4
For the tank heater system (Figure l.l>, the inputs Fi and T. are dis-
1
turbances, while F
S
and F are manipulated inputs. The output variables
V and T can be measured easily and they are considered measured outputs.
According to their direct measurability or not the disturbances are
classified into two categories: the measured and the unmeasured disturbances.- - - -
2 . 5Example
The disturbances Fi and Ti of the stirred tank heater (Figure 1.1)
are easily measured; thus they are considered measured disturbances.
On the other hand, the feed composition for a distillation column,
extraction unit, reactors and the like, is not normally measured and conse-
quently is considered an unmeasured disturbance.
As we will see later on, unmeasured disturbances generate difficult con-
trol problems.
Figure 2.1 sununarizes all the classes of variables that we have around a
5 chemical process.
2.2 ELEMENTS OF THE DESIGN OF A CONTROL SYSTEM
Let us see now what are the basic questions that we must ask while
attemptingto design a control system that will satisfy the control needs for
a chemical process.
A. Define Control Objectives
want
The central element in any control configuration is the process that we
to control. The first question that is raised by the control designer
is:
Question 1: "What are the operational objectives that a control
system is called to achieve?"
The answer to this question determines the so-called control objectives. They
may have to do with:
- Ensuring the stability of the process, or
- suppressing the influence of external disturbances, or
- optimizing the economic performance of a plant, or
' - combination of the above.
At the beginning the control objectives are 'defined qualitatively and sub-
sequently they are quantifi'ed, usually in terms of the output variables.
Example 2.6
For the CSTR system discussed in Example 1.2 (Figure 1.7), the control
objective (qualitatively defined) is to ensure the stability of the middle,
unstable steady state. But such a qualitative description of the control
objectives is not useful for the design of a control system and must be
quantified. A quantitative translation of the qualitative control objective
requires that the temperature (an output variable) does not deviate more than
5% from its nominal value at the unstable steady state. 8 L
Example 2.7
For the stirred tank heater of Example 1.1 the control objectives are to
maintain the temperature of the outlet (T) and the volume of the fluid in the
tank at desired values. For this example the quantification of the control
objectives is direct and straightforward, i.e. *
T = Ts
v = vs
where T and v
S s
are given, desired values.
Example 2.8
For the batch reactor of Example 1.3 the qualitative control objective
is the maxfmization of the profit. The quantitative description of this
objective is rather complex. It requires the solution of a maximization
problem, which will yield the value of the steam flowrate, Q(t), at each in-
stant during the reaction period.
B. Select Measurements
Whatever are our control objectives, we need some means to monitor the
performance of the chemical process. This is done by measuring the values of
certain processing variables (temperatures, pressures, concentrations, flow-
rates, etc.). The second question that arises is:
Question 2: "What variables should we measure in order to monitor
the operational performance of a plant?"
It is self-evident that we would like to monitor directly the variables that
represent our control objectives, and this is what is done whenever possible.
Such measurements are called primary measurements.
Example 2.9
For the tank heater system (Example 1.1) our control objectives are to
keep the volume and the temperature of the liquid in the tank at desired
levels, i.e.
keep T = T and V
S
= vs.
Consequently, our first attempt is to install measuring devices that will
monitor T and V directly. For the present system this is simple by using
a thermocouple (for T) and a differential pressure cell (for V).
Sometimes it happens that our control objectives are not measurable
quantities, i.e. they belong to the class of unmeasured outputs. In such
cases we must measure other variables which can be measured easily and
rcl..Lably. Such supporting measurements are called secondary measurements.- - --
Then we develop mathematical relationships between the unmeasured outputs
and the secondary measurements, i.e.
unmeasured output = f (secondary measurements)
which allow us to determine the values of the unmeasured outputs (once the
values of the secondary measurements are,available). In a subsequent chapter
we will see that the above mathematical relationship between measured and
unmeasured outputs results from empirical, experimental or theoretical
considerations.
Example 2.10
Consider a simple distillation column separating a binary mixture of
pentane and hexane into two produce streams of pentane (distillate) and
hexane (bottoms). Our control objective'is to maintain the production of a
distillate stream with 95% by mole in pentane in the presence of changes in
the feed composition
It is clear that our first reaction is to use a composition analyzer to
measure the concentration of pentane in the distillate and tllcn using fcrtl-
back control to manipulate the reflux ratio, so that we can keep the
distillate 95% in pentane. This control scheme is shown in Figure 2.2a. An
alternative control system is to use a composition analyzer to monitor the
concentration of pentane in the feed. Then in a feedforward arrangement we
can change the reflux ratio to achieve our objective. This control scheme is
shown in Figure 2.2b. Both of the a'bove control systems depend on the compo-
sition analyzers. It is possible that such measuring devices are either very
costly or of very low reliability for an industrial environment (failing
quite often or not providing accurate measurements). In such cases we can
measure the temperature at various plates along the length of the column quite
reliably, using simple thermocouples. Then using the material and energy
balances around the plates of the column and the thermodynamic equilibrium
relationship between liquid and vapor streams, we can develop a.mathematical
relationship that gives us the composition of the distillate if the tem-
peratures of some selected trays are known. Figure 2.2~ shows such a control
scheme that uses temperature measurements (secondary measurements) to estimate
or infer the composition of pentane in the distillate, i.e. the value of the
control objective.
The third class of measurements that we can make to monitor the behavior
of a chemical process includes the direct measurement of the external dis-
turbances. Measuring the disturbances before they enter the process can be
G
highly advantageous because it allows us to know a priori what the behavior
of the, chemical process will be and thus take remedial control action to
alleviate any undesired consequences. Feedforward control uses direct
measurements of the disturbances (see Figure 1.4).
c. Select Manipulated Variables
Once the control objectives have been specified and the various measure-
ments identified, the next question is how do we effect a change on the
process, i.e.
C&estion 3: "What are the manipulated variables to be used in order
to control a chemical process?"
Usually in a process we have a number of available input variables which
can be adjusted freely. Which ones we select' to use as manipulated variables
is a crucial question as the choice will affect the quality of the control
actions we take.
Example 2.11
In order to control the level of liquid in a tank we can either adjust._I
the flowrate of the inlet stream (Figure 1.3b) or the flowrate of the outlet
stream (Figure 1.3a). Which one is better is an important question that we
will analyse later.
31
D. Select the Control Configuration
After the control objectives, the possible measurements, and the available
manipulated variables have been identified, the final problem to be solved is
that of defining the control configuration.
Before we define what a control configuration is, let us look at some
control systems with different control configurations.
The two feedback control systems in Figures 1.3a and 1.3b constitute two
different control configurations. Thus, the same information (measurement of
liquid level) flows to different manipulated variables, i.e. F (Figure 1.3a)
and Fi (Figure 1.3b). Similarly, the feedback control system (Figure 1.2)
and the feedforward control system (Figure 1.4) for the tank heater constitute
two distinctly different control configurations.FOP these two control sys-
tems we use the same manipulated variable, i.e. Fs but different measurements.
Thus, for the feedback system of Figure~l.2 we use the temperature of the
liquid in the tank, while for the feedforward system of Figure 1.4 we measure
the temperature of the inlet.
In the above examples we notice that two control configurations differ
either in:
- The information (measurement) flowing to the same manipulated variable or
- the manipulated variable where the information flows to.
Thus, for the two feedback control systems in Figures 1.3a and 1.3b we
use the same information (measurement of the liquid level) but different
manipulated variables (F or Fi). On the contrary, for the control systems
in Figures 1.2 and 1.4, we have different measurements (T or Ti) which are
used to adjust the value of the same manipulated variable (Fs).
Later on we will also study other types 0E control configurations, but
for the time being we can define a control configuration (or control---.- ~. . . __structure_)
as follows: :
Definition--II_-
Control configuration we will call the information structure which is
used to connect the available measurements to the available manipulated
variables.
It is clear from the previous examples that normally we will have many
different control configurations for a given'chemical process, which raises
the following question:
Question 4: "What is the best control configuration for a given
chemical process control situation?"
The answer to this question is very critical for the quality of the con-
trol system we are asked to design.
Depending on how many controlled outputs and manipulated inputs we have
in,a chemical process we can distinguish the control configurations into:
single-input, single-output (SISO) or
multiple-input, multiple-output (MIMO) control systems.
For example, for the tank heater system:
- If the control objective (controlled output) is to keep the liquid level
at a desired value by manipulating the effluent flowrate, then we have a
SISO system.
- On the contrary, if our control objectives are (more than one) to keep the
level and the temperature of the liquid at desired values, by manipulating
(more than one) the steam flowrate and the effluent flowrate, then we have
a MIMO system.
In the chemical industry most of the processing systems are mulitple-
input, multiple-output systems. Since the design of SISO systems is simpler
we will start first with them and progressively we will cover the design of
MIMO systems.
Let us close this paragraph by defining three general types of control
configurations.
a. Feedback control configuration: Uses direct measurements of the con-- - -
trolled variables to adjust the values of the manipulated variables (Figure
2.3). The objective is to keep the controlled variables at desired levels
(set points). We can see examples of feedback control in Figures 1.2 and 1.3.
b. Inferential control configzration: Uses secondary measurements, because
the controlled variables are not measured, to adjust the values of the mani-
pulated variables (Figure 2.4). The objective here is to keep the (unmeasured)
controlled variables at desired levels.
The estimator uses the values of the available measured outputs, along
with the material and energy balances that govern the process, to compute
mathematically (estimate) the values of the unmeasured controlled variables.
These estimates in turn are used by the controller to adjust the values of the
manipulated variables. An example of inferential control configuration can be
seen in Figure 2.2~.
C . Feedforward control configuration. Uses direct measurements of the dis-
turbances to adjust the values of the manipulated variables (Figure 2.5).
The objective here is to keep the values of the controlled output variables
at desired levels. An example of feedforward control configuration we can see
in Figure 1.4.
E. Design the Controller
In every control configuration, the controller is the active element that
receives the information from the measurements and takes appropriate control
actions to adjust the values of the manipulated variables. For the design of
the controller we must answer the following question:
Question 5: "How is the information taken from the measurements-
used to adjllst the val.ues of the manipulated variables?"
The answer to this question constitutes the control law, which is imple-
_
mented automatically by the controller.
Example 2.12
Let us consider the problem of controlling the liquid level (h) in a
tank (Figure 2.6), in the presence of changes in the inlet flowrate Fi. Our
measurement will be the liquid level and the manipulated variable the outlet
flowrate. The feedback control configuration used is shown in Figure 2.6.
The question is: "How should F change with time to keep the liquid level
constant wlien 17 i changes?" In other words, we want to develop the control
law.
Let us assume that the heater has been operating for some time and that
1 its liquid level has been kept constant at hs while the liquid temperature
has remained constant at a value T We say that the heater has beens' I
operating, at a steady state (where nothing changes). Under these conditions
the material balance around the tank yields,
0 = F i,s - Fs (2.1)
where F
i,s
and Fs are the inlet and outlet flowrates at steady-state.
Let hs be the liquid level corresponding to steady state operation. Suppose
that the Fi increases suddenly as it is shown in Figure 2.7. If nothing is
done on F, the liquid level h will start rising with time. How h changes
with time will be given from the transient material balance around the tank,
i.e.
dV
dt = Fi - F
or
Adh=F -F
dt i
where A is the cross sectional area of the tank.
(2.2)
Subtract eqn. (2.1) from (2.2) and take
A * z
dt
(F
i - Fi,s)
- (F -u Fs)
A
d(h - hs>
dt = (Fi - Fi,s) - (F - Fs) (2.3)
since hS = const.
The variable h = h - hs denotes the error or deviation of the liquid- -
level from the desired value hs. We want to drive this error to zero by
manipulating the flowrate F.
The simplest control law is to require that the flowrate F increases
or decreases proportionally to the error h - h S ’ i.e.
F = a(h - hs) + b (2.4)
This law is called Proportional Control law, and the parameter a is known as
Proportional Gain.- -
From equation (2.4) we notice that when h - hs = 0 then F = Fs and
consequently b = Fs. Thus the proportional control takes the form,
F = Fs + a(h - hs) (2.5)
If we substitute F given from equation (2.5) into equation (2.3) we
take,
d(h
A
- $1
dt + a(h - hs) - Vi - Fi,J (2.6)
This last differential equation is solved for (h - hs), and for various
values of the proportional gain a yields the solutions shown in Figure 2.8.
We notice that none of the solutions is satisfactory since h - hs # 0. Thus,
we conclude that the proportional control law-is not acceptable.
Considerable improvement in the quality of the resulting control can be
obtained if we use a different control law known as Integral Control.
According to this law the value of the manipulated variable F is proportional
to the time integral of the error (h - hs), i.e.
F = a' (h - hs)dt + b'
0
When we are at steady statd (h - hs)dt = 0 and F = Fs. Consequently,
b' = Fs. Thus, the
0 integral control law takes the form
F=F + a '
S
(h - hs)dt
0
Substituting F from eqn. (2.7) into eqn. (2.3) we take,
(2.7)
(2.8)
The solution of eqn. (2.8) for various values of the parameter a' is shown
in Figure 2.9. We notice that integral control is an acceptable control law
since it drives the error h - h to zero. We also notice thatdepending on
1 S
the value of a' the error h - hs returns to zero faster or slower;
oscillates for a longer or shorter time, etc. In other words, the quality of
control depends on the value of a' in a very profound manner. Note: In
subsequent chapters we will see how to solve integrodifferential equations
like eqn. (2.8).
Combining the proportional control action with the integral control
action we have a new control law, known as Proportional-Integral Control.
According to this law the value of the outlet flowrate is given by,
F = Fs - a(h - hs> - a'
I
(h - hs)dt
0
37
In subsequent chapters we will study the characteristics of various forms
of control laws, but it should be remembered that the selection of the
appropriate control law is a very important question to be decided by the
chemical engineer control designer.
2.3 THE CONTROL ASPECTS OF A COMPLETE CHEMICAL PUNT- -
The examples that we discussed in the previous sections were concerned
with the control of single units like a CSTR, a tank heater, and a batch
reactor. lt should be emphasized a,s early as possible that rarely if ever is
a chemical process composed of one unit only. On the contrary, a chemical
process is composed of a large number of units (reactors, separators, heat
exchangers, tanks, pumps, compressors,, etc.) which are interconnected with ,
each other through the flow of materials and energy. For such a process the
problem of designing a control system is not simple but it requires experience
and good chemical engineering background.
Without dwelling too much on the control problems of integrated chemical
processes, let us see some of their characteristic features which do not show
up in the control of single units,,
Example 2.13
Consider a simple chemical plant composed of two units: a CSTR and a
distillation column (Figure 2.10). The raw materials entering the reactor are
A and B with flowrates FA, FB and temperatures TA, TB respectively.
They react to yield C, i.e.
A + B - C
The reaction is endothermic and the heat is supplied by steam around the
jacket of the reactor. The mixture of C, plus unreacted A and R enters
the distillation column where A + B is separated from the top as the over-
head product and C is taken as the bottoms product.
The operational objectives for this simple plant are:
1. Product specifications:
- keep the flowrate of the desired product stream
F
P
at the specified level, and
- keep the required purity of C in the product
stream.
ii. Operational constraints:
- do not overflow the CSTR, and
- do not flood the distillation column, or let it go dry.
iii. Economic considerations:
- Maximize the profit from the operation of this plant.
Since the flowrate and the composition of the product
stream are specified, maximizing the profit is
equivalent to minimizing the operating costs. It
should be noted that the operating cost involves the
cost for purchasing the raw materials, the cost of
steam used in the CSTR and the reboiler of the dis-
tillation column, as well as the cost of the cooling
water used in the condenser.
The disturbances that will affect the above operational objectives are:
- The flowrates, compositions, and temperatures of the streams of the two
raw materials.
- The pressure in the distillation column.
- The temperature of the coolant used in the condenser of the distillation
column. (For example, if the coolant is water it will have a different
temperature during the day time than during the night.)
At first glance the problem of designing a control system even for this
simple plant looks very complex. Indeed it is.
The basically new feature for the control design of such a system is the
interaction between the units (reactor, column). The output of the reactor
affects in a profound way the operation of the column and the overhead product
of the column influences the conversion in the CSTR. This tight interaction
between the two units complicates seriously the design of the control system
for the overall process.
Suppose that we want to control the composition of the bottoms product by
manipulating the steam in the reboiler. This control action will aEfect the
composition of the overhead product (A+B) which in turn will affect the
reaction conversion in the CSTR.
On the other hand in order to keep the conversion in the CSTR constant
at the desired level, we try to keep the ratio *A'53 = constant and the tem-
perature T in the CSTR constant. Any changes in FA/FB or T will affect
the conversion in the reactor and thus the composition of the feed in the
distillation column. A change in the feed composition of the column will
affect the purity of the two product streams.
The control of integrated processes is the basic objective for a chemical
engineer. Due to its complexity though, we will start by analyzing the cgn-
trol problems for single units and eventually we will treat the integrated
processes.
CHAPTER 3
HARDWARE FOR A PROCESS CONTROL SYSTEM
In the previous chapter we examined the various considerations that must be
taken into account during the design of a control system and the associated
problems that must be resolved. In this chapter we will discuss the physical
elements (hardware) constituting a control system as it is implemented in
practice for the control of real physical processes.
3.1 IIARDWARI:, ELRMMENTS OF A CONTROL SYSTEM.- - - -
In every control configuration we can distinguish the following hardware
elements:
a. The chemical process: It represents the material equipment together with
the physical or chemical operations that occur there,
b. The measuring instruments or sensors: Such instruments are used
to measure the disturbances, the controlled output variables or to measure
secondary variables, and are the main sources of information about what is going
on in the process. Characteristic examples are: ,
- thermocouples or resistance thermometers, for measuring the temperature,
- venturi meters, for measuring the flowrate,
- gas chromatographs, for measuring the composition of a stream, etc.
A mercury thermometer is not a good measuring device to be used for con-
trol since its measurement cannot be readily transmitted. On the other hand the
thermocouple is acceptable because it develops an electric voltage which can
be readily transmitted. Thus, transmission is a very crucial factor in selecting
the measuring devices.
Since good measurements are very crucial for good control, the measuring
devices should be rugged and reliable for an industrial environment.
C . Transducers or transmitters: Many measurements cannot be used for con-
trol until they are converted to physical quantities (like electric voltage
or current, or a pneumatic signal, i.e. compressed air or liquid) which can be
transmitted easily. The transducers or transmitters are used for that purpose.
For example, the Strain Gauges are metallic conductors which change their
resistance when subjected to mechanical strain. Thus, they can be used to
convert a pressure signal to an electric one.
d. Transmission lines: They are used to carry the measurement signal from
the measuring device to the controller. In the past the transmission lines
were pneumatic (compressed air or compressed liquids) but with the advent of
the electronic analog controllers and especially the expanding usage of
digital computers for control, the transmission lines carry electric signals.
Many times the measurement signal coming out from a measuring device is very
weak, and it cannot be transmitted over a long distance. In such cases the
transmission lines are equipped with amplifiers which raise the level of the
signal.For example, the output of a thermocouple is of the order of a few
mil 3. iv0I.t s . Before it is transmitted to the controller, it is amplified to
the level of a few volts.
e. The controller: This is the hardware element that has "intelligence".
It receives the information from the measuring devices and decides what
action should be taken. The older controllers were of limited ,"intelligence",
could perform very simple operations and implement simple control laws.
Today with the increasing usage of digital computers as controllers the
available machine intelligence has expanded tremendously, and very compli-
cated control laws can be implemented.
f. The final control element: This is the hardware element that implements
in real life the decision taken by the controller. For example, if the
controller “decides” that the flowrate of the outlet stream should be increased
(or decreased) in order to keep the liquid level in the tank at,the desired
value (see Example 1.1, Figure 1.3a), it is the valve (on the effluent stream)
:
that will implement this decision, opening (or closing) by the commanded
‘,
amount .
The controi valve is the most frequently encountered final control element but
not the only one. Other typical final control elements for a chemical proces,s
are : -
- Relay switches, providing on-off control,- Relay switches, providing on-off control,
,,
11 ‘I‘I,. *:‘~‘I,. *:‘~‘I ..
- variable speed pumps,-- variable speed pumps,-
‘I, 1‘I, 1 ,. . .,. . . i ti t ..
- variable speed compressors,- variable speed compressors,
.*.*ii I’I ’
etc.etc.
ll
,?,?
&.?’ ,’ .s ~!&.?’ ,’ .s ~! SiSi **
83.83. ‘Recording ‘elemen’ts :‘Recording ‘elemen’ts : These are used to provide. a visual demonstration ofThese are used to provide. a visual demonstration of
) si) si
how the chemical firoce&‘behaves.how the chemical firoce&‘behaves.
3:3: :: 11 :: i;i;
Usua%~y the variables recorded are theUsua%~y the variables recorded are the
I “~._<.I “~._<. :: -1 a,.‘$-1 a,.‘$ 2.2.
variables which are directly Ameasured as a part of the control &s‘tw.variables which are directly Ameasured as a part of the control &s‘tw.
2’:; ! ._ g:.2’:; ! ._ g:. . _,’ .) 3. _,’ .) 3II *,*, 1 .,.*1 .,.* .,.,
Various types-of ra~orders”,(te&erature, pre_ssure,“.flewrate; composition, etc.)Various types-of ra~orders”,(te&erature, pre_ssure,“.flewrate; composition, etc.)
.’. ’
can be seen in the control room of: a chtsmica), p&ant, monitor&q continuouslycan be seen in the control room of: a chtsmica), p&ant, monitor&q continuously
,.....,.....
the behavior of the p&e&$” “.the behavior of the p&e&$” “.
3.r” ,‘r..3.r” ,‘r.. ,.,: :,.,: : / ,.~J :, >;/ ,.~J :, >; *z*z ‘51 ”‘51 ”
The -recent introduction of the digital computersThe -recent introduction of the digital computers
in the processin the process
44 j ;j ; // ., .(^., .(^ ‘,‘, ,.=,.=‘“T” ,,I‘“T” ,,I
d&trol has also expanded the rekording opportunities, throughd&trol has also expanded the rekording opportunities, through
the video display units ‘(‘VQU).the video display units ‘(‘VQU). ‘.‘- ”‘.‘- ” LL
.G.G ,.,.,, f.,, f. .fi.fi
Figure 3.1 des&ib& the hhrdiare el.esien~ts used for the cqntrdl of theFigure 3.1 des&ib& the hhrdiare el.esien~ts used for the cqntrdl of the
: .:: .:
stirred tank heater.stirred tank heater.
.-.-
3.2, THE USE OP. DTCITAL -COMPUTES TN : PROCRSS. ,CONTRO&.3.2, THE USE OP. DTCITAL -COMPUTES TN : PROCRSS. ,CONTRO&.
,,
;; ::II
T h e r a p i d technologica+ @+opment of,d$gital.,.eomputers during t h e l a s t *The rapid technologica+ @velopment of,d$gital.,.eomputers during the last *
,,
ten years,ten years, coupled with. s$gpifieant .reduction of their cost, had a very pro-coupled with. s$gpifieant .reduction of their cost, had a very pro-
. ,. , ; . . .; . . .
found effect on how the ohemical-plants are controlled.*,‘The expected futurefound effect on how the ohemical-plants are controlled.*,‘The expected future
il’ :il’ ::: . .. .
,
,
ation of the control design tech& " ::improvements aqng with the growing sophistic
:. . ' i
niquesmake the digital computer the centerpiece.for the development of a 9 .,;'-~'-+:f7;r.
control syitem for chemical processes.. , .
.:' ,i 'i :I:,i -, ._ . .'
i Already large chemi'cal plants like petroleum refineries, ethylene pla&,.-. i,
:a i. I I 8. ti ' /
, 1~ Ji, O. .r
ammonia,plants and many others
.
, are wnder digital computer control. The ::I * -<
effects have* been-very substantial,I' 4‘! ._: , .*v
leading 'to better-control andreduced
i,
operating costs. 1 r '.,.,
-'~. _ 7 '.‘ : .. ).. ' '_ '.,
In the past the control laws that ceuld be imoloment& hv a-rontroller, ~ -..= ---_-__--- -, - --.
:.
were very simple like the proportional or progotifional-integral control wa) i
discussed in'section'2.2. .The fu
~. ,:i ,' 'i I '5 ," '. w
en& revolution introduced by,fhes., ". ,,
digital computer in the.prahtice'of process'Mntro~1 is the virtually unlimited,
"' !,. ._,; '.
intelligence that can be exhibited;by such 'un,irs. .,'I&& phencmenon imilies .
: >.';,'. _, :
that the control laws that can.be u,s‘ed are'&.u$ m&e comple?i ar&sophisficsted.
., 7". ,~ ,::, ( ) .;.z,: .‘C i *.. ,:.T.
Furthermore, the'digital computer with i!--,eas,ily yropr d inherent *!I
intelligence "
: ; . . J3 :, 1', ,~ 'II
can learn" as it receivks aieasur&en$s from-the proces,s,
r
and it
1 i ,', .,,*,. ,%' ;l;<:~, >: : 79; 1
can' change the control law that is imple&en&& in:tfie 3
;1_ . 7:s: ,.-4, '.
actual' :.operation of*-' 1 ,(
the plant.
< .:. ; ' b ,c>.: ,:
The digita computers have found very~~diversi$&@- control applicat$+s
I, ,, j I . 3 '~ * i ,". 2'.
in the process industry. In subsequent cha'&zrs we,pill.study both the. .';. j - !?'. ,::,c* 'p : -*, : .&',I',, ,*, '.
theoretical and practical aspects associated with the us,e of,,digital computers
'** "j$ 7 J,( ‘&A
for process control. In thefollow%ng psragrophs~,$a i'the time being, we
./ #~,*":.; j : :. :.'r.",, ,J,( l,r *_. ,,'.*, '5::" .
will diecues some applications characreristic'of'.the diverse usaBe gf the
'; 1~ '.
digital computers.
;)
*f.
',.l,.,
a. , Direct Dig&al Control (DDC$i .'~R,.BUldhl86~~'i~~~~o~~~ the c&put& riceivesII <,+. : , ?>_
directly the measurements from'theSproces8' and b&&6'&~theicontrol law, which/ I
is @ready programmed and,resides %a ite:?eolrjrjr,~~alh~ata;Lb~the'valuos of the
,, :,
manipulated variables, i These,dec&ons, are,nois- implemented direc$ly on the
process by the computer through the proper adjustment of the final control,
elements (valves, pumps, compressors, switches, etc.). This dfrect imple-
mentation of the control decisions gave rise to .the name direct digital con-
trol, or sim& DDC.' Figure 3.2 illustrates a typical DDC configuration.
The process can be a&of the units'we,have already considered such as; heaters, reac
separators, etc. The two interfaceslbefore and after' the &&pitter are hard-
ware element6 and they are used to create the interface 1 between the computer
and the' process.: In a let& cbapter"we.wiil diecuss the nature of these'
interfaces. Finally., the human operator c&"%nteradt~‘ititb 'the Computir and
affect the operation of the DDC'si
Today the chemical industry is moving more and more towards the DDC of
the plants. A typical system oYf DDC's for an ethylene plant can includei ' ,.*.P
between 300 and 400 control loops. aAl1 the compan&es which furnish the con-
'., i -,, ‘, r /: ,,.," '
trol systems for the chemical industry: rely 'more and more on.,DDC.
1 ' ,_ ad,,, '; L ,-. ! I " v.
b . Supervisory computer control: -Aswe discussed earlier oneof ;the
incentives for process control is the .opt&zat%on,of the‘ pla&'s economic
.. i _ . I, i I I,a A.. .:r " .; i :
performance. Many times the human operator‘does not or cannot find the best ,
.z *;,- *,'&! .'. :".r. ' :A. ' ; *$..j
operating policy for a plant which will minidil&th~ operating cost. This'y.. _.( t ?'S '/, I1 ,.. ; is. : ! p '
deficiency is due to the -enormous esmplexity of.a'typlcal chemical plant.'
,.. ; ," t,, j .*$~1 , j ; I,' : ( >ti L +..i \ I,:..
In such cases we can use the,s#eed &d the progreamn;hd intelligence of a
:' 4; ..J.% .: /" * I..:,* 1 .: /,_.b. 5" :j: .%%. ,,. j : .,i'I
digital computer to analyze the sit&j&on and'to‘suggest the best policy... . , 2;s ," ,. j .: 1 _ I': I. , j
In doing so the computer coordinates the act$vit&es of the basjc DDC loops, :
(see Figure 3.3).
C* Sch,eduling computer control. Finally, the computer can be.used to-.I
schedule the operation kof a plant. For example, the conditions in the market
(demand, supply, prices) change with time, requiring the'management of the ):
chem&l plant to change its op.erational schedule like cutting:production to
avoid overstocking, increasing prodticti'on to meet the demand, changing-over
to a new production line, etc.
,
.,
,, !..,, !..
These decision can be $made rationally with then aid &.a digital cpmputerThese decision can be $made rationally with then aid of.a digital computer
. . .’. . .' ii ,_.‘i, I,_.'i, I ~~ . . r. . r -3-3 77
which in, turn will communicate these ds$.sions to the supenrisptiy computerwhich in, turn will communicate these ds$.sions to the supenrisptiy computer./ .;./ .;
controllers.controllers.. .. . Pinally, these supervisory eontrollers will implement the,sePinally, these supervisory eontrollers will implement the,se.I.I ; / . ..'I; / . ..'I ,<,< .i".i",, 22 .,..'.,..'
decisions on the chemical plant through$the ;DDC'8+decisions on the chemical plant through$the ;DDC'8+
-II-II !. .L!. .L.i.i ,, *,, * II
In subsequent shapters we ~i$l. +++Z .px!,edominantly~with &he DDC and aIIn subsequent shapters we ~i$l. +++Z .px!,edominantly~with &he DDC and aI;";" ',', // .s.s , !, ;‘, !, ;‘ -^-^ .'.' ,- .:,- .: ii
little with superyisory computer %ent&.~,wh~ile we..$lllittle with superyisory computer %ent&.~,wh~ile we..$ll not'conkern ourselves -': .I: .I ii not'conkern ourselves'.i'.i,'.t :,'.t :/I . ,./I . ,. 2.2.
with 'the scheguling computer c*t$;ol $$ch $~,the subject u&pr qf ii dif- :with 'the scheguling computer c*t$;ol $$ch $~,the subject u&pr qf ii dif- :
I. :I. :
ferent field.ferent field. ';'; i-i- ._' / "._' / " _, .I_, .I
'_'_.<'.<' ,.,.
CONCLJDlNG R&g ON PART ICONCLJDlNG R&g ON PART I
r d,. _,r d,. _, / './ '. ..;' ,,..;' ,,
',',
LL i.i.:(.:(. : .j: .j ',',
It is hoped that the reader now his a sk&chy outl$ne oftIt is hoped that the reader now his a sk&chy outl$ne oft
,.*:. -;:..,.*:. -;:.. ..,Tf 6 _' , ~5:,Tf 6 _' , ~5: :,:' . i ,;, ;:,:' . i ,;, ; _ I_ I
I.- 'I%0 iced8 &id 'the incen~tives for' 'procees ~:onerol,:~I'~ .<I.- 'I%0 iced8 &id 'the incen~tives for' 'procees ~:onerol,:~I'~ .<
I ,l.I ,l. ,,_,,_
St \,St \,
,* /_ ‘:;;“‘,* /_ ‘:;;“‘ ,~ 1 > -i $ ',, ',,~ 1 > -i $ ',, ', .',..',. 1. .:1. .: ,;,.$;t "' :,;,.$;t "' : ;* :;* :
- the basic questions involved'during the design 6f'a control syst.en‘for a- the basic questions involved'during the design 6f'a control syst.en‘for a
/ ** */ ** * : 3,.: 3,..,,r+ .' :- '.,,r+ .' :- ' ~~ : 14: 14/'l.l :/'l.l :
chemical process,chemical process, b ( * .,'b ( * .,' III.,. . II.,. . I , :a:$,' ', :a:$,' ' ,s , (' ),,s , (' ),,, .,, .
- the‘hardware elements involved in a; &on& 8ys't&~;&,4- the‘hardware elements involved in a; &on& 8ys't&~;&,4
II :: 'j-k'* .;' 'fJ :" * ,?j;i -,z.f ,,'j-k'* .;' 'fJ :" * ,?j;i -,z.f ,, .:," ,'.:," ,' -F ..;i-F ..;i
- the importance of the digital,comput&s~f& the pres.en.t"a~ future- the importance of the digital,comput&s~f& the pres.en.t"a~ future
,, '; .,, '; . * ,* ,~I~I ,z d$:'yje ; I,z d$:'yje ; I ‘‘
implementation of advanced control'teohriiques.~ '~~~'~~~~implementation of advanced control'teohriiques.~ '~~~'~~~~
, :, :
__I. jI. j I *:,rI *:,r ,,&:$;.! -1,. ,$;? : '. I (.: b,,&:$;.! -1,. ,$;? : '. I (.: b ""
In the remainingIn the remaining chapters we~will.~~s&~t'~ ay~tkmatic analysis &,thechapters we~will~~s&~t'~ ay~tkmatic analysis &,the
various questions raised in thi.s chept$F:, -wfW'the final,
design a rational control system f,or a':$i.v&n proce:.,. ,I ,) ,( ‘i :; (. :' _ " .',,. ;:.‘i$. i. ,.
chapters will be leas chatty and more ‘&&xH$~‘~‘~-~’
*’
I,
REFERENCES
i :I ( 1
. ..
ChaRter 1: Numerous examples of the needs and %ncent%ves'for prowess control*'
can bc'foun&'& the following booti:
(1) Techn-Jl&@ of Process .Cqmts@‘, by Fi S‘i 'Buckley, John Wiley &
Son&, Inc. , N&# T*yii (~9~4),V _ “', : c
',
(2) Process Control Systems, /2nd edition, by F. G. Shifnsky,.*
McGraiw-Hi&I, dew York -(19@]:;' ' ', 4;
, I
More on the stability &haracter,istics of, &TR's tith'exokhermfq reactions,
can be found in: ' c i:b,. - /, ; ., I .
.
(31 Ele
I& p. 2 (1976)‘ r.>> (
The reader is encouraged to return to these articles later after he has become': ".,I
familiar w&h the terminology' Included in the above refere&ea,n .
Chapter 3: Details on the chslracteristice and th6 design of the measuring+
devices, Oransducersi transmitters, controllers, final control elements and
recorders, can be found in: : d 4 $
1
L 4
,
I
3%
(7) The Chemidal Engineer\8 Handbook; J. H. Perry (editor), 5th
edi$n, MqGrqyHill, New Vprk (1974). ,.
.* I
(8). Pro&a Instruments and,bontrdls X&dbqqk,, D. M. Considine
,:
(editor.), ,2qd eaitiqn, l&&aw$iill;. New York (19Jk)..,.*I __, .:
, An excellent reference for the cor&ter; contgo;;l ,& th&_ch+cel pro-
:.:
cessea is the boa&: ?(~‘ SC.' ,i.' -I ;: ._c_ s. .
(9) Digital Computer Pn,,c&s Con&&, by,,C,:L, Smi&, Intext Educ,,
.Publ. ,. New York' (l!T$TZ$, ..I' ..', ,' ;,I ,>
Applications of computer contro4 qan be found in the following articles:-
(10) "Digida Cmtro~ oi a Dis.~~~Jatisn,Sye'~,l~.by, ~.~~.~~+~~ellano,* .:' ,I.
C. A.,McCain'and F. W."fFblas, me+. J&. Erogr., -.:74(4), 56
.
(197t3j. ,: ./ (1 i )L, : :I (3 (. _“ <i ',,
I
-.' (11) "Ener@ Conser&ionl~ia Process Computer Cont.p3i,*!..by P. R.zs‘i.
.I , nI, . '_ ,,'
LaWuS,,, Chem., Fpg,; Pr0&~.,,;12(4) , 76*;.(19i@b ~' " _/ ‘ :'; ,,
!>
7' (52) 'Qhnppr Co&l of Aqm+&&anfq~,ll,,:
. .
!yL. C. Daig$e;III and
.i.' ~,
.;;1. G. I(, Nieman, C&m. .&g, progri;',.~70(2)j..‘Hf.11974),,~ ": ' .',
;- ;.:.i. _, '_ ,_ "
" ,
(13) "Applying Cpn*ol, (Sompuzt&/ t&a'& X~t$y$ .'
.,
.* ,,I.(
Nisenfeld, Ch". Eng. Progr.;.,-
-- - -- - - -
, , :
.-b---b
.
..-----------------,
c..
i
,,'
Coolant Water
Controller I
COLUMN
Contrdller
I ”
I-----y----, .: ’
5-J
.
Feed I/
-4
--a
I
. c
Reflux Distillate '
_ ' 1 feedback (a)'; fet%-lforward (b); inferentia) (c)
The three control schemes of the Example 2.8:
a
I
-1
: I d
1
t
.
. kimat& o f t h e
. ” Values zrf the
‘k-ti’ -4 VariabIes
Unmeasured CX&rolled
f ’
----w-a
‘Estimates
o f t h e ’
,’
, :
Unmrzrsured
Controlhd ./
Variables i’
I. : a
3,. :.,
T h e g e n e r a l s t r u c t u r e o f t h e dnFetenfia1 c o n t r o l configurntim.
Measured,,
Oukputs-
.’
,
U n m e a s u r e d
outputs
The gcnernl. s t r u c t u r e OC t h e CeodCorward control COIIC J:;+II-;:t i,,lI. ’
4: ” .,
C
,
,
. . . . C-...-w-. * -...a -. .-...L-w-..