Coulson and Richardson’s Chemical Engineering: Volume 3B: Process Control

630 Pages·2017·31.12 MB·English

by  Sohrab Rohani

Coulson and Richardson’s
Chemical Engineering
This page intentionally left blank
Coulson and Richardson’s
Chemical Engineering
Volume 3B: Process Control
Fourth edition
Sohrab Rohani
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Contents
Contributors.....................................................................................................xv
About Prof. Coulson........................................................................................xvii
About Prof. Richardson....................................................................................xix
Preface...........................................................................................................xxi
Introduction ....................................................................................................xxv
Chapter 1: Introduction......................................................................................1
1.1 Definition of a Chemical/Biochemical Process....................................................1
1.1.1 A Single Continuous Process............................................................................1
1.1.2 A Batch and a Semibatch or a Fed-Batch Process...........................................3
1.2 Process Dynamics..................................................................................................4
1.2.1 Classification of Process Variables...................................................................5
1.2.2 Dynamic Modeling............................................................................................5
1.3 Process Control......................................................................................................8
1.3.1 Types of Control Strategies...............................................................................9
1.4 Incentives for Process Control............................................................................11
1.5 Pictorial Representation of the Control Systems................................................12
1.6 Problems..............................................................................................................16
References...................................................................................................................16
Chapter 2: Hardware Requirements for the Implementation of Process
Control Systems...............................................................................................17
2.1 Sensor/Transmitter...............................................................................................17
2.1.1 Temperature Transducers................................................................................17
2.1.2 Pressure Transducers.......................................................................................18
2.1.3 Liquid or Gas Flow Rate Transducers............................................................18
2.1.4 Liquid Level Transducers................................................................................19
2.1.5 Chemical Composition Transducers...............................................................19
2.1.6 Instrument or Transducer Accuracy................................................................19
2.1.7 Sources of Instrument Errors...........................................................................20
2.1.8 Static and Dynamic Characteristics of Transducers.......................................21
2.2 Signal Converters................................................................................................21
2.3 Transmission Lines..............................................................................................22
2.4 The Final Control Element..................................................................................23
2.4.1 Control Valves.................................................................................................23
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Contents
2.5 Feedback Controllers...........................................................................................26
2.5.1 The PID (Proportional-Integral-Derivative) Controllers................................26
2.5.2 The PID Controller Law..................................................................................27
2.5.3 The Discrete Version of a PID Controller......................................................28
2.5.4 Features of the PID Controllers......................................................................28
2.6 A Demonstration Unit to Implement A Single-Input, Single-Output
PID Controller Using the National InstrumentR Data Acquisition
(NI-DAQ) System and the LabVIEW.................................................................34
2.7 Implementation of the Control Laws on the Distributed Control Systems........35
2.8 Problems..............................................................................................................38
References...................................................................................................................38
Chapter 3: Theoretical Process Dynamic Modeling ..............................................39
3.1 Detailed Theoretical Dynamic Modeling............................................................39
3.2 Solving an ODE or a Set of ODEs.....................................................................42
3.2.1 Solving a Linear or a Nonlinear Differential Equation in MATLAB............42
3.2.2 Solving a Linear or a Nonlinear Differential Equation on Simulink.............44
3.3 Examples of Lumped Parameter Systems...........................................................46
3.3.1 A Surge Tank With Level Control..................................................................46
3.3.2 A Stirred Tank Heater With Level and Temperature Control.......................60
3.3.3 A Nonisothermal Continuous Stirred Tank Reactor.......................................65
3.3.4 A CSTR With Liquid Phase Endothermic Chemical Reactions....................70
3.4 Examples of Stage-Wise Systems.......................................................................72
3.4.1 A Binary Tray Distillation Column................................................................73
3.5 Examples of Distributed Parameter Systems......................................................84
3.5.1 A Plug Flow Reactor.......................................................................................84
3.6 Problems..............................................................................................................92
References...................................................................................................................94
Chapter 4: Development of Linear State-Space Models and Transfer Functions
for Chemical Processes.....................................................................................95
Part A—Theoretical Development of Linear Models...............................................95
4.1 Tools to Develop Continuous Linear State-Space and Transfer
Function Dynamic Models..................................................................................96
4.1.1 Linearization of Nonlinear Differential Equations.........................................96
4.1.2 The Linear State-Space Models....................................................................100
4.1.3 Developing Transfer Function Models (T.F.)...............................................101
4.2 The Basic Procedure to Develop the Transfer Function of SISO
and MIMO Systems...........................................................................................117
4.3 Steps to Derive the Transfer Function (T.F.) Models......................................118
4.4 Transfer Function of Linear Systems................................................................121
4.4.1 Simple Functional Forms of the Input Signals.............................................121
4.4.2 First-Order Transfer Function Models..........................................................123
4.4.3 A Pure Capacitive or An Integrating Process...............................................130
4.4.4 Processes With Second-Order Dynamics......................................................132
4.4.5 Significance of the Transfer Function Poles and Zeros...............................143
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Contents
4.4.6 Transfer Functions of More Complicated Processes—An Inverse
Response (A Nonminimum Phase Process), A Higher Order Process
and Processes With Time Delays..................................................................146
4.4.7 Processes With Nth-Order Dynamics............................................................151
4.4.8 Transfer Function of Distributed Parameter Systems...................................153
4.4.9 Processes With Significant Time Delays......................................................155
Part B—The Empirical Approach to Develop Approximate
Transfer Functions for Existing Processes...............................................................161
4.5 The Graphical Methods for Process Identification...........................................162
4.5.1 Approximation of the Unknown Process Dynamics by a First-Order
Transfer Function With or Without a Time Delay.......................................162
4.5.2 Approximation by a Second-Order Transfer Function
With a Time Delay........................................................................................164
4.6 Process Identification Using Numerical Methods............................................167
4.6.1 The Least Squares Method............................................................................168
4.6.2 Using the “Solver” Function of Excel for the Estimation of the
Parameter Vector in System Identification...................................................169
4.6.3 A MATLAB Program for Parameter Estimation..........................................169
4.6.4 Using System Identification Toolbox of MATLAB.....................................172
4.7 Problems............................................................................................................175
References.................................................................................................................180
Chapter 5: Dynamic Behavior and Stability of Closed-Loop Control
Systems—Controller Design in the Laplace Domain...........................................181
5.1 The Closed-Loop Transfer Function of a Single-Input,
Single-Output (SISO) Feedback Control System.............................................181
5.2 Analysis of a Feedback Control System...........................................................183
5.2.1 A Proportional Controller..............................................................................183
5.2.2 A Proportional-Integral (PI) Controller........................................................184
5.3 The Block Diagram Algebra.............................................................................188
5.4 The Stability of the Closed-Loop Control Systems..........................................189
5.5 Stability Tests....................................................................................................191
5.5.1 Routh Test......................................................................................................191
5.5.2 Direct Substitution Method...........................................................................193
5.5.3 The Root Locus Diagram..............................................................................194
5.6 Design and Tuning of the PID Controllers.......................................................199
5.6.1 Controller Design Objectives........................................................................200
5.6.2 Choosing the Appropriate Control Law........................................................201
5.6.3 Controller Tuning..........................................................................................201
5.6.4 The Use of Model-Based Controllers to Tune a PID Controller
(Theoretical Method).....................................................................................203
5.6.5 Empirical Approaches to Tune a PID Controller.........................................209
5.7 Enhanced Feedback and Feedforward Controllers...........................................210
5.7.1 Cascade Control.............................................................................................211
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Contents
5.7.2 Override Control............................................................................................215
5.7.3 Selective Control...........................................................................................217
5.7.4 Control of Processes With Large Time Delays............................................218
5.7.5 Control of Nonlinear Processes.....................................................................222
5.8 The Feedforward Controller (FFC)...................................................................224
5.8.1 The Implementation of a Feedforward Controller........................................226
5.8.2 The Ratio Control..........................................................................................228
5.9 Control of Multiinput, Multioutput (MIMO) Processes...................................229
5.9.1 The Bristol Relative Gain Array (RGA) Matrix...........................................231
5.9.2 Control of MIMO Processes in the Presence of Interaction
Using Decouplers...........................................................................................235
5.10 Problems............................................................................................................236
References...................................................................................................................242
Chapter 6: Digital Sampling, Filtering, and Digital Control................................243
6.1 Implementation of Digital Control Systems...................................................244
6.2 Mathematical Representation of a Sampled Signal........................................245
6.3 z-Transform of a Few Simple Functions........................................................246
6.3.1 A Discrete Unit Step Function....................................................................246
6.3.2 A Unit Impulse Function.............................................................................247
6.3.3 A Discrete Exponential Function................................................................247
6.3.4 A Discrete Delayed Function Where θ Is the Delay Time........................247
6.4 Some Useful Properties of the z-Transform...................................................248
6.5 Inverse z-Transform........................................................................................249
6.6 Conversion of an Equation From the z-Domain to a Discrete Equation
in the Time Domain........................................................................................250
6.7 Derivation of the Closed-Loop Transfer Function (CLTF)
of a Digital Control System............................................................................250
6.8 The Closed-Loop Pulse Transfer Function of a Digital Control System.......254
6.9 Selection of the Sampling Interval..................................................................254
6.10 Filtering............................................................................................................255
6.11 Mapping Between the s-Plane and the z-Plane...............................................256
6.11.1 The Concept of Stability in the z-Plane....................................................257
6.11.2 Routh-Hurwitz and Bilinear Transformation Test....................................258
6.11.3 Jury’s Stability Test in the z-Domain.......................................................258
6.12 Design of Digital Feedback Controllers for SISO Plants...............................260
6.13 Design of Model-Based SISO Digital Controllers.........................................262
6.13.1 The Deadbeat Controllers (DB)................................................................263
6.13.2 The Dahlin Controller...............................................................................266
6.13.3 The Smith Predictor...................................................................................268
6.13.4 The Kalman Controller..............................................................................271
6.13.5 Internal Model Controller (IMC)..............................................................272
6.13.6 The Pole Placement Controller.................................................................275
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Contents
6.14 Design of Feedforward Controllers.................................................................278
6.15 Control of Multi-Input, Multi-Output (MIMO) Processes.............................280
6.15.1 Singular Value Decomposition (SVD) and the Condition
Number (CN).............................................................................................282
6.15.2 Design of Multivariable Feedback Controllers for MIMO Plants...........283
6.15.3 Dynamic and Steady-State Interaction Compensators
(Decouplers) in the z-Domain...................................................................283
6.15.4 Multivariable Smith Predictor...................................................................285
6.15.5 Multivariable IMC Controller...................................................................286
Problems...................................................................................................................289
References.................................................................................................................292
Further Reading........................................................................................................292
Chapter 7: Control System Design in the State Space and Frequency Domain ......293
7.1 State-Space Representation...............................................................................293
7.1.1 The Minimal State-Space Realization...........................................................294
7.1.2 Canonical Form State-Space Realization......................................................296
7.1.3 Discretization of the Continuous State-Space Formulation.........................297
7.1.4 Discretization of Continuous Transfer Functions.........................................299
7.1.5 Conversion of Plant Models From the Discrete State Space
to the z-Domain.............................................................................................300
7.1.6 Conversion From z-Domain to Discrete State Space...................................301
7.2 Design of Controllers in the State Space..........................................................304
7.2.1 Solution of the State-Space Equation...........................................................304
7.2.2 Controllability................................................................................................305
7.2.3 Observability..................................................................................................305
7.2.4 The State Feedback Regulator (SFR)...........................................................307
7.2.5 The State Feedback Control With Incomplete State Information................307
7.2.6 Time Optimal Control...................................................................................309
7.3 Frequency Response of Linear Systems and the Design of PID
Controllers in the Frequency Domain...............................................................312
7.3.1 Definition of the Amplitude Ratio and Phase Difference of
a Linear System.............................................................................................312
7.3.2 Review of Complex Numbers.......................................................................314
7.3.3 The Shortcut Method to Determine AR(ω) and ϕ(ω) of
Linear Systems..............................................................................................315
7.3.4 Graphical Representation of AR and ϕ and Their Applications..................318
7.3.5 Graphical Construction of the Approximate Bod(cid:1)e Plots..............................319
7.3.6 Graphical Construction of the Approximate Nyquist Plot...........................320
7.3.7 Numerical Construction of Bod(cid:1)e and Nyquist Plots....................................320
7.3.8 Applications of the Frequency Response Technique....................................322
7.4 Problems............................................................................................................330
References.................................................................................................................332
Further Reading........................................................................................................332
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