This book delivers real world experience covering full-scale industrial control design, for students and professional control engineers
Inspired by the authors’ industrial experience in control, Practical Control System Design: Real World Designs Implemented on Emulated Industrial Systems captures that experience, along with the necessary background theory, to enable readers to acquire the tools and skills necessary to tackle real world control engineering design problems. The book draws upon many industrial projects conducted by the authors and associates; these projects are used as case studies throughout the book, organized in the form of Virtual Laboratories so that readers can explore the studies at their own pace and to their own level of interest. The real-world designs include electromechanical servo systems, fluid storage, continuous steel casting, rolling mill center line gauge control, rocket dynamics and control, cross directional control in paper machines, audio quantisation, wind power generation (including 3 phase induction machines), and boiler control.
To facilitate reader comprehension, the text is accompanied by software to access the individual experiments. A full Solutions Manual for the questions set in the text is available to instructors and practicing engineers.
Background theory covered in the text includes control as an inverse problem, impact of disturbances and measurement noise, sensitivity functions, Laplace transforms, Z-Transforms, shift and delta operators, stability, PID design, time delay systems, periodic disturbances, Bode sensitivity trade-offs, state space models, linear quadratic regulators, Kalman filters, multivariable systems, anti-wind up strategies, Euler angles, rotational dynamics, conservation of mass, momentum and energy as well as control of non-linear systems.
Practical Control System Design: Real World Designs Implemented on Emulated Industrial Systems is a highly practical reference on the subject, making it an ideal resource for undergraduate and graduate students on a range of control system design courses. The text also serves as an excellent refresher resource for engineers and practitioners.
Table of Contents
Preface xix
About the Authors xxi
Acknowledgements xxiii
About the Companion Website xxiv
Part I Modelling and Analysis of Linear Systems 1
1 Introduction to Control System Design 3
1.1 Introduction 3
1.2 A Brief History of Control 4
1.3 Digital Control 5
1.4 Our Selection 5
1.5 Thinking Outside the Box 6
1.6 How the Book Is Organised 6
1.7 Testing the Reader’s Understanding 6
1.8 Revision Questions 7
Further Reading 7
2 Control as an Inverse Problem 9
2.1 Introduction 9
2.2 The Elements 9
2.3 Using Eigenvalue Analysis 10
2.4 The Effect of Process and Disturbance Errors 11
2.5 Feedback Control 11
2.6 The Effect of Measurement Noise 12
2.7 Sensitivity Functions 14
2.8 Reducing the Impact of Disturbances and Model Error 14
2.9 Impact of Measurement Noise 14
2.10 Other Useful Sensitivity Functions 14
2.11 Stability (A First Look) 15
2.12 Sum of Sensitivity and Complementary Sensitivity 15
2.13 Revision Questions 16
Further Reading 16
3 Introduction to Modelling 17
3.1 Introduction 17
3.2 Physical Modelling 17
3.2.1 Radio Telescope Positioning 17
3.2.2 Band-Pass Filter 19
3.2.3 Inverted Pendulum 19
3.2.4 Flow of Liquid out of a Tank 20
3.3 State-Space Model Representation 21
3.3.1 Systems Without Zeros 22
3.3.2 Systems Which Depend on Derivatives of the Input 23
3.3.3 Example: State-Space Representation 24
3.4 Linearisation and Approximation 25
3.4.1 Linearisation of Inverted Pendulum Model 26
3.5 Revision Questions 27
Further Reading 28
4 Continuous-Time Signals and Systems 29
4.1 Introduction 29
4.2 Linear Continuous-Time Models 29
4.3 Laplace Transforms 30
4.4 Application of Laplace Transforms to Linear Differential Equations 31
4.4.1 Example: Angle of Radio Telescope 32
4.4.2 Example: Modelling the Angular Velocity of Radio Telescope 33
4.5 A Heuristic Introduction to Laplace Transforms 33
4.6 Transfer Functions 34
4.6.1 High-Order Differential Equation Models 34
4.6.2 Example: Transfer Function for Radio Telescope 35
4.6.3 Transfer Functions for Continuous-Time State-Space Models 35
4.6.4 Example: Inverted Pendulum 36
4.6.5 Poles, Zeros and Other Properties of Transfer Functions 36
4.6.6 Time Delays 36
4.6.7 Heuristic Development of Transfer Function of Delay 37
4.6.8 Example: Heating System 37
4.7 Stability of Transfer Functions 38
4.7.1 Example: Poles of the Radio Telescope Model 38
4.8 Impulse Response of Continuous-Time Linear Systems 38
4.8.1 Impulse Response 38
4.8.2 Convolution and Transfer Functions 39
4.9 Step Response 39
4.10 Steady-State Response and Integral Action 40
4.11 Terms Used to Describe Step Responses 40
4.12 Frequency Response 41
4.12.1 Nyquist Diagrams 43
4.12.2 Bode Diagrams 43
4.12.3 Example: Simple Transfer Function 44
4.13 Revision Questions 45
Further Reading 46
5 Laboratory 1: Modelling of an Electromechanical Servomechanism 47
5.1 Introduction 47
5.2 The Physical Apparatus 47
5.3 Estimation of Motor Parameters 49
5.3.1 Motivation for Building a Model 50
5.3.2 Experiment: Why Build a Model? 50
5.3.3 Step Response Testing 50
5.3.4 Experiment: Measuring the Open-Loop Gain and Time Constant 51
5.3.5 Frequency Response 51
5.3.6 Experiment: Measuring Frequency Response 52
5.3.7 Experiment: Alternative Measurement of Frequency Response 52
5.4 Revision Questions 53
Further Reading 53
Part II Control System Design Techniques for Linear Single-input Single-output Systems 55
6 Analysis of Linear Feedback Systems 57
6.1 Introduction 57
6.2 Feedback Structures 57
6.3 Nominal Sensitivity Functions 59
6.4 Analysing Stability Using the Characteristic Polynomial 60
6.4.1 Example: Pole-Zero Cancellation 61
6.5 Stability and Polynomial Analysis 61
6.5.1 Stability via Evaluation of the Roots 61
6.6 Root Locus (RL) 61
6.7 Nominal Stability Using Frequency Response 63
6.8 Relative Stability: Stability Margins and Sensitivity Peaks 67
6.9 From Polar Plots to Bode Diagrams 68
6.10 Robustness 69
6.10.1 Achieved Sensitivities 69
6.10.2 Robust Stability 69
6.11 Revision Questions 71
Further Reading 72
7 Design of Control Laws for Single-Input Single-Output Linear Systems 73
7.1 Introduction 73
7.2 Closed-Loop Pole Assignment 73
7.2.1 Example: Steam Receiver 74
7.3 Using Root Locus 75
7.3.1 Example: Double Integrator 75
7.3.2 Example: Unstable Process 76
7.4 All Stabilising Control Laws 77
7.5 Design Using the Youla-Kucera Parameterisation 79
7.5.1 Example: Simple First-Order Model 80
7.6 Integral Action 80
7.7 Anti-Windup 81
7.8 PID Design 82
7.8.1 Structure 82
7.8.2 Using the Youla-Kucera Parameterisation for PID Design 84
7.9 Empirical Tuning 84
7.10 Ziegler-Nichols (Z-N) Oscillation Method 84
7.10.1 Example: Third-Order Plant 85
7.11 Two Degrees of Freedom Design 86
7.12 Disturbance Feedforward 86
7.13 Revision Questions 87
Further Reading 88
8 Laboratory 2: Position Control of Electromechanical Servomechanism 89
8.1 Introduction 89
8.2 Proportional Feedback 89
8.2.1 Experiment: Testing a Proportion only Control Law 91
8.3 Using Proportional Plus Derivative Feedback 91
8.3.1 Experiment: Testing a PD Control Law 92
8.4 Tachometer Feedback 92
8.5 PID Design 92
8.5.1 Output Disturbances 92
8.5.2 Input Disturbance 93
8.5.3 A Simple Design Procedure 94
8.5.4 Experiment: Testing a PID Control Law 94
8.6 Revision Questions 95
Further Reading 95
9 Laboratory 3: Continuous Casting Machine: Linear Considerations 97
9.1 Introduction 97
9.2 The Physical Equipment 97
9.3 Modelling of Continuous Casting Machine 99
9.4 Proportional Control 102
9.5 Response to Set-Point Changes 103
9.6 Experiments 103
9.6.1 Experiment: Model Parameter Estimation 103
9.6.2 Low Gain Feedback 104
9.6.3 High Gain Feedback 104
9.7 Effect of Measurement Noise 104
9.7.1 Experiment: Measuring the Impact of Measurement Noise 105
9.8 Pure Integral Control 105
9.8.1 Experiment: Testing Pure Integral Control 106
9.9 PI Control 106
9.9.1 Experiment: Testing PI Control 107
9.9.2 Experiment: Testing the Response to Varying Casting Speed 108
9.10 Feedforward Control 108
9.10.1 Experiment: Testing Feedforward Control 109
9.10.2 Experiment: Testing Sensitivity to the Feedforward Gain 110
9.11 Revision Questions 110
Further Reading 110
10 Laboratory 4: Modelling and Control of Fluid Level in Tanks 113
10.1 Introduction 113
10.2 The Controllers 113
10.3 Physical Modelling 113
10.3.1 Experiment: Estimating Plant Gain and Time Constant 117
10.4 Closed-Loop Level Control for a Single Tank 117
10.4.1 Proportional Only Control 117
10.4.2 Experiment: Testing Proportional Control 117
10.4.3 Integral Only Control 118
10.4.4 Experiment: Testing Integral Control 118
10.4.5 Proportional Plus Integral Control 119
10.4.6 Experiment: Testing PI Control 119
10.4.7 Experiment: Alternative PI Controller 119
10.5 Closed-Loop Level Control of Interconnected Tanks 119
10.6 Revision Questions 120
Further Reading 121
11 Laboratory 5: Wind Power (Mechanical Components) 123
11.1 Introduction 123
11.2 Yaw Control 123
11.2.1 Experiment: Estimating the Yaw Time Constant 127
11.2.2 Design of Yaw Controller 127
11.2.3 Experiment: Testing the Yaw Controller 128
11.3 Rotational Velocity Control 129
11.3.1 Experiment: Testing the Rotational Velocity Control Law 133
11.4 Pitch Control 133
11.5 Experiment: Testing the Pitch Controller 134
11.6 Revision Questions 135
Further Reading 135
Part III More Complex Linear Single-Input Single-Output Systems 137
12 Time Delay Systems 139
12.1 Introduction 139
12.2 Transfer Function Analysis 139
12.3 Classical PID Design Revisited 140
12.4 Padé Approximation 140
12.5 Using the Youla-Kucera Parameterisation 140
12.6 Smith Predictor 141
12.7 Modern Interpretation of Smith Predictor 142
12.8 Sensitivity Trade-Offs 142
12.9 Theoretical Analysis of Effect of Delay Errors on Smith Predictor 143
12.10 Revision Questions 144
Further Reading 145
13 Laboratory 6: Rolling Mill (Transport Delay) 147
13.1 Introduction 147
13.2 The Physical System 147
13.3 Modelling 149
13.3.1 Description of the Process 149
13.3.2 Sensors and Actuators 149
13.3.3 Disturbances 149
13.3.4 Aims of the Control System 149
13.4 Building a Model 150
13.4.1 The Mill Frame 150
13.4.2 Strip Deformation 150
13.4.3 Composite Model 151
13.4.4 Open-Loop Steady-State Performance 152
13.5 Basic Control System Design 152
13.6 Linear Control Ignoring the Time Delay 153
13.6.1 Experiment: Testing a PI Controller 154
13.7 Linear Control Based on Rational Approximation to the Time Delay 155
13.7.1 Experiment: Testing PID Design 156
13.8 Control System Design Based on Smith Predictor 156
13.8.1 Experiment: Testing Smith Predictor 157
13.9 Use of a Soft Sensor 158
13.9.1 The BISRA Gauge 158
13.9.2 Experiment: Testing the BISRA Gauge 159
13.10 Robustness of BISRA Gauge 159
13.10.1 Experiment: Testing Sensitivity to Mill Modulus 159
13.10.2 Experiment: Alternative Solution to Achieve Steady-State Tracking 159
13.11 Revision Questions 159
Further Reading 160
14 Control System Design for Open-Loop Unstable Systems 161
14.1 Introduction 161
14.2 Some Simple Examples of Open-Loop Unstable Systems 161
14.3 All Stabilising Control Laws for Systems Having Undesirable Open-Loop Poles 163
14.4 Revision Questions 164
Further Reading 165
15 Laboratory 7: Control of a Rocket 167
15.1 Introduction 167
15.2 Dynamics of a Rocket in 2D Flight 167
15.2.1 Coordinate Systems 167
15.2.2 Forces 169
15.2.3 Translational Dynamics 170
15.2.4 Rotational Dynamics 170
15.2.5 Composite Model 171
15.3 Equilibrium 171
15.4 Linearised Model 171
15.5 Open-Loop Flight 172
15.6 Controller Design for the Rocket 172
15.6.1 Simplified Design of PID 172
15.6.2 Frequency Domain Design 173
15.7 Experiment: Testing the Control Law 174
15.7.1 Testing the Design Mode in Section 15.6.1 174
15.7.2 Testing the Design Made in Section 15.6.2 175
15.8 Revision Questions 175
Further Reading 175
16 Bode Sensitivity Trade-Offs 177
16.1 Introduction 177
16.2 System Properties 177
16.3 Bode Integral Constraints 178
16.3.1 Open-Loop Stable Systems 178
16.4 Examples of Bode Sensitivity Trade-Offs 178
16.4.1 Open-Loop Unstable Systems 180
16.5 Bode Complementary Sensitivity Integrals 180
16.5.1 Minimum Phase Plants 180
16.5.2 Non-minimum Phase Plants 180
16.6 Bode Sensitivity for Time-Delay Systems 180
16.7 Revision Questions 181
Further Reading 181
Part IV Sampled Data Control Systems 183
17 Principles of Sampled-Data Control System Design 185
17.1 Introduction 185
17.2 A/D Conversion 185
17.3 Sampled Output Noise 185
17.4 D/A Conversion 186
17.5 Sampled-Data Models 187
17.6 Shift Operator Models 187
17.7 Divided Difference Models 187
17.8 Euler Approximate Model 188
17.9 Euler Approximate Model in Delta Domain 188
17.10 Delta Analysis 189
17.11 Historical Notes 189
17.12 An Example of Shift and Delta Models 189
17.13 Sampled-Data Stability 190
17.14 Bode Sensitivity Integrals (Sampled Data Case) 190
17.14.1 Z-Domain 192
17.14.2 Delta Domain 192
17.15 Sampling Zeros 193
17.16 Revision Questions 193
Further Reading 194
18 Laboratory 8: Audio Signal Processing and Optimal Noise Shaping Quantisers 197
18.1 Introduction 197
18.2 The Physical Apparatus 197
18.3 Psychoacoustic Issues 198
18.3.1 Experiment: Testing Your Hearing Sensitivity 199
18.4 Nearest Neighbour Quantisation 200
18.4.1 Experiment: Testing the Nearest Neighbour Quantiser 200
18.5 Optimal Noise Shaping Quantiser 201
18.5.1 Feedback Quantiser 201
18.5.2 Experiment: Test the Feedback Quantiser 202
18.6 Utilising Your Own Hearing Sensitivity 202
18.6.1 Experiment: Test the Feedback Quantiser Using Your Hearing Sensitivity 204
18.7 Audio Quantisation from a Bode Sensitivity Integral Perspective 204
18.7.1 Experiment: Spectrum of Errors 205
18.7.2 Experiment: Testing Bode Sensitivity Integral 205
18.8 Audio Quantisation for More Complex Cases 205
18.8.1 Experiment: More Complex Case 206
18.9 Revision Questions 206
Further Reading 207
Part V Simple Multivariable Control Problems 209
19 Tools Used for Simple Multivariable Control Problems 211
19.1 Introduction 211
19.2 Cascade Control 211
19.2.1 Example of Cascade Control 212
19.3 Imposed SISO Architectures 214
19.4 Relative Gain Array 215
19.5 An Industrial Example 215
19.5.1 The Relative Gain Array 215
19.5.2 A Simple MV Transformation 216
19.6 Revision Questions 216
Further Reading 216
20 Laboratory 9: Wind Power (Electrical Components) 217
20.1 Introduction 217
20.2 Generator Choices 217
20.3 Physical Parameters for the Laboratory Wind Turbine 217
20.4 The Generator and Grid Side Architectures 219
20.5 Background Theory 219
20.5.1 Alpha, Beta Coordinates 220
20.5.2 dq Frame 220
20.5.3 The Inverse Transformation 221
20.5.4 First-Order Dynamics in dq Frame 221
20.6 Generator Side Model 222
20.7 Generator Side Control Law 223
20.7.1 Regulation of I Sd 224
20.7.2 Regulation of I Sq 224
20.7.3 Alignment of dq Frame 224
20.7.4 Conversion of V Sd , V Sq Back to Time Domain 225
20.8 The Link Capacitor Model 225
20.8.1 Current into the Capacitor 225
20.8.2 Dynamics of the Capacitor 225
20.9 Regulation of the Capacitor Voltage 226
20.10 Model for the Grid Side Transformer 226
20.11 The Grid Side Control Law 226
20.11.1 Regulation of I Cq 227
20.11.2 Regulation of I cd 227
20.12 Complete Electrical System Control Law 227
20.13 Testing the Electrical Control Laws 229
20.13.1 Generator Side 229
20.13.2 Grid Side 229
20.14 Experiments on the Complete System 229
20.14.1 Experiment: Testing the Impact of Wind Direction 230
20.14.2 Experiment: Testing the Impact of Wind Speed 231
20.15 Revision Questions 231
Further Reading 233
21 Laboratory 10: Cross-Directional Control in Paper Machines: PID Control 235
21.1 Introduction 235
21.2 Web-Forming Process 235
21.3 Basis Weight Control in a Paper Machine 237
21.4 Process Model 237
21.4.1 Experiment: Measuring the Cross-Directional Profile 241
21.4.2 Experiment: Measuring the Machine Direction Dynamics 241
21.5 Simple SISO Design Ignoring Coupling 241
21.5.1 Experiment: Testing Simple PID Controllers 242
21.6 Simple SISO Design Accounting for Coupling 242
21.6.1 Experiment: Testing a Decoupled PID Structure 243
21.7 Summary 243
21.8 Revision Questions 244
Further Reading 244
Part VI Multivariable Control Systems (More General Methods) 247
22 State Variable Feedback 249
22.1 Introduction 249
22.2 Sampled-Data Control 249
22.2.1 Pole Assignment 249
22.2.2 Linear Quadratic Regulator (LQR) 249
22.3 Dynamic Programming 250
22.4 Infinite Horizon Linear Quadratic Optimal Problem 251
22.5 Delta-Domain Result 251
22.6 Continuous-Time Linear Quadratic Regulator 252
22.6.1 Pole Assignment 252
22.6.2 Continuous-Time Linear Quadratic Regulator 252
22.7 Regulation to a Fixed Set-Point 253
22.8 Frequency Domain Insights into the Linear Quadratic Regulator 254
22.9 Output Feedback 255
22.9.1 A State Estimator (or Observer) 255
22.9.2 Certainty Equivalence 255
22.10 Separation 256
22.11 Achieving Integral Action 256
22.11.1 The Problem 256
22.11.2 The Remedy 256
22.11.3 Properties 257
22.12 All Stabilising Control Laws Revisited 258
22.12.1 Stable Open-Loop Plants 259
22.12.2 Adding Stable Uncontrollable Disturbance States 259
22.12.3 Adding Non-stabilisable Disturbance States 260
22.13 Model Predictive Control 260
22.14 Revision Questions 260
Further Reading 261
23 The Kalman Filter 263
23.1 Introduction 263
23.2 Periodic Disturbances 263
23.2.1 Continuous-Time Model 263
23.2.2 Sampled-Data Process Noise 264
23.2.3 Sampled-Data Measurement Noise 265
23.2.4 The Full Sampled-Data Model 265
23.3 The Best Observer Gain 266
23.4 Steady-State Optimal Estimator 267
23.5 Treating Non-White Noise 268
23.6 Dealing with Constant Disturbances 268
23.7 Periodic Disturbances 268
23.8 Accounting for Delays 269
23.9 Multiple Output Measurements 269
23.10 Continuous-Time Kalman Filter 270
23.11 Linking Continuous Kalman Filter and Discrete Kalman Filter 270
23.12 The Linear Quadratic Regulator Revisited 271
23.13 Quantifying the Performance 271
23.14 Revision Questions 272
Further Reading 274
24 Laboratory 11: Rolling Mill Revisited (Periodic Disturbances) 275
24.1 Introduction 275
24.2 Disturbances 275
24.3 Effects of Roll Eccentricity 276
24.3.1 Experiment: Measuring the Impact of Roll Eccentricity 277
24.4 Tight Feedback Control 277
24.4.1 Experiment: Testing the Impact of Eccentricity on the BISRA Gauge 278
24.4.2 Analysis of the Effect of Control Law Bandwidth 278
24.5 Eccentricity Compensation 278
24.5.1 A Simple Eccentricity Predictor 278
24.6 Optimal Observer Design 279
24.6.1 Experiment: Testing the Eccentricity Estimator 280
24.7 Eccentricity Compensation Using the Kalman Filtering 281
24.7.1 Experiment: Testing the Kalman Filter for Eccentricity Estimation 281
24.8 Conclusion 282
24.9 Revision Questions 282
Further Reading 283
Part VII Introduction to the Modelling and Control of Nonlinear Systems 285
25 Modelling and Analysis of Simple Nonlinear Systems 287
25.1 Introduction 287
25.2 Errors Arising from Large Actuator Movement 287
25.3 Nonlinear Correction by Gain Change 288
25.4 Nonlinear Correction by Cascade Control 288
25.5 Saturation 289
25.5.1 Achieving Integral Action via Feedback 289
25.5.2 Introducing Anti-Windup in Control Laws Implemented via the Youla-Kucera Parameterisation 290
25.5.3 Anti-Windup When an Observer is Used 290
25.6 Extension to Rate Limitations 291
25.7 Minimal Actuator Movement 291
25.8 Describing Function Analysis 291
25.9 Predicting the Period and Amplitude of Oscillations 293
25.10 Revision Questions 293
Further Reading 294
26 Laboratory 12: Continuous Casting Machine (Nonlinear Considerations) 297
26.1 Introduction 297
26.2 The Slide Gate Valve 297
26.3 Investigation of Effect of Nonlinear Valve Geometry 298
26.3.1 Experiment: Testing Impact of the Nonlinear Geometry of the Valve 299
26.3.2 Other Nonlinear Phenomena 300
26.4 An Explanation for the Observed Oscillations 300
26.5 A Redesign to Account for Slip-Stick Friction 302
26.5.1 Experiment: Testing the Impact of Slip-Stick Friction 302
26.6 Revision Questions 303
Further Reading 303
27 Laboratory 13: Cross-Directional Control (Robustness and Impact of Actuator Saturation) 305
27.1 Introduction 305
27.2 Effect of Actuator Saturation Without Anti-Windup Protection 305
27.2.1 Experiment: Impact of Actuator Saturation 305
27.2.2 Experiment: Impact of Actuator Saturation with Decoupled PID Design 306
27.3 PI Decoupled Design with Simple Anti-Windup Protection 306
27.3.1 Experiment: Testing the Simple Anti-Windup Scheme 307
27.4 Conditioning Problems 308
27.4.1 Experiment: Testing Actuator Profile 310
27.5 PI Decoupled Design with Anti-Windup Protection Limited to Low Spatial Frequencies 310
27.5.1 Experiment: Limiting Spatial Frequencies Used in the Controller 310
27.6 PI Decoupled Design with Adaptive Spatial Frequency Selection 311
27.6.1 Experiment: Testing Adaptive Spatial Frequency Selection 312
27.7 Conclusions 312
27.8 Revision Questions 312
Further Reading 312
Part VIII Modelling and Control of More Complex Nonlinear Systems 315
28 Modelling of a Rocket in Three-Dimensional Flight 317
28.1 Introduction 317
28.2 Preliminaries 317
28.2.1 Coordinate Systems 317
28.2.2 Euler Angles in Three Dimensions 318
28.2.3 Time Derivative of Rotation Matrices 320
28.2.4 Angular Velocities 321
28.2.5 Angular Acceleration 321
28.2.6 Cross-Products 323
28.3 Translational Dynamics 323
28.3.1 Forces 323
28.3.2 Model for Translational Dynamics 324
28.4 Rotational Dynamics 324
28.4.1 Torque 324
28.4.2 Model for Rotational Dynamics 325
28.5 Stable or Unstable Rocket 325
28.6 Revision Questions 326
Further Reading 326
29 Modelling of a Steam-Generating Boiler 327
29.1 Introduction 327
29.2 Physical Principles 328
29.2.1 Internal Energy and Enthalpy 328
29.2.2 Ideal Gases 328
29.2.3 Steam 328
29.3 Physical Principles Used in Boiler Modelling 329
29.4 Mass Balances 329
29.5 Constant Volume of Drum, Risers and Downcomers 331
29.5.1 Consequence of Constant Volume of the Drum 332
29.5.2 Consequence of Constant Volume of the Risers 332
29.6 Energy Balances 333
29.6.1 Consequence of Drum Energy Balance 334
29.6.2 Consequences of Energy Balance in the Risers 335
29.7 A Model for Boiler Pressure 335
29.8 A Model for Drum Water Level 336
29.9 Spatial Discretisation and Homogeneous Mixing in the Risers 337
29.9.1 Spatial Discretisation 338
29.9.2 Homogeneous Mixing in a Section of the Risers 339
29.10 Water Flow in the Downcomers 340
29.11 Superheaters 341
29.12 Steam Receiver 341
29.12.1 Mass Balance 342
29.12.2 Energy Balance 342
29.12.3 Constant Volume of the Steam Receiver 342
29.12.4 Summary of the Model for the Steam Receiver 343
29.13 Other Model Components 343
29.13.1 Mass Flow out of Drum 343
29.13.2 Feedwater Mass Flow 344
29.13.3 Total Heat 344
29.13.4 Disturbances 344
29.13.5 A Preliminary Simulation 344
29.14 Revision Questions 344
Further Reading 346
30 Laboratory 14: Control of a Steam Boiler 347
30.1 Introduction 347
30.2 Extracting an Approximate Linear Model 347
30.2.1 Introduction 347
30.2.2 Sine Wave Testing in Closed-Loop (Scalar Case) 348
30.2.3 Application to the Boiler Model 349
30.2.4 The Steam Receiver 350
30.3 The Control Architecture 351
30.4 Regulating Steam Flow from the Boiler 351
30.5 Boiler Pressure Controller 351
30.6 Drum Water Level Controller 352
30.6.1 Experiment: Implementing Drum Water Level Control Law 352
30.7 Steam Receiver Controller 353
30.7.1 Experiment: Testing Steam Receiver Control Law 353
30.8 Experiments 353
30.8.1 Set Up 353
30.8.2 Small Load Change 354
30.8.3 Faster Outer Loop 354
30.8.4 Slower Outer Loop 354
30.8.5 Large Decrease in Load 355
30.8.6 Constraints 355
30.8.7 Large Load Change with ‘Fast’ Outer Loop 355
30.8.8 Large Increase in Load 355
30.9 Summary 355
30.10 Revision Questions 355
Further Reading 356
Index 357
