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Practical Control System Design. Real World Designs Implemented on Emulated Industrial Systems. Edition No. 1

  • Book

  • 384 Pages
  • February 2024
  • Region: Global
  • John Wiley and Sons Ltd
  • ID: 5839073
Practical Control System Design

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

Authors

Adrian Medioli University of Newcastle, Australia. Graham Goodwin University of Newcastle, Australia.