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.
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
Adrian Medioli is the automation engineer for Whiteley Corp. Pty. Ltd. After graduating, he spent 11 years as a senior automation engineer before completing his PhD. in Electrical Engineering in 2008 at the University of Newcastle, Australia. From 2008-2021 he was employed as a research academic for Complex Dynamic Systems and Control at the University of Newcastle. Graham Goodwin is Emeritus Laureate Professor, University of Newcastle, Australia. He is a Fellow of the Royal Society, a Foreign Member of the Royal Swedish Academy of Sciences and in 2021 he was awarded the American Control Council John Ragazzini Education Award.
