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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 Appro