Control theory: a guided tour

Front Matter......Page 1
Introduction to the Second Edition......Page 4
Z......Page 5
Table of Contents......Page 0
Table of Contents......Page 8
12.7.2 Physically based models for prediction......Page 13
15.2.2 A \'Fourier type\' approach, in which an arbitrary function f on an interval [0, 1] is approximated by a summation of functions fi......Page 14
Z......Page 10
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D......Page 18
G......Page 19
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1.2 What is Control Theory? - An Initial Discussion......Page 22
1.3 What is Automatic Control?......Page 25
1.4 Some Examples of Control Systems......Page 27
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2.3 Requirements for an Automatic Control System......Page 30
2.5 Diagrams Illustrating and Amplifying Some of the Concepts Described so Far and Showing Relationships to a Software Engineering Context......Page 32
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3.2 What Sorts of Control Laws are There?......Page 39
3.3 How Feedback Control Works - A Practical View......Page 40
3.4 General Conditions for the Success of Feedback Control Strategies......Page 45
3.5 Alternatives to Feedback Control......Page 46
Z......Page 47
4A Convergence of the Integral that Defines the Laplace Transform......Page 48
4.3 Use of the Laplace Transform in Control Theory......Page 49
4.5 System Simplification Through Block Manipulation......Page 50
4.6 How a Transfer Function Can be Obtained from a Differential Equation......Page 51
4.8 Understanding System Behaviour from a Knowledge of Pole and Zero Locations in the Complex Plane......Page 52
4.9 Pole Placement: Cynthesis of a Controller to Place the Closed Lloop Poles in Desirable Positions......Page 56
4.10 Moving the Poles of a Closed Loop System to Desirable Locations - The Root Locus Technique......Page 57
4.11 Obtaining the Transfer Function of a Process from Either a Frequency Response Curve or a Transient Response Curve......Page 58
4C Convolution - what It Is......Page 59
4D Calculation of resonant frequencies from the pole-zero diagram......Page 61
4E Derivation of a Formula for Damped Natural Frequency......Page 63
4F The Root Locus of a System with Open-Loop Poles and Zeros Located as in Figure 4.19 Will Include a Circle Centred on the Zero......Page 64
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5.4 The Bode Diagram......Page 66
5.5 Frequency Response and Stability: an Important Idea......Page 67
5.6 Simple Example of the Use of the Foregoing Idea in Feedback Loop Design......Page 68
5.8 General Idea of Control Design Using Frequency Response Methods......Page 69
5.10 Design Based on Knowledge of the Response of a System to a Unit Step Input......Page 70
5.11 How Frequency Response is Obtained by Calculation from a Differential Equation......Page 71
5.12 Frequency Response Testing can Give a Good Estimate of a System\'s Transfer Function......Page 73
5.13 Frequency Response of a Second Order System......Page 74
5B Some Interesting and Useful Ideas that were Originated by Bode......Page 76
5.14 Nyquist Diagram and Nichols Chart......Page 78
Z......Page 79
6.3 Modelling a System that Exists, Based on Data Obtained byExperimentation......Page 80
6.5 Methods/Approaches/Techniques for Parameter Estimation......Page 82
6.6 Why Modelling is Difficult - An Important Discussion......Page 84
6.9 Regression Analysis......Page 85
6A Doubt and Certainty......Page 86
6B Anticipatory Systems......Page 88
6C Chaos......Page 89
6D Mathematical Modelling - Some Philosophical Comments......Page 91
6E A Still Relevant Illustration of the Difficulty of Mathematical Modelling: The Long March Towards Developing a Quantitative Understanding of the Humble Water Wheel, 1590-1841......Page 94
6G Experimentation on Plants to Assist in Model Development - the Tests that you Need may Not be in the Textbook!......Page 97
Z......Page 100
7A Stability Theory - A Long Term Thread that Binds......Page 101
7.2 Stability for Control Systems - How it is Quantified......Page 103
7.4 Stability Margin......Page 105
7.5 Stability Tests for Non-Linear Systems......Page 106
7.6 Local and Global Stability......Page 107
7.7 Lyapunov\'s Second (Direct) Method for Stability Determination......Page 108
7C Geometric Interpretation of Lyapunov\'s Second Method......Page 109
7.8 What Sets the Limits on the Control Performance?......Page 111
7.9 How Robust Against Changes in the Process is a Moderately Ambitious Control Loop?......Page 113
7.11 Systems that are Difficult to Control: Unstable Systems......Page 115
7D Cancellation of an Unstable Pole by a Matching Zero in the Controller......Page 116
7E Shifting an Unstable Pole by Feedback......Page 117
7.12 Systems that are Difficult to Control - Non-Minimum Phase Systems......Page 118
7.13.1 Sensitivity Functions and their Interrelation......Page 119
7F Motivation for the Name: Non-Minimum Phase Systems......Page 120
7.13.2 Integral Constraints in the Time Domain......Page 121
7.13.3 Design Constraints Caused by Bode\'s Theorem......Page 122
7G Mapping of Complex Functions - A Few Points that Underlie Classical Control Theory......Page 123
7I Singularities of a Complex Function G(s)......Page 125
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8.2.2 Illustration of the Value of an Integral Term in Removing any Constant Error......Page 129
8.2.4 How Can the Three Coefficients of a Three-term Controller be Chosen Quickly in Practice?......Page 130
8A How to Learn Something from the First Part of a Step Response......Page 136
8B New York to San Francisco telephony - An Early Illustration of the Spectacular Success of Feedback in Achieving High-Fidelity Amplifications of Signals......Page 138
8.3 Converting a User\'s Requirements into a Control Specification......Page 139
8.4.1 Methodologies and Illustrations......Page 140
8.5 References on Methodologies for Economic Justification of Investment in Automation......Page 146
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9.2.2 Comments......Page 148
9.3 Linearisation About a Nominal Trajectory: Illustration......Page 149
9.4 The Derivative as Best Linear Approximation......Page 150
9A The Inverse Function Theorem......Page 151
9B The Concept of Transversality......Page 152
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10.2 State Space Representations......Page 154
10.4 Time Solution of the State Space Equation......Page 155
10.5 Discrete and Continuous Time Models: A Unified Approach......Page 157
10B Generation of a Control Sequence......Page 158
10C Conservation of Dimension Under Linear Transformations......Page 159
Z......Page 161
11A  A Simple and Informative Laboratory Experiment......Page 162
11.2 Discrete Time Algorithms......Page 163
11.3 Approaches to Algorithm Design......Page 164
11B A Clever Manipulation - How the Digital to Analogue Convertor (Zero Order Hold) is Transferred for Calculation Purposes to Become Part of the Process to be Controlled......Page 165
11C Takahashi \'s Algorithm......Page 167
11.4 Overview: Concluding Comments, Guidelines for Algorithm choice and Some Comments on Procedure......Page 168
11E Discretisation......Page 169
11F A Simple Matter of Quadratic Behaviour......Page 170
11G Continuous is not the Limit of Discrete as T → 0......Page 172
11I Stability is Normally Considered to be a Property of a System so that for any Bounded Input a Stable System ShouId produce a Bounded Output......Page 173
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12.3 The Kalman Filter- More Detail......Page 176
12.4 Obtaining the Optimal Gain Matrix......Page 178
12.6 Discussion of Points Arising......Page 179
12.7 Planning, Forecasting and Prediction......Page 180
12.8 Predictive Control......Page 182
Z......Page 183
13.2 Approaches to the Analysis of Non-Linear Systems......Page 185
13.3 The Describing Function Method for Analysis of Control Loops Containing Non-Linearities......Page 186
13.4 Linear Second-Order Systems in the State Plane......Page 188
13.5 Non-Linear Second-Order Systems in the State Plane......Page 190
13.7 Process Non-Linearity - Small Signal Problems......Page 192
Z......Page 194
14.2.1 Discussion......Page 200
14.3 Time-Optimal Control......Page 201
14A Time-Optimal Control - a Geometric View......Page 203
14B The following Geometric Argument can Form a Basis for the Development of Algorithms or for the Proof of the Pontryagin Maximum Principle......Page 206
14C Construction of Time-Optimal Controls......Page 207
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15.2.1 The representation of a spatial region as the summation of elemental regions......Page 210
15.2.2 A \'Fourier type\' approach, in which an arbitrary function f on an interval [0, 1 ] is approximated by a summation of functions fi......Page 211
15A When Can the Behaviour in a Region be well Approximated at a Point?......Page 212
15B Oscillating and Osculating Approximation of Curves......Page 213
Z......Page 214
16.3.1 Guaranteed Stability of a Feedback Loop......Page 217
16.3.2 Robust Stability of a Closed Loop......Page 218
16.4.1 Setting the Scene......Page 219
16.4.2 Robust Stability......Page 220
16.4.3 Disturbance Rejection......Page 221
16.5 Specification of the ΔG Envelope......Page 223
16.6.1 Singular Values and Eigenvalues......Page 224
16.6.2 Eigenvalues of a Rectangular Matrix A......Page 225
16.6.4 Relations Between Frequency and Time Domains......Page 226
16.7.1 Introduction......Page 227
16.7.3 More About the Two Metrics δν and bG,D......Page 228
16.7.4 The Insight Provided by the v Gap Metric......Page 230
16.7.6 A Discussion on the two Metrics δν and bG,D......Page 231
16.8 Adaptivity Versus Robustness......Page 232
16A A Hierarchy of Spaces......Page 233
16.9 References on Hp Spaces and on H∞ Control......Page 235
Z......Page 237
17.2.1 Motivation......Page 238
17.2.3 Simple Properties of a Neuron Demonstrated in the two Dimensional Real Plane......Page 239
17.2.4 Multilayer Networks......Page 241
17.2.5 Neural Network Training......Page 242
17.2.6 Neural Network  Architectures to Represent Dynamic Processes......Page 243
17.2.7 Using Neural Net Based Self-Organising Maps for Data-Reduction and Clustering......Page 245
17.2.9 Neural Nets - Summary......Page 246
17.3.1 Introduction and Motivation......Page 247
17.3.2 Some Characteristics of Fuzzy Logic......Page 249
17.4.1 Basic Ideas......Page 250
17.4.2 Artificial Genetic Algorithms......Page 251
17.4.3 Genetic Algorithms as Design Tools......Page 252
17.4.4 GA Summary......Page 253
17.5.1 Basic Ideas......Page 254
17.5.3 Structural Characteristics of an Abstract Learning System......Page 255
17.6.1 The Properties that an Intelligent System Ought to Possess......Page 256
17A The Idea of a Probing Controller......Page 258
Z......Page 260
18.2 The Emergence of AI Techniques......Page 263
18.5 How Intelligent are AI (Artificial Intelligence) Methods?......Page 264
18.6 What is Intelligent Control?......Page 265
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19.4 Older Mainstream Control Books......Page 267
19.8 Optimisation......Page 268
19.11 Neural Networks and support Vector Methods......Page 269
19.15 Adaptive and Model-Based Control......Page 270
19.18 General Mathematics References......Page 271
19.20 Differential Topology/Differential Geometry/Differential Algebra......Page 272
19.22 Operator Theory and Functional Analysis Applied to Linear Control......Page 273
19.23 Books of Historical Interest......Page 274
19.26 Alphabetical List of References and Suggestions for Further Reading......Page 275
C......Page 295
D......Page 296
G......Page 297
I......Page 298
M......Page 299
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T......Page 302
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