Control theory

Front Matter......Page 1
Introduction to the Second Edition......Page 4
Z......Page 5
Index......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
Z......Page 17
1.2 What is Control Theory? - An Initial Discussion......Page 19
1.3 What is Automatic Control?......Page 22
1.4 Some Examples of Control Systems......Page 24
Z......Page 26
2.3 Requirements for an Automatic Control System......Page 27
2.5 Diagrams Illustrating and Amplifying Some of the Concepts Described so Far and Showing Relationships to a Software Engineering Context......Page 29
Z......Page 34
3.2 What Sorts of Control Laws are There?......Page 36
3.3 How Feedback Control Works - A Practical View......Page 37
3.4 General Conditions for the Success of Feedback Control Strategies......Page 42
3.5 Alternatives to Feedback Control......Page 43
Z......Page 44
4A Convergence of the Integral that Defines the Laplace Transform......Page 45
4.3 Use of the Laplace Transform in Control Theory......Page 46
4.5 System Simplification Through Block Manipulation......Page 47
4.6 How a Transfer Function Can be Obtained from a Differential Equation......Page 48
4.8 Understanding System Behaviour from a Knowledge of Pole and Zero Locations in the Complex Plane......Page 49
4.9 Pole Placement: Cynthesis of a Controller to Place the Closed Lloop Poles in Desirable Positions......Page 53
4.10 Moving the Poles of a Closed Loop System to Desirable Locations - The Root Locus Technique......Page 54
4.11 Obtaining the Transfer Function of a Process from Either a Frequency Response Curve or a Transient Response Curve......Page 55
4C Convolution - what It Is......Page 56
4D Calculation of resonant frequencies from the pole-zero diagram......Page 58
4E Derivation of a Formula for Damped Natural Frequency......Page 60
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 61
Z......Page 62
5.4 The Bode Diagram......Page 63
5.5 Frequency Response and Stability: an Important Idea......Page 64
5.6 Simple Example of the Use of the Foregoing Idea in Feedback Loop Design......Page 65
5.8 General Idea of Control Design Using Frequency Response Methods......Page 66
5.10 Design Based on Knowledge of the Response of a System to a Unit Step Input......Page 67
5.11 How Frequency Response is Obtained by Calculation from a Differential Equation......Page 68
5.12 Frequency Response Testing can Give a Good Estimate of a System's Transfer Function......Page 70
5.13 Frequency Response of a Second Order System......Page 71
5B Some Interesting and Useful Ideas that were Originated by Bode......Page 73
5.14 Nyquist Diagram and Nichols Chart......Page 75
Z......Page 76
6.3 Modelling a System that Exists, Based on Data Obtained byExperimentation......Page 77
6.5 Methods/Approaches/Techniques for Parameter Estimation......Page 79
6.6 Why Modelling is Difficult - An Important Discussion......Page 81
6.9 Regression Analysis......Page 82
6A Doubt and Certainty......Page 83
6B Anticipatory Systems......Page 85
6C Chaos......Page 86
6D Mathematical Modelling - Some Philosophical Comments......Page 88
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 91
6G Experimentation on Plants to Assist in Model Development - the Tests that you Need may Not be in the Textbook!......Page 94
Z......Page 97
7A Stability Theory - A Long Term Thread that Binds......Page 98
7.2 Stability for Control Systems - How it is Quantified......Page 100
7.4 Stability Margin......Page 102
7.5 Stability Tests for Non-Linear Systems......Page 103
7.6 Local and Global Stability......Page 104
7.7 Lyapunov's Second (Direct) Method for Stability Determination......Page 105
7C Geometric Interpretation of Lyapunov's Second Method......Page 106
7.8 What Sets the Limits on the Control Performance?......Page 108
7.9 How Robust Against Changes in the Process is a Moderately Ambitious Control Loop?......Page 110
7.11 Systems that are Difficult to Control: Unstable Systems......Page 112
7D Cancellation of an Unstable Pole by a Matching Zero in the Controller......Page 113
7E Shifting an Unstable Pole by Feedback......Page 114
7.12 Systems that are Difficult to Control - Non-Minimum Phase Systems......Page 115
7.13.1 Sensitivity Functions and their Interrelation......Page 116
7F Motivation for the Name: Non-Minimum Phase Systems......Page 117
7.13.2 Integral Constraints in the Time Domain......Page 118
7.13.3 Design Constraints Caused by Bode's Theorem......Page 119
7G Mapping of Complex Functions - A Few Points that Underlie Classical Control Theory......Page 120
7I Singularities of a Complex Function G(s)......Page 122
Z......Page 124
8.2.2 Illustration of the Value of an Integral Term in Removing any Constant Error......Page 126
8.2.4 How Can the Three Coefficients of a Three-term Controller be Chosen Quickly in Practice?......Page 127
8A How to Learn Something from the First Part of a Step Response......Page 133
8B New York to San Francisco telephony - An Early Illustration of the Spectacular Success of Feedback in Achieving High-Fidelity Amplifications of Signals......Page 135
8.3 Converting a User's Requirements into a Control Specification......Page 136
8.4.1 Methodologies and Illustrations......Page 137
8.5 References on Methodologies for Economic Justification of Investment in Automation......Page 143
Z......Page 144
9.2.2 Comments......Page 145
9.3 Linearisation About a Nominal Trajectory: Illustration......Page 146
9.4 The Derivative as Best Linear Approximation......Page 147
9A The Inverse Function Theorem......Page 148
9B The Concept of Transversality......Page 149
Z......Page 150
10.2 State Space Representations......Page 151
10.4 Time Solution of the State Space Equation......Page 152
10.5 Discrete and Continuous Time Models: A Unified Approach......Page 154
10B Generation of a Control Sequence......Page 155
10C Conservation of Dimension Under Linear Transformations......Page 156
Z......Page 158
11A A Simple and Informative Laboratory Experiment......Page 159
11.2 Discrete Time Algorithms......Page 160
11.3 Approaches to Algorithm Design......Page 161
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 162
11C Takahashi 's Algorithm......Page 164
11.4 Overview: Concluding Comments, Guidelines for Algorithm choice and Some Comments on Procedure......Page 165
11E Discretisation......Page 166
11F A Simple Matter of Quadratic Behaviour......Page 167
11G Continuous is not the Limit of Discrete as T → 0......Page 169
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 170
Z......Page 172
12.3 The Kalman Filter- More Detail......Page 173
12.4 Obtaining the Optimal Gain Matrix......Page 175
12.6 Discussion of Points Arising......Page 176
12.7 Planning, Forecasting and Prediction......Page 177
12.8 Predictive Control......Page 179
Z......Page 180
13.2 Approaches to the Analysis of Non-Linear Systems......Page 182
13.3 The Describing Function Method for Analysis of Control Loops Containing Non-Linearities......Page 183
13.4 Linear Second-Order Systems in the State Plane......Page 185
13.5 Non-Linear Second-Order Systems in the State Plane......Page 187
13.7 Process Non-Linearity - Small Signal Problems......Page 189
Z......Page 191
14.2.1 Discussion......Page 197
14.3 Time-Optimal Control......Page 198
14A Time-Optimal Control - a Geometric View......Page 200
14B The following Geometric Argument can Form a Basis for the Development of Algorithms or for the Proof of the Pontryagin Maximum Principle......Page 203
14C Construction of Time-Optimal Controls......Page 204
Z......Page 206
15.2.1 The representation of a spatial region as the summation of elemental regions......Page 207
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 208
15A When Can the Behaviour in a Region be well Approximated at a Point?......Page 209
15B Oscillating and Osculating Approximation of Curves......Page 210
Z......Page 211
16.3.1 Guaranteed Stability of a Feedback Loop......Page 214
16.3.2 Robust Stability of a Closed Loop......Page 215
16.4.1 Setting the Scene......Page 216
16.4.2 Robust Stability......Page 217
16.4.3 Disturbance Rejection......Page 218
16.5 Specification of the ΔG Envelope......Page 220
16.6.1 Singular Values and Eigenvalues......Page 221
16.6.2 Eigenvalues of a Rectangular Matrix A......Page 222
16.6.4 Relations Between Frequency and Time Domains......Page 223
16.7.1 Introduction......Page 224
16.7.3 More About the Two Metrics δν and bG,D......Page 225
16.7.4 The Insight Provided by the v Gap Metric......Page 227
16.7.6 A Discussion on the two Metrics δν and bG,D......Page 228
16.8 Adaptivity Versus Robustness......Page 229
16A A Hierarchy of Spaces......Page 230
16.9 References on Hp Spaces and on H∞ Control......Page 232
Z......Page 234
17.2.1 Motivation......Page 235
17.2.3 Simple Properties of a Neuron Demonstrated in the two Dimensional Real Plane......Page 236
17.2.4 Multilayer Networks......Page 238
17.2.5 Neural Network Training......Page 239
17.2.6 Neural Network Architectures to Represent Dynamic Processes......Page 240
17.2.7 Using Neural Net Based Self-Organising Maps for Data-Reduction and Clustering......Page 242
17.2.9 Neural Nets - Summary......Page 243
17.3.1 Introduction and Motivation......Page 244
17.3.2 Some Characteristics of Fuzzy Logic......Page 246
17.4.1 Basic Ideas......Page 247
17.4.2 Artificial Genetic Algorithms......Page 248
17.4.3 Genetic Algorithms as Design Tools......Page 249
17.4.4 GA Summary......Page 250
17.5.1 Basic Ideas......Page 251
17.5.3 Structural Characteristics of an Abstract Learning System......Page 252
17.6.1 The Properties that an Intelligent System Ought to Possess......Page 253
17A The Idea of a Probing Controller......Page 255
Z......Page 257
18.2 The Emergence of AI Techniques......Page 260
18.5 How Intelligent are AI (Artificial Intelligence) Methods?......Page 261
18.6 What is Intelligent Control?......Page 262
Z......Page 263
19.4 Older Mainstream Control Books......Page 264
19.8 Optimisation......Page 265
19.11 Neural Networks and support Vector Methods......Page 266
19.15 Adaptive and Model-Based Control......Page 267
19.18 General Mathematics References......Page 268
19.20 Differential Topology/Differential Geometry/Differential Algebra......Page 269
19.22 Operator Theory and Functional Analysis Applied to Linear Control......Page 270
19.23 Books of Historical Interest......Page 271
19.26 Alphabetical List of References and Suggestions for Further Reading......Page 272
C......Page 292
D......Page 293
G......Page 294
I......Page 295
M......Page 296
P......Page 297
S......Page 298
T......Page 299
Z......Page 300
Z......Page 301
D......Page 302
G......Page 303