Table of Contents
Preface v
Acknowledgments vii
1 Imperfect Uncertain Systems 1
1.1 Introduction 1
1.2 Examples 3
1.2.1 Friction in a sliding wheel 3
1.2.2 Nonidealities in electronic devices 4
1.2.3 Oscillations in a single transistor circuit 6
1.2.4 Chaotic behavior of operational amplifiers 7
1.2.5 Chaotic actuation of a microrobot 8
1.3 Understanding Imperfect Uncertain Systems 9
1.3.1 Stochastic vs. deterministic systems 10
1.3.2 Imperfections and uncertainties 10
1.4 Main Ideas to Control Imperfect Uncertain Systems 12
1.5 Case Studies 14
2 Modeling and Control Strategy 17
2.1 General Remarks 17
2.2 Mathematical Model of an Imperfect Uncertain System 18
2.3 Vibrational Control 19
2.3.1 Classical vibrational control 19
2.3.2 Closed-loop vibrational control 21
2.3.3 General remarks on vibrational control 22
2.4 A Control Strategy for Uncertain Imperfect Systems 22
2.4.1 Vibrational control signals: periodic and chaotic actuation 23
2.5 Mathematical Model of Large-scale Imperfect Uncertain Systems 24
3 Overview of the Electromechanical Structures 25
3.1 Model of the Coil 25
3.1.1 Constructive details of the single coil-magnet system 25
3.1.2 Mathematical model of the single rotating coil 28
3.1.3 Sensors equipments for coil model validation 29
3.2 Mechanical Supports 35
3.2.1 General description 35
3.2.2 Construction details of the rectangular and circular structures 37
4 Large-scale Electromechanical Systems with Passive and Active Vibrations 41
4.1 Modeling the Rectangular Structure 42
4.1.1 Simulation of the start-up phase 42
4.1.2 Simulation of the control phase (regularization) 43
4.2 Modeling the Circular Structure 43
4.2.1 Simulation of the start-up phase 44
4.2.2 Simulation of the control phase (regularization) 44
5 Equipments and a Gallery of Experiments 49
5.1 Overview of the Experimental Setup 49
5.1.1 Measurement systems 50
5.1.2 Generation of the control signals 52
5.1.3 Actuation systems 55
5.2 Working Principle and Genesis of Horizontal and Vertical Vibrations 59
5.3 Experiments on the Rectangular Structure 63
5.3.1 Mechanical behavior 65
5.3.2 Start-up phase and angular speeds characterization 65
5.3.3 Regularizing the angular speeds: weak vibrational control 69
5.4 Experiments on the Circular Structure 77
5.4.1 Mechanical behavior 77
5.4.2 Start-up phase and angular speeds characterization 78
5.4.3 Regularizing the angular speeds: weak vibrational control 79
6 Active Imperfect Systems to Realize Chaotic Mechanical Oscillators 99
6.1 A New Electromechanical Oscillator 99
6.1.1 The electro-mechanical setup 100
6.1.2 Mathematical model of the oscillator 101
6.1.3 Experimental results 104
6.2 A Driven Chaotic Rotating Coil 105
6.2.1 Driving a single coil-magnet system 106
6.2.2 Mathematical model of the driven chaotic rotating coil and experimental results 106
7 Conclusions 115
8 Epilogue 117
8.1 A Route to Engineering Studies 117
8.2 Towards an Electromechanical Spiking Neuron 120
Appendix A Appendix 123
A.1 Microcontroller Code 123
Bibliography 129
Index 133
