The main objective of this book is to provide to mechanical scientists and engineers the kinetic modeling tools necessary for predicting the damage state of organic composite matrices submitted to hydrolytic and oxidative ageing. These tools are derived from the degradation mechanisms and their validity is successfully checked from many experimental data. They can be interfaced with existing or under development computer codes for predicting the lifetime of composite structures. Particular attention is paid to the relationships between damage state and use properties in view of defining structural end-of-life criteria.
For this purpose the book is divided into three main parts. The first one is devoted to the presentation of the common aspects to all types of chemical degradation processes. Emphasis is put on specific aspects of composite structures, such as the role of interphase/interface or the anisotropy of reagent diffusion, but also on current issues in the field of material ageing such as the study of multiphysics couplings. The second part is focused on humid ageing. Physical processes linked to plasticization and swelling, are distinguished from chemical processes in particular from the matrix hydrolysis and its resulting damages at the microstructural scale (osmotic cracking, blistering, etc.). The third part concerns thermal ageing. The ultimate objective is to predict the consequences of thermal oxidation on thermomechanical properties of organic composite matrices, in particular on their glass transition temperature and elastic and fracture properties. In each part, the kinetic approach is illustrated by several practical examples.
Preface xi
Book Structure and Content xvii
Chapter
1. The Control Loop: Characterization and Behavior in Open Loop and
Closed Loop 1
1.1. Introduction 1
1.2. Definition and terminology 2
1.3. The plant 2
1.4. Functional representation of the control loop 5
1.5. Open-loop transmittance 9
1.6. Closed-loop transmittances 19
1.7. Input sensitivity 23
1.8. Behavior and frequency performances in tracking and regulation 34
1.9. Dynamics in tracking and regulation 40
1.10. Charts in tracking and regulation 42
Chapter
2. The Control Loop: Stability and Stability Degree, Precision,
Dynamic Performances and Controller Synthesis 51
2.1. Introduction 51
2.2. Stability 52
2.3. Stability margins 58
2.4. Stability degree. 69
2.5. Precision 73
2.6. Stability degree-precision dilemma 77
2.7. Dynamics 80
2.8. Time dynamic performances 80
2.9. Frequency dynamic performances 81
2.10. Determination of dynamics 81
2.11. Study consideration for the controller synthesis 83
2.12. Controller phase at frequency 84
2.13. Type of controller 85
2.14. Example of a practical task: detailed study of the single phase-lead
controller 90
Chapter
3. An Overview of Linearizing Approaches 95
3.1. Introduction 95
3.2. Linearization by immersion 96
3.3. Linearization by high gain 102
3.4. Linearization by disturbance rejection 105
3.5. Linearization of the plant around a nominal trajectory: tangent
linearized 107
3.6. Additional discussion provided by Brigitte d'Andréa-Novel 116
Chapter
4. High-Gain, Feedforward, Internal-Model, Quadratic-Criterion and
Predictive Controls: From Principle to Control Loop 119
4.1. Introduction 119
4.2. High-gain control 122
4.3. Feedforward control 127
4.4. Internal-model control 131
4.5. Quadratic-criterion control 141
4.6. Predictive control 153
Chapter
5. On the Three Generations of CRONE Control 175
5.1. Introduction 175
5.2. From the porous dyke to first- and second-generation CRONE control 177
5.3. Second-generation CRONE control and uncertainty domains 185
5.4. Generalization of the vertical template through the third-generation
CRONE control 189
5.5. An appendix on the frequency response describing the generalized
template 203
Solved Problems 205
Presentation of Problem 1: Elementary Synthesis of a PID Regulator Based on
the Single Phase-Lead Controller 207
Presentation of Problem 2: Improvement of the Elementary Synthesis of a PID
Regulator by Reducing Transitional Frequency Dispersion 219
Presentation of Problem 3: Synthesis of a PID Regulator Based on Three
Phase-Lead Controller Structures: Comparison and Choice of the Best Structure
229
Presentation of Problem 4: Linearizing Control of a Motor Shaft:
Linearization by Immersion 241
Presentation of Problem 5: Linearizing Control of a Motor Shaft:
Linearization by Disturbance Rejection 255
Presentation of Problem 6: High-Gain Control: Characterization in Tracking
and Regulation 265
Presentation of Problem 7: Feedforward Control: Characterization in Tracking
and Regulation by a Direct Approach and by an Indirect Approach via a
Reference Prefilter 275
Presentation of Problem 8: Synthesis of an Internal-Model Control Using a
PID Controller of the Equivalent Elementary Control Loop 283
Presentation of Problem 9: Quadratic-Criterion Control 295
Presentation of Problem 10: Synthesis of a Constant Phase-Lead CRONE
Controller: The Essential Stage in the Synthesis of the Fractional PID Whose
(Integer) Integration at Low Frequency Simply Results from a Cascade
Proportional-Integral 305
Presentation of Problem 11: Synthesis of a Constant Phase-Lead CRONE
Controller with Successively Symmetrical and Asymmetrical Frequency Placement
319
Presentation of Problem 12: Synthesis of a Constant Phase-Lag CRONE
Controller and Synthesis Parameters of the Third-Generation CRONE Control
331
Presentation of Problem 13: Synthesis of a Variable-Phase CRONE Controller
for the Synthesis of a Narrow-Band (Vertical and Generalized) Template 347
Appendices 365
Appendix 1: From Regulation Function to Active Noise Control 367
Appendix 2: Closed-Loop Behavior and Dynamic Performance of
Second-Generation CRONE Control 375
Appendix 3: Iso-overshoot Contours and Isodamping Contours 389
References 409
Index 413
Alain Oustaloup is an engineer from the École Nationale Supérieure d'Électronique et de Radioélectricité de Bordeaux and is currently Emeritus Professor at the Polytechnic Institute of Bordeaux, France. He was the founder of the first automatic control team on non-integer systems, inventor of the CRONE control and the CRONE suspension and is the author or coauthor of a large number of publications and a dozen books, including seven monographs.
