In order to ensure a pedagogical presentation of the fundamentals, this book, which is based on 45 years of experience, endeavors to identify the main principles of the control scheme and its dynamics. The control loop is extensively developed because of the reference it constitutes in control. By establishing the control loop as equivalent to any other control or, more precisely, by making an elementary control loop appear, it becomes possible to reveal a part of this loop in other controls and, thanks to its regulator, qualitatively evaluate the control strategy. A comparative analysis then shows that the complexification of the control scheme does not necessarily go hand in hand with a better control strategy and therefore a better performance. Since robustness results from innovations in terms of performance desensitization, the CRONE control is presented, in view of the genuine domains of uncertainty taken into account and the small number of parameters to be optimized. The educational nature of this book is enhanced by numerous solved problems that develop examples of synthesis of different controls. Control in System Dynamics is intended for a very wide audience, including engineers, researchers, teachers and students hoping to expand their knowledge of control and dynamics in automatic control.

Table of Contents:
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