Control in System Dynamics

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.

• Preface xiBook Structure and Content xviiChapter 1. The Control Loop: Characterization and Behavior in Open Loop and Closed Loop 11.1. Introduction 11.2. Definition and terminology 21.3. The plant 21.4. Functional representation of the control loop 51.5. Open-loop transmittance 91.6. Closed-loop transmittances 191.7. Input sensitivity 231.8. Behavior and frequency performances in tracking and regulation 341.9. Dynamics in tracking and regulation 401.10. Charts in tracking and regulation 42Chapter 2. The Control Loop: Stability and Stability Degree, Precision, Dynamic Performances and Controller Synthesis 512.1. Introduction 512.2. Stability 522.3. Stability margins 582.4. Stability degree. 692.5. Precision 732.6. Stability degree-precision dilemma 772.7. Dynamics 802.8. Time dynamic performances 802.9. Frequency dynamic performances 812.10. Determination of dynamics 812.11. Study consideration for the controller synthesis 832.12. Controller phase at frequency 842.13. Type of controller 852.14. Example of a practical task: detailed study of the single phase-lead controller 90Chapter 3. An Overview of Linearizing Approaches 953.1. Introduction 953.2. Linearization by immersion 963.3. Linearization by high gain 1023.4. Linearization by disturbance rejection 1053.5. Linearization of the plant around a nominal trajectory: tangent linearized 1073.6. Additional discussion provided by Brigitte d'Andréa-Novel 116Chapter 4. High-Gain, Feedforward, Internal-Model, Quadratic-Criterion and Predictive Controls: From Principle to Control Loop 1194.1. Introduction 1194.2. High-gain control 1224.3. Feedforward control 1274.4. Internal-model control 1314.5. Quadratic-criterion control 1414.6. Predictive control 153Chapter 5. On the Three Generations of CRONE Control 1755.1. Introduction 1755.2. From the porous dyke to first- and second-generation CRONE control 1775.3. Second-generation CRONE control and uncertainty domains 1855.4. Generalization of the vertical template through the third-generation CRONE control 1895.5. An appendix on the frequency response describing the generalized template 203Solved Problems 205Presentation of Problem 1: Elementary Synthesis of a PID Regulator Based on the Single Phase-Lead Controller 207Presentation of Problem 2: Improvement of the Elementary Synthesis of a PID Regulator by Reducing Transitional Frequency Dispersion 219Presentation of Problem 3: Synthesis of a PID Regulator Based on Three Phase-Lead Controller Structures: Comparison and Choice of the Best Structure 229Presentation of Problem 4: Linearizing Control of a Motor Shaft: Linearization by Immersion 241Presentation of Problem 5: Linearizing Control of a Motor Shaft: Linearization by Disturbance Rejection 255Presentation of Problem 6: High-Gain Control: Characterization in Tracking and Regulation 265Presentation of Problem 7: Feedforward Control: Characterization in Tracking and Regulation by a Direct Approach and by an Indirect Approach via a Reference Prefilter 275Presentation of Problem 8: Synthesis of an Internal-Model Control Using a PID Controller of the Equivalent Elementary Control Loop 283Presentation of Problem 9: Quadratic-Criterion Control 295Presentation 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 305Presentation of Problem 11: Synthesis of a Constant Phase-Lead CRONE Controller with Successively Symmetrical and Asymmetrical Frequency Placement 319Presentation of Problem 12: Synthesis of a Constant Phase-Lag CRONE Controller and Synthesis Parameters of the Third-Generation CRONE Control 331Presentation of Problem 13: Synthesis of a Variable-Phase CRONE Controller for the Synthesis of a Narrow-Band (Vertical and Generalized) Template 347Appendices 365Appendix 1: From Regulation Function to Active Noise Control 367Appendix 2: Closed-Loop Behavior and Dynamic Performance of Second-Generation CRONE Control 375Appendix 3: Iso-overshoot Contours and Isodamping Contours 389References 409Index 413