Diversity and non-integer differentiation for system dynamics / / Alain Oustaloup ; series editor Bernard Dubuisson

• Record Nr.: UNINA9910132160703321
• Autore: Oustaloup Alain
• Pubbl/distr/stampa: London, [England] ; ; Hoboken, New Jersey : , : ISTE : , : Wiley, , 2014; ©2014
• ISBN: 1-118-76082-4; 1-118-76086-7; 1-118-76092-1
• Descrizione fisica: 1 online resource (383 p.)
• Collana: Control, Systems and Industrial Engineering Series
• Disciplina: 003.85
• Soggetti: Dynamics - Mathematical models; System analysis - Mathematical models
• Lingua di pubblicazione: Inglese
• Formato: Materiale a stampa
• Livello bibliografico: Monografia
• Note generali: Description based upon print version of record.
• Nota di bibliografia: Includes bibliographical references at the end of each chapters and index.
• Nota di contenuto: Cover; Title Page ; Copyright; Contents; Acknowledgments; Preface; Introduction; Chapter 1: From Diversity to Unexpected Dynamic Performances; 1.1. Introduction; 1.2. An issue raising a technological bottle-neck; 1.3. An aim liable to answer to the issue; 1.4. A strategy idea liable to reach the aim; 1.4.1. Why diversity?; 1.4.2. What does diversity imply?; 1.5. On the strategy itself; 1.5.1. The study object; 1.5.2. A pore: its model and its technological equivalent; 1.5.2.1. The model; 1.5.2.2. The technological equivalent; 1.5.3. Case of identical pores; 1.5.4. Case of different pores; 1.5.4.1. On differences coming from regional heritage1.5.4.1.1 Differences of technological origin; 1.5.4.1.2. A difference of natural origin; 1.5.4.1.3. How is difference expressed?; 1.5.4.2. Transposition to the study object; 1.6. From physics to mathematics; 1.6.1. An unusual model of the porous face; 1.6.1.1. A smoothing remarkable of simplicity: the one of crenels; 1.6.1.2. A non-integer derivative as a smoothing result; 1.6.1.3. An original heuristic verification of differentiation non-integer order; 1.6.2. A just as unusual model governing water relaxation; 1.7.2.1. Taking into account the past1.7.2.2. Memory notion; 1.7.2.3. A diversion through an aspect of human memory; 1.7.2.3.1. The serial position effect; 1.7.2.3.2. A model of the primacy effect; 1.8. On the nature of diversity; 1.8.1. An action level to be defined; 1.8.2. One or several forms of diversity?; 1.8.2.1. Forms based on the invariance of the elements; 1.8.2.2. A singular form based on the time variability of an element; 1.9. From the porous dyke to the CRONE suspension; 1.10. Conclusion; 1.11. Bibliography; Chapter 2: Damping Robustness; 2.1. Introduction; 2.2. From ladder network to a non-integer derivative as a water-dyke interface model2.2.1. On the admittance factorizing; 2.2.2. On the asymptotic diagrams at stake; 2.2.3. On the asymptotic diagram exploiting; 2.2.3.1. Step smoothing; 2.2.3.2. Crenel smoothing; 2.2.3.3. A non-integer differentiator as a smoothing result; 2.2.3.4. A non-integer derivative as a water-dyke interface model; 2.3. From a non-integer derivative to a non-integer differential equation as a model governing water relaxation; 2.3.1. Flow-pressure differential equation; 2.3.2. A non-integer differential equation as a model governing relaxation
• Sommario/riassunto: Based on a structured approach to diversity, notably inspired by various forms of diversity of natural origins, Diversity and Non-integer Derivation Applied to System Dynamics provides a study framework to the introduction of the non-integer derivative as a modeling tool. Modeling tools that highlight unsuspected dynamical performances (notably damping performances) in an ""integer"" approach of mechanics and automation are also included. Written to enable a two-tier reading, this is an essential resource for scientists, researchers, and industrial engineers interested in this subject area. Ta