Diversity and Non-integer Differentiation for System Dynamics

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.

Table of Contents:

1. From Diversity to Unexpected Dynamic
Performance.
2. The Robustness of Damping.
3. Fractional Differentiation and its Memory.
4. CRONE Suspension Idea.
5. CRONE Control Idea

1. From Diversity to Unexpected Dynamic Performances.

2. Damping Robustness.

3. Non-Integer Differentiation, its Memory and its Synthesis.

4. On the CRONE Suspension.

5. On the CRONE Control.

6. Recursivity and Non-Integer Differentiation.

Appendix 1. Damping of a Usual Automotive Suspension.

Appendix 2. Relaxation of Water on a Porous Dyke.

Appendix 3. Systems with Explicit and Implicit Generalized Derivative.

Appendix 4. Generalized Differential Equation and Generalized Characteristic Equation.

Appendix 5. CRONE Control Response with Initial Conditions.

Appendix 6. Fractality and Non-integer Differentiation.

Alain Oustaloup is Professor in automatic control at the Institut Polytechnique de Bordeaux, Enseirb-Matmeca, France. His research works focus on non-integer differentiation and its applications in engineering sciences. In the 1980s, he developed a realistic synthesis method of non-integer differentiation. This method, which is at the origin of several applications of non-integer differentiation, has enabled him to invent both the CRONE control and the CRONE suspension.