Fractional Order Differentiation and Robust Control Design: CRONE, H-infinity and Motion Control

This book provides an overview of the research done and results obtained during the last ten years in the fields of fractional systems control, fractional PI and PID control, robust and CRONE control, and fractional path planning and path tracking. Coverage features theoretical results, applications and exercises.

The book will be useful for post-graduate students who are looking to learn more on fractional systems and control. In addition, it will also appeal to researchers from other fields interested in increasing their knowledge in this area.

This monograph collates the past decade’s work on fractional models and fractional systems in the fields of analysis, robust control and path tracking. Themes such as PID control, robust path tracking design and motion control methodologies involving fractional differentiation are amongst those explored. It juxtaposes recent theoretical results at the forefront in the field, and applications that can be used as exercises that will help the reader to assimilate the proposed methodologies.

The first part of the book deals with fractional derivative and fractional model definitions, as well as recent results for stability analysis, fractional model physical interpretation, controllability, and H-infinity norm computation. It also presents a critical point of view on model pseudo-state and “real state”, tackling the problem of fractional model initialization.

Readers will find coverage of PID, Fractional PID and robust control in the second part of the book, which rounds off with an extension of H-infinity control to fractional models. An exhaustive description of the three generations of CRONE is also provided, along with several useful academic examples, treated with the CRONE control Matlab toolbox, which illustrate the various control strategies.

Since prefilters are additional but often under-studied degrees of freedom to tune a control loop, the last part of this book presents three different approaches: fractional prefilter, input shaping and flatness principles that have been extended to fractional models. All these approaches are applied to experimental closed loop systems.