Jean-Claude Trigeassou - Böcker

This book introduces an original fractional calculus methodology (‘the infinite state approach’) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation.

This book introduces an original fractional calculus methodology (�the infinite state approach�) which is applied to the modeling of fractional order differential equations (FDEs) and systems (FDSs). Its modeling is based on the frequency distributed fractional integrator, while the resulting model corresponds to an integer order and infinite dimension state space representation. This original modeling allows the theoretical concepts of integer order systems to be generalized to fractional systems, with a particular emphasis on a convolution formulation. With this approach, fundamental issues such as system state interpretation and system initialization – long considered to be major theoretical pitfalls – have been solved easily. Although originally introduced for numerical simulation and identification of FDEs, this approach also provides original solutions to many problems such as the initial conditions of fractional derivatives, the uniqueness of FDS transients, formulation of analytical transients, fractional differentiation of functions, state observation and control, definition of fractional energy, and Lyapunov stability analysis of linear and nonlinear fractional order systems. This second volume focuses on the initialization, observation and control of the distributed state, followed by stability analysis of fractional differential systems.

Monitoring and diagnosis of electrical machine faults is a scientific and economic issue which is motivated by objectives for reliability and serviceability in electrical drives.This book provides a survey of the techniques used to detect the faults occurring in electrical drives: electrical, thermal and mechanical faults of the electrical machine, faults of the static converter and faults of the energy storage unit.Diagnosis of faults occurring in electrical drives is an essential part of a global monitoring system used to improve reliability and serviceability. This diagnosis is performed with a large variety of techniques: parameter estimation, state observation, Kalman filtering, spectral analysis, neural networks, fuzzy logic, artificial intelligence, etc. Particular emphasis in this book is put on the modeling of the electrical machine in faulty situations.Electrical Machines Diagnosis presents original results obtained mainly by French researchers in different domains. It will be useful as a guideline for the conception of more robust electrical machines and indeed for engineers who have to monitor and maintain electrical drives. As the monitoring and diagnosis of electrical machines is still an open domain, this book will also be very useful to researchers.

The authors then proceed to show how these tools can be used for the identification of continuous-time linear models, discrete-time linear models, continuous-time linear state-space models, linear parameter-varying models and multidimensional models based on partial differential equations.