https://recipp.ipp.pt/bitstream/10400.22/4149/4/ART_TenreiroMachado_2011_DEE.pdf

Recent history of fractional calculus

Tuning and auto-tuning of fractional order controllers for industry applications

Many real dynamic systems are better characterized using a non-integer order dynamic model based on fractional calculus or, differentiation or integration of non-integer order. Traditional calculus is based on integer order differentiation and integration. The concept of fractional calculus has tremendous potential to change the way we see, model, and control the nature around us. Denying fractional derivatives is like saying that zero, fractional, or irrational numbers do not exist. In this paper, we offer a tutorial on fractional calculus in controls. Basic definitions of fractional calculus, fractional order dynamic systems and controls are presented first. Then, fractional order PID controllers are introduced which may make fractional order controllers ubiquitous in industry. Additionally, several typical known fractional order controllers are introduced and commented. Numerical methods for simulating fractional order systems are given in detail so that a beginner can get started quickly. Discretization techniques for fractional order operators are introduced in some details too. Both digital and analog realization methods of fractional order operators are introduced. Finally, remarks on future research efforts in fractional order control are given.

/pdf/fractional-order-control-a-tutorial-4zjusf99pg.pdf

Fractional order control - A tutorial

A recent article published in this magazine has labeled fractional-order continuous-time systems as the "21st century systems". Indeed, this emerging research area is slowly gaining momentum among electrical engineers while its deeply rooted mathematical concepts also slowly migrate to various engineering disciplines. A very important aspect of research in fractional-order circuits and systems is that it is an interdisciplinary subject. Specifically, it is an area where biochemistry, medicine and electrical engineering over-lap giving rise to many new potential applications. This article aims to provide an overview of the current status of research in this area, highlighting specific problems which need to be addressed particularly by electrical engineers.

Fractional-order circuits and systems: An emerging interdisciplinary research area

Review of fractional PID controller

Solving an inverse heat conduction problem using a non-integer identified model

A new CAD tool, the CRONE Matlab toolbox, is presented for engineers and researchers in mathematics and engineering sciences, particularly for electrical and electronic engineering and automatic control. The originality, aims, form and use of the toolbox are presented. The three main modules are described: their content, principle, algorithms, and applications for identification and control. Examples of their use are given. The original theoretical mathematical concepts developed in our laboratory based on noninteger differentiation are used for the computation. CRONE control is a typical application. The toolbox is not only for researchers, including Ph.D students, but also for industrials whose growing interest in noninteger integration, and their readiness to invest in the development of its applications, are manifest. The paper is divided into four sections: aims and organization of the toolbox, "mathematical tools" module, "identification by noninteger model" module, and the "CRONE CSD" module. The final section discusses perspectives.

The CRONE toolbox for Matlab

Utilisation de modèles d'identification non entiers pour la résolution de problèmes inverses en conduction

This article deals with modeling and identification of fractional systems in the time domain. Fractional state-space representation is defined, and a stability condition for fractional systems given. A new identification method for fractional systems is then proposed. The method is based on the generalization to fractional orders of classical methods based on State Variable Filters (SVF). A particular case of fractional SVF, fractional Poisson filters, is studied. Parameter estimation is then performed, through the conventional least squares method, and then through the instrumental variable method which permits unbiased parameter estimation. Monte Carlo simulations are then performed, using various noise levels, to compare the identification performance of these two methods, and of a prediction error method based on a fractional ARX model.

Olivier Cois

Papers

Solving an inverse heat conduction problem using a non-integer identified model

The CRONE toolbox for Matlab

Utilisation de modèles d'identification non entiers pour la résolution de problèmes inverses en conduction

Fractional state variable filter for system identification by fractional model

Non Integer Model from Modal Decomposition for Time Domain System Identification