Application of fractional order calculus to control theory

Abstract

The principal goal of this paper is to introduce the fundamentals of the Fractional Order Calculus (FOC), outline its possible application to the field of analysis and synthesis of control systems, and present several existing Matlab toolboxes related to FOC. The basic theoretical concepts of FOC are followed by methodologies for potential fractional order systems description and their stability investigation. Furthermore, the paper offers brief overview of the fractional order controllers which can be found in the scientific literature and highlights the benefits of the fractional approach in comparison with the classical integer one. On top of that, the Matlab toolboxes, useful for the practical design and analyses connected with fractional order control, are also discussed in the paper.