Controller design methodologies for fractional order system models

Abstract

Fractional order calculation deals with cases where the derivative and integral order is non-integer. Although the notion of fractional order was introduced at the end of the 17th century, this concept in engineering was employed after the first quarter of the 19th century. Its first application to control engineering areas was made after the second quarter of the 20th century. Since fractional calculus is a generalized version of integer order calculus, it provides great flexibility in system modeling and controller design. In other words, fractional calculus offers three different combinations in terms of the controller and system types: Fractional order control for integer order system, Fractional order control for fractional order system, and Integer order control for fractional order system. In this respect, fractional calculus is an excellent tool to describe a control system compared to integer order calculus. Besides the flexibility, the notion brings more complexity to system modeling and controller tuning. Therefore, many studies over the last half-century have been trying to overcome these difficulties. Numerous real-time systems have nonlinear characteristics and high-order system dynamics. In literature, simple integer-order models, i.e. the first and second order with or without time delay, are used to represent system dynamics.