Design of Fractional Calculus Free Controllers with Fractional Behaviors

Abstract

Faced with the complexity and drawbacks of fractional calculus highlighted in the literature, this paper proposes simple solutions to avoid its use in the field of feedback control and especially to define fractional PID- and CRONE-like controllers. It shows that it is possible to generate fractional behaviors, which are known since the work of Bode to be useful in the field of control, without invoking fractional calculus and fractional models. Fractional calculus based models and fractional behaviors are indeed two different concepts: one denotes a particular class of models and the other a class of dynamical behaviors that can be generated and modelled by a wide variety of mathematical tools other than fractional calculus. Solutions to tune the fractional PID- and Crone-like controllers defined in this paper are proposed.