Fractional calculus has been studied for over three centuries, and it has multifarious
applications in science and engineering. This review investigates its progress since the first …

Fractional-order proportional integral derivative (FOPID) controllers are becoming
increasingly popular for various industrial applications due to the advantages they can offer …

A new lemma for the Caputo fractional derivatives, when 0< α< 1, is proposed in this paper.
This result has proved to be useful in order to apply the fractional-order extension of …

This paper presents two new lemmas related to the Caputo fractional derivatives, when α∈
0, 1, for the case of general quadratic forms and for the case where the trace of the product …

The interest in fractional-order (FO) control can be traced back to the late nineteenth century.
The growing tendency towards using fractional-order proportional-integral-derivative …

Electricity generation from renewable sources is on the rise. The irregular presence of these
sources increases the frequency variations induced by the load variance. The penetration of …

Considering the superior control characteristics and increased tuning flexibility of the
Fractional-Order Proportional Integral Derivative (FOPID) controller than the conventional …

This paper presents a hybrid metaheuristic method for optimal tuning of four different types
of proportional-integral-derivative (PID) controller for an automatic voltage regulator (AVR) …

Induction motor (IM) drives, specifically the three-phase IMs, are a nonlinear system that are
difficult to explain theoretically because of their sudden changes in load or speed conditions …

Abstract Design of an effective and efficient fractional order PID (FOPID) controller, as a
generalization of a standard PID controller based on fractional order calculus, for an …