IEEE Access, vol.1, no.1, pp.1-27, 2021 (SCI-Expanded)
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 (FOPID)
control has been fueled mainly by the fact that these controllers have additional “tuning knobs” that
allow coherent adjustment of the dynamics of control systems. For instance, in certain cases, the capacity
for additional frequency response shaping gives rise to the generation of control laws that lead to superior
performance of control loops. These fractional-order control laws may allow fulfilling intricate control
performance requirements that are otherwise not in the span of conventional integer-order control systems.
However, there are underpinning points that are rarely addressed in the literature: (1) What are the
particular advantages (in concrete figures) of FOPID controllers versus conventional, integer-order (IO)
PID controllers in light of the complexities arising in the implementation of the former? (2) For real-time
implementation of FOPID controllers, approximations are used that are indeed equivalent to high-order
linear controllers. What, then, is the benefit of using FOPID controllers? Finally, (3) What advantages
are to be had from having a near-ideal fractional-order behavior in control practice? In the present paper,
we attempt to address these issues by reviewing a large portion of relevant publications in the fastgrowing FO control literature, outline the milestones and drawbacks, and present future perspectives
for industrialization of fractional-order control. Furthermore, we comment on FOPID controller tuning
methods from the perspective of seeking globally optimal tuning parameter sets and how this approach
can benefit designers of industrial FOPID control. We also review some CACSD (computer-aided control
system design) software toolboxes used for the design and implementation of FOPID controllers. Finally,
we draw conclusions and formulate suggestions for future research.