A Survey of Fractional Order Calculus Applications of Multiple-Input, Multiple-Output (MIMO) Process Control

Abstract

Multiple-input multiple-output (MIMO) systems are usually present in process systems engineering. Due to the interaction among the variables and loops in the MIMO system, designing efficient control systems for both servo and regulatory scenarios remains a challenging task. The literature reports the use of several techniques mainly based on classical approaches, such as the proportional-integral-derivative (PID) controller, for single-input single-output (SISO) systems control. Furthermore, control system design approaches based on derivatives and integrals of non-integer order, also known as fractional control or fractional order (FO) control, are frequently used for SISO systems control. A natural consequence, already reported in the literature, is the application of these techniques to MIMO systems to address some inherent issues. Therefore, this work discusses the state-of-the-art of fractional control applied to MIMO systems. It outlines different types of applications, fractional controllers, controller tuning rules, experimental validation, software, and appropriate loop decoupling techniques, leading to literature gaps and research opportunities. The span of publications explored in this survey ranged from the years 1997 to 2019.

Design of ℓ1 New Suboptimal Fractional Delays Controller for Discrete Non-Minimum Phase System under Unknown-but-Bounded Disturbance

“…Various modifications of fractionalorder controllers for controlling non-minimum phase systems was discussed in [43,44]. A comprehensive overview of fractional order control, fractional PID controllers, and fractional order calculus application for MIMO plants was described in [45][46][47][48] . The fundamental methods of fractional control were described in [49][50][51][52].…”

A Review of Recent Developments in Autotuning Methods for Fractional-Order Controllers

“…for frequencies ω ≥ ω T , with A a scalar. Further information regarding the tuning, implementation and related topics to fractional order PIDs can be found in some excellent review papers [15,16,[18][19][20][21][22][23][24]. The phase shaper [25] is among the first automatic controller designs that uses fractional calculus tools.…”

Evolution of fractional mathematical model for drinking under Atangana-Baleanu Caputo derivatives

“…For more advances in this direction the reader can see recent manuscripts like [44,45]. There are clearly advantages of ABC and CF formulations for some models (see for example see [46,47] ). But in the same time the standard fractional operators have also some advantages for various phenomena over the integer models and over some other fractional calculus operators (with or whiteout singular kernel).…”