The FraCAL Research Group

Welcome to Fractional Calculus Applications (FraCAL@USP) Group!

This group is working on applied fractional calculus theory for identification and control. As recent studies show that FraCal is being applied to build new mathematical models and presented outstanding results to counter a classical calculus. The latest trends on this subject can offer novel and practical solutions in multidisciplinary areas such as computer science, control engineering, electronics engineering, electrical engineering, chemical engineering, and bioengineering research. Last few years, this group has published some remarkable solutions, in particular, new identification and modeling methods for linear and nonlinear processes, control structures for unstable and integrating systems such as quadrotor unmanned aerial vehicles, fractional filter designs, modeling Super-capacitors and batteries, and some efficient techniques to handle of fractional-order integrodifferential operators using operational matrices.

Currently, the group is working on Wireless Energy System and Fractional Neural Network.

Areas of Research and Topics

This multi-disciplinary group researches a broad range of topics including:

Modeling and Control of linear and nonlinear processes
Modeling Energy Storage devices
Fractional control on unstable and integrating plants such as coupled tank, quadrotor, or twin-rotor systems
Realization of fractional-order filters and controllers
Mechatronics Applications

Journals published from FraCAL Lab:

A novel approach of fractional-order time delay system modeling based on Haar wavelet
https://doi.org/10.1016/j.isatra.2018.07.019
Optimized fractional low and highpass filters of (1 + α) order on FPAA
https://doi.org/10.24425/bpasts.2020.133123
Parametric identification of nonlinear fractional Hammerstein models
https://doi.org/10.3390/fractalfract4010002

Generalized formulation to estimate the Supercapacitor’s R-C series impedance using fractional order model
https://doi.org/10.1016/j.aej.2021.04.018

Flexible Fractional Supercapacitor Model Analyzed in Time Domain.
https://doi.org/10.1109/ACCESS.2019.2938543
https://ieeexplore.ieee.org/ielx7/6287639/8600701/8821292/graphical_abstract/access-gavideo-2938543.mp4

Two degree of freedom fractional PI scheme for automatic voltage regulation
https://doi.org/10.1016/j.jestch.2021.08.003

Fractional-order two-input two-output process identification based on Haar operational matrix
https://doi.org/10.1080/00207721.2020.1857503

A single-step identification strategy for the coupled TITO process using fractional calculus
https://doi.org/10.1177/0142331221992732

Identification scheme for fractional Hammerstein models with the delayed Haar wavelet
https://doi.org/10.1109/JAS.2020.1003093

Modeling and parametric identification of Hammerstein systems with time delay and asymmetric dead-zones using fractional differential equations
https://doi.org/10.1016/j.ymssp.2021.108568

Fractional-order PI plus D controller for second-order integrating plants: Stabilization and tuning method
https://doi.org/10.1016/j.isatra.2021.12.012

Improved Performance in Quadrotor Trajectory Tracking Using MIMO PI^λ-D Control
https://doi.org/10.1109/ACCESS.2022.3214810

Fractional filter IMC-TDD controller design for integrating processes
https://doi.org/10.1016/j.rico.2022.100155

Fractional-Order Impedance Identification for Inductors
http://dx.doi.org/10.18576/pfda/080310

Fractional-order tilt integral derivative controller design using IMC scheme for unstable time-delay processes
https://doi.org/10.1007/s40313-023-01020-6

Novel Fractional-Order Proportional-Integral Controller for Hybrid Power System with Solar Grid and Reheated Thermal Generator
https://doi.org/10.3390/solar3020018

Improved control of integrating cascade processes with time delays using fractional-order internal model controller with the Smith predictor
https://doi.org/10.1177/09596518231168510

A comprehensive review of modified Internal Model Control (IMC) structures and their filters for unstable processes
https://doi.org/10.1016/j.arcontrol.2023.04.006

Modelling of an Optimized Polymer Electrolyte Membrane Fuel Cell (PEMFC) Using Fractional-Order
https://doi.org/10.1109/IC_ASET58101.2023.10151016

Tri-parametric Fractional-order Controller Design for Integrating Systems with Time Delay
https://doi.org/10.1109/TCSII.2023.3269819
Fractional internal-model-control filter-based controller tuning for series cascade unstable plants
https://doi.org/10.1007/s40435-023-01162-0
Fractional dual-tilt control scheme for integrating time delay processes: Studied on a two-tank level system
https://doi.org/10.1109/ACCESS.2024.3351183

A comprehensive review of wireless power transfer systems: Focused study with fractional-order elements
https://doi.org/10.1002/cta.3921

Enhancing neural network classification using fractional-order activation functions
https://doi.org/10.1016/j.aiopen.2023.12.003

Novel Approach to Modeling Incommensurate Fractional Order Systems Using Fractional Neural Networks
https://doi.org/10.3390/math1201008