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

 Experimental setups