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 result 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 vehicle, fractional filter designs, modeling Super-capacitors and batteries, and some efficient techniques to handle of fractional-order integro-differential operators using operational matrices.

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 quadrotor or twin-rotor systems
• Realization of fractional-order filters
• Mechatronics Applications

Selected research works from this group:

• 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
  

• Fractional filter IMC-TDD controller design for integrating processes https://doi.org/10.1016/j.rico.2022.100155
• Fractional-Order Impedance Identification for Inductors doi:10.18576/pfda/080310