[ Log In | Register]
! Skip Navigation Links
Skip Navigation Links
Image of Journal of Applied Nonlinear Dynamics
ISSN:2164-6457 (print)
ISSN:2164-6473 (online)
Journal of Applied Nonlinear Dynamics
Miguel A. F. Sanjuan (editor), Albert C.J. Luo (editor)
Miguel A. F. Sanjuan (editor)

Department of Physics, Universidad Rey Juan Carlos, 28933 Mostoles, Madrid, Spain

Email: miguel.sanjuan@urjc.es

Albert C.J. Luo (editor)

Department of Mechanical and Industrial Engineering, Southern Illinois University Ed-wardsville, IL 62026-1805, USA

Fax: +1 618 650 2555 Email: aluo@siue.edu

A Method for Minimizing the Control Calculation Time of Fractional Systems

Journal of Applied Nonlinear Dynamics 9(1) (2020) 153--164 | DOI:10.5890/JAND.2020.03.012

Khaled Hcheichi, Faouzi Bouani

University Tunis EL Manar - National Engineering School of Tunis - Analysis, Conception and Control of Systems Laboratory, University Tunis EL Manar, 1068 Tunis, Tunisia

Download Full Text PDF

 

Abstract

This article deals with the non-commensurate fractional systems represented by a state-space model. It presents the advantages and disadvantages of using this type of model. It focuses on the disadvantages of fractional systems, especially the increase of computing time due to the accumulation of history. A method is proposed to minimize the calculation time, it consists in limiting the use of history of the state variables to a reduced number and taking into account the uncertainty of model in the predictive control. This method will be compared to the classical method in term of performance and calculation time.

References

  1. [1]  Monje, C.A., Chen, Y., Vinagre, B.M., Xue, D., and Feliu-Batlle, V. (2010), Fractional-order Systems and Controls: Fundamentals and Applications, Springer-Verlag: London.
  2. [2]  Oustaloup, A., Sabatier, J., Lanusse, P., Malti, R., Melchior, P., Moreau, X., and Moze, M. (2008), An overview of the CRONE approach in system analysis, modeling and identification, observation and control, IFAC Proceedings Volumes: 17th IFAC World Congress, 41(2), 14254-14265.
  3. [3]  Sun, H., Zhang, Y., Baleanu, D., Chen, W., and Chen, Y.Q. (2018), A new collection of real world applications of fractional calculus in science and engineering, Communications in Nonlinear Science and Numerical Simulation, 64, 213-231.
  4. [4]  Tenreiro-Machado, J.A., Silva, M.F., Barbosa, R.S., Jesus, I.S., Reis, C.M., Marcos, M.G., and Galhano, A.F. (2010), Some applications of fractional calculus in engineering, Mathematical Problems in Engineering, 34 pages.
  5. [5]  Ouhsaine, L., Boukal, Y., El-Ganaoui, M., Darouach, M., Zasadzinski, M., Mimet, A., and Radhy, N.E. (2017), A General fractional-order heat transfer model for Photovoltaic/Thermal hybrid systems and its observer design, Energy Procedia, 139, 49-54.
  6. [6]  Blasiak, S. (2016), Time-fractional heat transfer equations in modeling of the non-contacting face seals, International Journal of Heat and Mass Transfer, 100, 79-88.
  7. [7]  Belkhatir, Z. and Laleg-Kirati, T.M. (2017), High-order sliding mode observer for fractional commensurate linear systems with unknown input, Automatica, 82, 209-217.
  8. [8]  Martìnez-Guerra, R., Cruz-Ancona, C.D., and Pérez-Pinacho, C.A. (2017), Estimators for a class of commensurate fractional order systems with caputo derivative. In: 14th International Conference on Electrical Engineering, Computing Science and Automatic Control (CCE), Mexico City, Mexico, October 2017.
  9. [9]  Saxena, S., Yogesh, V., and Arya, P.P. (2016), Reduced-order modeling of commensurate fractional-order system. In: 14th International Conference on Control, Automation, Robotics and Vision (ICARCV), Porto, Portugal, Nov 2016, 1-6.
  10. [10]  Zou, Q., Jin, Q., and Zhang, R. (2016), Design of fractional order predictive functional control for fractional industrial processes, Chemometrics and Intelligent Laboratory Systems, 152, 34-41.
  11. [11]  Soorki, M.N. and Tavazoei, M.S. (2018), Adaptive robust control of fractional-order swarm systems in the presence of model uncertainties and external disturbances, IET Control Theory and Applications, 12(7), 961-969.
  12. [12]  Basiri, M.H. and Tavazoei, M.S. (2015), On robust control of fractional order plants: invariant phase margin, ASME. J. Comput. Nonlinear Dynam, 10(5).
  13. [13]  Belkhatir, Z. and Laleg-Kirati, T.M. (2018), Parameters and fractional differentiation orders estimation for linear continuous-time non-commensurate fractional order systems, Systems and Control Letters , 115, 26-33.
  14. [14]  Dzieliński, A. and Sierociuk, D. (2007), Ultracapacitor modelling and control using discrete fractional order state-space models and Fractional Kalman Filters, In: European Control Conference (ECC), Kos, Greece, July 2007, 2916-2922.
  15. [15]  Abedini, M., Nojoumian, M.A., Salarieh, H., and Meghdari, A. (2015), Model reference adaptive control in fractional order systems using discrete-time approximation methods, Communications in Nonlinear Science and Numerical Simulation, 25(1-3), 27-40.
  16. [16]  Dzieliński, A. and Sierociuk, D. (2011), Adaptive Feedback Control of Fractional Order Discrete State-Space Systems. In: International Conference on Computational Intelligence for Modelling, Control and Automation and International Conference on Intelligent Agents, Web Technologies and Internet Commerce (CIMCAIAWTIC’ 06, Vienna, Austria, December 2011, 1-6.
  17. [17]  Ostalczyki, P. and Mozyrska, D. (2016), The second form of the variable-, fractional-order discrete-time integrator. In: 21st International Conference on Methods and Models in Automation and Robotics (MMAR), Miedzyzdroje, Poland, August 2016, 859-864.
  18. [18]  Aboukheir, H. (2012), Predictive control of fractional order systems IFAC Proceedings Volumes, 45(13), 622-626.
  19. [19]  Joshi, M.M., Vyawahare, V.A., and Patil, M.D. (2014), Model predictive control for fractional-order system a modeling and approximation based analysis. In: International Conference on Simulation and Modeling Methodologies, Technologies and Applications (SIMULTECH), Vienna, Austria, August 2014, 361-372.
  20. [20]  Rawlings, J.B. (2000), Tutorial overview of model predictive control, IEEE Control Systems, 20(3), 38–52.
  21. [21]  Rhouma, A. and Bouani, F. (2014), Robust model predictive control of uncertain fractional systems: a thermal application, IET Control Theory Applications, 8(17), 1986-1994.
  22. [22]  Li, L. and Liao, F. (2018), Design of a robust H∞ preview controller for a class of uncertain discrete-time systems Transactions of the Institute of Measurement and Control, 40(8), 2639-2650.
  23. [23]  Bayrak, A., Gursoy, H., and Efe, M.O. (2017), A novel robust fuzzy control of an uncertain system, Transactions of the Institute of Measurement and Control, 39(3), 324-333.
  24. [24]  Sikora, B. and Klamka, J. (2017), Constrained controllability of fractional linear systems with delays in control, Systems and Control Letters, 106, 9-15.
  25. [25]  Rhouma, A., Bouani, F., Bouzouita, B., and Ksouri, M. (2014), Model Predictive Control of Fractional Order Systems, Journal of Computational and Nonlinear Dynamics, 9, 310111-310117.

Copyright © 2011-2023 L & H Scientific Publishing. All rights reserved. Wildcard SSL Certificates