IDEAS home Printed from https://ideas.repec.org/a/wsi/fracta/v30y2022i10ns0218348x22402435.html
   My bibliography  Save this article

Computational Model Of A Fractional-Order Chemical Reactor System And Its Control Using Adaptive Sliding Mode Control

Author

Listed:
  • ALI ALLAHEM

    (Department of Mathematics, College of Science, Qassim University, Saudi Arabia)

  • ANITHA KARTHIKEYAN

    (Department of Electronics and Communications Engineering, University Centre for Research & Development, Chandigarh University, Mohali 140413, Punjab, India)

  • MANISEKARAN VARADHARAJAN

    (Department of Metallurgical and Materials Engineering, Defence University, Bishoftu, Ethiopia)

  • KARTHIKEYAN RAJAGOPAL

    (Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India)

Abstract

Dynamics of chemical reactor systems are found with highly nonlinear behavior. Computational modeling of a fractional-order chemical reactor system and investigating nonlinear dynamical changes and its control are the main focus of this research work. Chaos theory is a blooming fertile field in recent years, which is used widely to quantify nonlinear behaviors such as quasi-oscillations, bi-stability and bifurcation. The work starts from deriving state-space model of the system with first-order differential equations. There are six equilibrium points and the Jacobian matrix is derived for investigating the stability of the equilibrium points. Eigenvalues of each equilibrium point are calculated. Based on the sign of the real part of the eigenvalues and the existence of imaginary part, we found two equilibrium points behave as saddle spirals and the remaining four equilibrium points are saddle nodes. The stability of the system for different parameter values is investigated and presented. The influence of parameters in the system dynamics is discussed and significant parameter values are highlighted for further study. We considered Caputo’s definition for formulating the fractional-order (FO) model of the system based on the advantages highlighted in various literatures. The stable and unstable regions are portrayed with parameter variations. The results clarified that the analysis can be refined using fractional-order treatment of chaotic systems. We proceeded with our investigation towards obtaining different oscillations, particularly chaotic oscillations. The challenges lie in finding the proper fractional order to handle the system. We showed the bifurcation diagram for a range of fractional-order values and clarified the transitions from periodic oscillations to chaotic behavior and period-doubling bifurcations. The phase portraits are presented to show the limit cycle oscillations for fractional-order 0.95, period-doubling during 0.98, and chaotic oscillations for higher values. We proceeded with our investigation with fractional-order as 0.99. Bifurcation plots for parameter variation are obtained. Chaotic regions, periodic oscillations, period-halving and period-doubling are observed and the influences are discussed. We emphasize the intricate properties which are not addressed during the integer-order treatment of the system and nail the importance of fractional-order treatment. An adaptive sliding mode (ASM) controller is derived and implemented to control the system precisely. The effectiveness is shown by providing simulation results of the system with parameter estimation and controlled state time history plots. The work can be extended to verify the simulated results with equivalent electronic circuits.

Suggested Citation

  • Ali Allahem & Anitha Karthikeyan & Manisekaran Varadharajan & Karthikeyan Rajagopal, 2022. "Computational Model Of A Fractional-Order Chemical Reactor System And Its Control Using Adaptive Sliding Mode Control," FRACTALS (fractals), World Scientific Publishing Co. Pte. Ltd., vol. 30(10), pages 1-11, December.
  • Handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402435
    DOI: 10.1142/S0218348X22402435
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0218348X22402435
    Download Restriction: Access to full text is restricted to subscribers

    File URL: https://libkey.io/10.1142/S0218348X22402435?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Andrade, Dana I. & Specchia, Stefania & Fuziki, Maria E.K. & Oliveira, Jessica R.P. & Tusset, Angelo M. & Lenzi, Giane G., 2024. "Dynamic analysis and SDRE control applied in a mutating autocatalyst with chaotic behavior," Chaos, Solitons & Fractals, Elsevier, vol. 183(C).

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:fracta:v:30:y:2022:i:10:n:s0218348x22402435. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: https://www.worldscientific.com/worldscinet/fractals .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.