Model-Based Stabilization of a Fermentation Process Using Output Feedback with Discrete Time Delay

  • Milen K. BorisovEmail author
  • Neli S. Dimitrova
  • Mikhail I. Krastanov
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11189)


The present study is devoted to the stabilization of a bioreactor model, describing an anaerobic fermentation process for biological degradation of organic wastes with methane production. The stabilization is realized by means of a feedback control law related to the model output and involving a discrete time delay. We determine a nontrivial equilibrium point of the closed-loop system and investigate its asymptotic stability as well as the appearance of bifurcations with respect to the delay parameter. We establish the existence of an attracting and invariant region around the equilibrium such that all trajectories enter this region in finite time for some values of the delay and remain there. An iterative numerical extremum seeking algorithm is applied to the closed-loop system aimed to maximize the methane flow rate in real time. Simulation results are presented to illustrate the theoretical studies.



The work of the first and the second author has been partially supported by the Bulgarian Academy of Sciences, the Program for Support of Young Scientists and Scholars, grant No. DFNP-17-25/25.07.2017. The work of the third author has been partially supported by the Sofia University “St. Kl. Ohridski” under contract No. 80-10-133/25.04.2018.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  • Milen K. Borisov
    • 1
    Email author
  • Neli S. Dimitrova
    • 1
  • Mikhail I. Krastanov
    • 1
    • 2
  1. 1.Institute of Mathematics and InformaticsBulgarian Academy of SciencesSofiaBulgaria
  2. 2.Faculty of Mathematics and InformaticsSofia UniversitySofiaBulgaria

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