On the Structure of the Space of States for a Thermal Model of Fluidized-Bed Reactor–Regenerator Units and Control Visualization Principles

  • A. G. NagievEmail author
  • G. A. Nagiev
  • N. A. Gulieva


A system of differential equations for the dynamics of thermal states in reactor–regenerator units with finely dispersed catalysts is proposed. Special attention is paid to the existence of positive feedback between thermal and chemical processes by two mutually connected channels, such as the temperature and the degree of residual cocking on a catalyst after regeneration. It has been shown that this system of model equations for the thermal dynamics of a reactor–regenerator unit is characterized by the multiplicity of steady states in the space of the mentioned variables. The three-dimensional phase patterns of the system are analyzed, and the bifurcations of steady-state solutions in the parametric region are studied. The problem of operative control based on state space structure visualization algorithms is considered.


fluidized-bed reactor–regenerator units hydrocarbon dehydrogenation processes three-dimensional phase portraits control on the basis of the qualitative theory of differential equations nonlinear dynamics man–machine systems control visualization 



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© Pleiades Publishing, Ltd. 2019

Authors and Affiliations

  1. 1.Sumqayit State UniversitySumqayitAzerbaijan
  2. 2.Institute of Mathematics and Mechanics, National Academy of Sciences of AzerbaijanBakuAzerbaijan

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