Methods and models in economy
A.N. Kirillov, A.M. Sazonov The modeling of the biological wastewater treatment process on the base of the Schumpeterian dynamics
Dynamical Systems
Applied aspects in informatics
Системный анализ в медицине
A.N. Kirillov, A.M. Sazonov The modeling of the biological wastewater treatment process on the base of the Schumpeterian dynamics
Abstract. 

In the paper the simple model of the biological wastewater sludges treatment system consisting of the aerotank with ideal displacement, the settler and return element developed on the base of the model of the Schumpeterian dynamics. The boundedness of the biomass concentration growth is modeled via the logistic differential equations. The global stability of the equilibrium of this dynamic system is proved, which allows for the prediction of the biological treatment system statement and for control of the system by changing of the return stream velocity.

Keywords: 

biological treatment, stability, stabilization, dynamic systems.

DOI: 10.14357/20790279200303

PP. 24-28.
 
References

1. Vavilin V.A. 1986. Vremya oborota biomassy i destrukciya organicheskogo veshchestva v sistemah biologicheskoj ochistki [Turnover time of the biomass and organic substance destruction in the biological treatment systems]. M.: Nauka. 144 p.
2. Vavilin V.A. 1983. Nelinejnye modeli biologicheskoj ochistki i processov samoochishcheniya v rekah [Nonlinear models of the biological wastewater treatment and the processes of the self-purification in rivers]. M.: Nauka. 185 p.
3. Kirillov A.N., Sazonov A.M., Bryksenkova N.K. 2019. Stabilizatsiya processa bioochistki s peremennym sostavom biomassy [Stabilization of the biological waste-water treatment process with variable biomass structure]. Trudy KarNC RAN [Transactions of KarRC RAS] 7:15-20. DOI: 10.17076/mat1065
4. Kirillov A.N., Sazonov A.M. 2019. Global schumpeterian dynamics with structural variations. Vestnik YUrGU. Ser. Matematicheskoe modelirovanie i programmirovanie [Bulletin SUSU Ser. Mathematical Modelling, Programming & Computer Software] 12(3):17-27. DOI: 10.14529/mmp190302
5. Polterovich V.M., Henkin G.M. 1988. Evolucionnaya model vzaimodeystviya processov sozdaniya i zaimstvovamiya tehnologij [Evolutionary model of the interaction of creating and borrowing technologies processes]. Ekonomika I matematicheskie metody [Economics and Mathematical Methods] 24:1071-1083.
6. Kirillov A.N. Dinamicheskoe modelirovanie i stabilizaciya processa biologicheskoj ochistki stochnyh vod [Dynamical modeling and process stabilization of the biological wastewater treatment]. Cellyuloza. Bumaga. Karton [Cellulose. Paper. Carton] 2008. 5:66.
7. Kirillov A.N. 2008. Nekotorye metody kusochno-postoyannoj stabilizacii nelinejnyh dinamicheskih sistem [Some methods of the piecewise constant stabilization of the nonlinear dynamical systems]. Materialy 5-j Nauchno-tehnicheskoj Konferencii “Mehatronika, avtomatizaciya, upravlenie” [Proceedings of the 5th scientific and technical conference “Mechatronics, automation, control”]. SPb. 5:70-71.
8. Kirillov A.N. 2006. Upravlenie mnogostadijnymi tekhnologicheskimi processami [The multistage technological processes control]. Vestnik SPbGU. Prikladnaya matematika. Informatika. Processy upravleniya [Vestnik SPbSU. Applied Mathematics. Computer Science. Control Processes] 4:127-131.
9. Henze M., Grady C.P.L.Jr., Gujer W., Marais G.v.R., Matsuo T. 1987. A general model for single-sludge activated sludge wastewater treatment systems. Water Research. 21:505-515.
10. Brune D. 1985. Optimal control of the complete-mix activated sludge process. Environmental Technology Letters. 6:467-476.
11. Pu T. 1993. Nonlinear Economic Dynamics. Springer-Verlag, Berlin. 222 p. DOI: 10.1007/978-3-642-97450-2
12. Zhang W.-B. 1991. Synergetic Economics: Time and Change in Nonlinear Economics. Springer-Verlag, Berlin. 246 p. DOI: 10.1007/978-3-642-75909-3
 
2024-74-3
2024-74-2
2024-74-1
2023-73-4

© ФИЦ ИУ РАН 2008-2018. Создание сайта "РосИнтернет технологии".