Numerical Simulation of Nonlocal Delayed Feedback Controller for Simple Bioreactors

Čiegis, Raimondas; Suboč, Olga; Čiegis, Remigijus

doi:10.15388/Informatica.2018.165

Informatica

Numerical Simulation of Nonlocal Delayed Feedback Controller for Simple Bioreactors

Volume 29, Issue 2 (2018), pp. 233–249

Raimondas Čiegis Olga Suboč Remigijus Čiegis

https://doi.org/10.15388/Informatica.2018.165

Pub. online: 1 January 2018 Type: Research Article

Open Access

Received
1 September 2017

Accepted
1 February 2018

Published
1 January 2018

Abstract

The new nonlocal delayed feedback controller is used to control the production of drugs in a simple bioreactor. This bioreactor is based on the enzymatic conversion of substrate into the required product. The dynamics of this device is described by a system of two nonstationary nonlinear diffusion-reaction equations. The control loop defines the changes of the substrate concentration delivered into the bioreactor at the external boundary of the bioreactor depending on the difference of measurements of the produced drug delivered into the body and the flux of the drug prescribed by a doctor in accordance with the therapeutic protocol. The system of PDEs is solved by using the finite difference method, the control loop parameters are defined from the analysis of stationary linearized equations. The stability of the algorithm for the inverse boundary condition is investigated. Results of computational experiments are presented and analysed.

References

Aster, R., Borchers, B., Thurber, C. (2012). Parameter Estimation and Inverse Problems. Elsevier.

Čiegis, R., Tumanova, N. (2010). Numerical solution of parabolic problems with nonlocal boundary conditions. Numerical Functional Analysis and Optimization, 31(12), 1318–1329.

Čiegis, R., Bugajev, A. (2012). Numerical approximation of one model of the bacterial self-organization. Nonlinear Analysis: Modelling and Control, 17(3), 253–270.

Hillen, T., Painter, K.J. (2009). A users guide to PDE models for chemotaxis. J. Math. Biol., 58(1–2), 183–217.

Hundsdorfer, W., Verwer, J.G. (2003). Numerical Solution of Time-Dependent Advection-Difusion-Reaction Equations. Springer Series in Computational Mathematics, Vol. 33. Springer, Berlin, Heidelberg, New York, Tokyo.

Ivanauskas, F., Laurinavičius, V., Sapagovas, M., Nečiporenko, A. (2017). Reaction-diffusion equation with nonlocal boundary condition subject to PID-controlled bioreactor. Nonlinear Analysis: Modelling and Control, 22(2), 261–272.

Kok Kiong, T., Wang, Q.-G., Hang, C.C. (1999). Advances in PID Control. Springer-Verlag, London, UK.

Leonavičienė, T., Bugajev, A., Jankevičiūtė, G., Čiegis, R. (2016). On stability analysis of finite difference schemes for generalized Kuramoto-Tsuzuki equation with nonlocal boundary conditions. Mathematical Modelling and Analysis, 21(5), 630–643.

Murray, J.D. (2002). Mathematical Biology I: An Introduction. Springer, Berlin.

Murray, J.D. (2003). Mathematical Biology II: Spatial Models and Biomedical Applications. Springer, Berlin.

Novičenko, V. (2015). Delayed feedback control of synchronization in weakly coupled oscillator networks. Physical Review E, 92, 022919.

Pyragas, K. (2006). Delayed feedback control of chaos. Philosophical Transactions of The Royal Society A, 364, 2309.

Tikhonov, A.N., Arsenin, V.Y. (1977). Solutions of Ill Posed Problems. V.H. Winston and Sons, New York.

Yordanova, S., Ichtev, A. (2017). A model-free neuro-fuzzy predictive controller for compensation of nonlinear plant inertia and time delay. Informatica, 28(4), 749–766.

Biographies

Čiegis Raimondas

Raimondas Čiegis has graduated from Vilnius University Faculty of Mathematics in 1982. He received the PhD degree from the Institute of Mathematics of Byelorussian Academy of Science in 1985 and the degree of habil. doctor of mathematics from the Institute of Mathematics and Informatics, Vilnius in 1993. He is a professor and the head of Mathematical Modeling department of Vilnius Gediminas Technical University. His research interests include numerical methods for solving nonlinear PDE, parallel numerical methods, mathematical modelling in nonlinear optics, porous media flows, technology, image processing, biotechnology.

Suboč Olga

os@vgtu.lt

O. Suboč has graduated from Vilnius University Faculty of Mathematics in 1998. She received the PhD degree from the Institute of Mathematics and Informatics and Vytautas Magnus University in 2002. She is an associated professor in Vilnius Gediminas Technical University. Her research interests include numerical methods for solving nonlinear PDE, mathematical modelling, technology, image processing, non-local conditions, biotechnology.

Čiegis Remigijus

Remigijus Čiegis has graduated from Kaunas Polytechnical Institute Faculty of Chemical Engineering in 1982 and Vilnius University Kaunas Faculty in 1989. He received the PhD degree in economics from the Vilnius University in 1995 and the degree of habil. doctor of management from the Kaunas Vytautas Magnus University in 2002. He is a professor of Vilnius University. His research interests include environmental economics, sustainable economic development, macroeconomics, regional economics.

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Keywords

nonlocal delayed feedback numerical simulation bioreactor

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