Numerical Simulation of Nonlocal Delayed Feedback Controller for Simple Bioreactors

Article type: Research Article

Authors: Čiegis, Raimondas¹ | Suboč, Olga^{1; *} | Čiegis, Remigijus²

Affiliations: [1] Vilnius Gediminas Technical University, Saulėtekio al. 11, LT-10223 Vilnius, Lithuania. E-mail: os@vgtu.lt | [2] Vilnius University Kaunas Faculty, Muitinės St 8, LT-44280 Kaunas, Lithuania

Correspondence: [*] Corresponding author.

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.

Keywords: nonlocal delayed feedback, numerical simulation, bioreactor

Journal: Informatica, vol. 29, no. 2, pp. 233-249, 2018