| Title |
Mathematical modeling of bioreactor control / |
| Translation of Title |
Bioreaktoriaus valdymo matematinis modeliavimas. |
| Authors |
Nečiporenko, Anatolij |
| DOI |
10.15388/vu.thesis.195 |
| Full Text |
|
| Pages |
92 |
| Keywords [eng] |
mathematical modeling ; numerical methods ; bioreactor |
| Abstract [eng] |
The main research topic of this thesis is numerical methods for systems of nonlinear partial differential equations with nonlocal boundary conditions and nonlocal conditions. Systems of reaction-diffusion, convection-reaction-diffusion and convection-reaction equations are considered. This research presents a distinct application of nonlocal boundary conditions in process monitoring and control. Nonlocal conditions are defined as the PID (proportional-integral-derivative controller) control algorithm or a subset of its terms (PI, I). Mathematical modeling of bioreactor control has been applied in the fields of drug delivery and water denitrification. The distinct feature of the model is the nonlocal boundary condition that combines two different components of the solution containing a double integral in space and time. The stability of a difference scheme for a reaction-diffusion equation system was analyzed. Eigenvalue spectrum analysis for control and equation system parameters was carried out. Sufficient conditions for numerical algorithm difference scheme stability were obtained. |
| Dissertation Institution |
Vilniaus universitetas. |
| Type |
Doctoral thesis |
| Language |
English |
| Publication date |
2021 |
