Mathematical Model of the pH Control System in an In Vitro Model of the Gastrointestinal Tract of Poultry
Authors: Donskoy D. Yu. , Lukyanov A. D. , Filipović V. , Asten T. B. 
Published: April 2023

Introduction. Essential nonlinearity of the chemical reactions of acids and bases determines the control algorithms in the mode of acidification or alkalization, that is, periodic dosing of a minimum volume of acid or alkali. Such regulation may be ineffective, specifically, it allows insufficient or excessive concentration of the controlled substance. The article discusses the problem of precise regulation of the hydrogen index in mini-bioreactors. It is proposed to use a digital model of the acidity control system to select the concentrations of topped-up solutions, determine the regulation methodology, and improve accuracy. The objective of the work is the assurance of required accuracy of pH regulation in an in vitro mini-model of the gastrointestinal tract of a static type.Materials and Methods. The initial block diagram of the model included accumulators and flows. It was the base for the main differential equations characterizing the change in volume and acidity. To correct the acidity readings of the resulting solution by temperature, a static model based on the polynomial approximation of experimental data using the least squares method was created. The structural elements of the mathematical model were investigated in the Matlab Simulink application package. To validate the adequacy of the mathematical model, transient characteristics were determined on a real system of in vitro modeling of the artificial gastrointestinal tract of poultry.Results. Within the framework of this work, the authors created and analyzed a nonlinear mathematical model of pH changes in a bioreactor taking into account external control actions. The flows of hydrochloric acid solution, alkali solution and drain from the reactor were presented as elements of a differential equation describing the accumulation of liquid in the reactor. To improve the accuracy, the solution was modified taking into account the temperature dependence of the hydrogen index. A dosing mathematical model based on a regulator with alkali and acid channels was proposed. The data obtained made it possible to generate a combined model of the pH regulation process in the bioreactor. The adequacy of the solution was confirmed empirically. The models of pH regulator, regulation of the volume of contents in the reactor and chemical reactions were shown in the form of structural diagrams. The transients of a mathematical model and a real control system were compared. It was established that the transient characteristics of the mathematical model and the real system were identical in terms of regulation time. The relative error of regulation of the real system was 0.35 %, and the mathematical model — 0.1 %, which corresponded to the required accuracy of regulation ± 0.1 pH. The influence of the studied flows on the neutralization reaction was shown in the form of graphs.Discussion and Conclusions. The proposed mathematical model will provide selecting optimal methods and algorithms for regulating acidity, which will accelerate the creation of a regulator for the nonlinear process of regulating the hydrogen index. In the future, these developments can be integrated into a comprehensive digital model of the entire artificial gastrointestinal tract of poultry to optimize control algorithms (dosing, mixing, periodicity, etc.), as well as approximation to objects in vivo.