家禽离体胃肠道pH控制系统的数学模型

D. Donskoy, A. Lukyanov, V. Filipović, T. B. Asten
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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. 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引用次数: 0

摘要

介绍。酸和碱化学反应的本质非线性决定了酸化或碱化模式中的控制算法,即周期性地添加最小体积的酸或碱。这种管制可能是无效的,具体来说,它允许控制物质的浓度不足或过高。本文讨论了微型生物反应器中氢指数的精确调节问题。建议使用酸度控制系统的数字模型来选择充值溶液的浓度,确定调节方法,并提高准确性。这项工作的目的是保证在一个静态类型的胃肠道的体外微型模型pH调节所需的准确性。材料与方法。模型的初始框图包括累加器和流。它是描述体积和酸度变化的主要微分方程的基础。为了根据温度校正所得溶液的酸度读数,利用最小二乘法对实验数据进行多项式近似,建立了一个静态模型。在Matlab Simulink应用程序包中对数学模型的结构要素进行了研究。为了验证数学模型的充分性,在一个真实的家禽人工胃肠道体外模型系统上测定了其瞬态特性。在这项工作的框架内,作者创建并分析了考虑外部控制作用的生物反应器中pH变化的非线性数学模型。将反应器中盐酸溶液、碱溶液和废液的流动表示为描述反应器中液体积累的微分方程的元素。为了提高计算精度,考虑了氢指数的温度依赖性,对溶液进行了修正。提出了一种基于碱、酸通道调节器的加药数学模型。所获得的数据使生成生物反应器中pH调节过程的组合模型成为可能。该方案的充分性得到了实证验证。以结构图的形式给出了pH调节剂模型、反应器内内容物体积调节模型和化学反应模型。对数学模型和实际控制系统的暂态进行了比较。结果表明,数学模型与实际系统的暂态特性在调节时间上是一致的。实际系统调节的相对误差为0.35%,数学模型的相对误差为- 0.1%,对应的调节精度为±0.1 ph。用图形表示了所研究的流动对中和反应的影响。讨论和结论。所提出的数学模型将提供调节酸度的最佳方法和算法的选择,这将加速调节氢指数非线性过程的调节器的创建。在未来,这些发展可以集成到家禽整个人工胃肠道的综合数字模型中,以优化控制算法(给药、混合、周期等),以及对体内物体的近似。
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Mathematical Model of the pH Control System in an In Vitro Model of the Gastrointestinal Tract of Poultry
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.
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