Passivity-Based Control of a Bioreactor System

This article deals with an example of advance control techniques applied to a biochemical system, the mathematical model and the constrains derived from the discrete implementation of a continuous control policy. The theory is developed on a simplified model of a bioreactor to be regulated and passivity-based control is used. The biological interpretation of the results derived from the mathematical model takes into account the time required for chemical processes in order to obtain cells and nutrients.     

改进计时电流法的数学模型和电路实现

当采用电化学计时电流法对样品进行检测时,由于检测系统的延迟,采集到的电化学信号会产生偏差,这种现象在多通道电化学信号快速采集时尤为明显.为克服该问题,我们提出一种新的电化学方法来快速产生电流峰值,通过测量峰值快速准确地测出被测物浓度.本文首先为该方法建立理论模型,推导出电流峰值与被测物的浓度关系;再引入经典控制理论中的控制环节来改进传统电化学电路以实现该方法,并加入峰值检测电路来准确获取电流峰值信号;最后,利用该方法研究K3[Fe(CN)6]和3,3′,5,5′-四甲基联苯胺(TMB)溶液的电化学反应,证明了本方法相比传统计时电流法具有更高的信噪比和灵敏度,电流峰值与浓度呈线性关系,并且检测结果不受采样时间延迟的影响,克服了计时电流法的不足.     

Comprehensive model of electromigrative transport in microfluidic paper based analytical devices

A complete mathematical model for electromigration in paper-based analytical devices is derived, based on differential equations describing the motion of fluids by pressure sources and EOF, the transport of charged chemical species, and the electric potential distribution. The porous medium created by the cellulose fibers is considered like a network of tortuous capillaries and represented by macroscopic parameters following an effective medium approach. The equations are obtained starting from their open-channel counterparts, applying scaling laws and, where necessary, including additional terms. With this approach, effective parameters are derived, describing diffusion, mobility, and conductivity for porous media. While the foundations of these phenomena can be found in previous reports, here, all the contributions are analyzed systematically and provided in a comprehensive way. Moreover, a novel electrophoretically driven dispersive transport mechanism in porous materials is proposed. Results of the numerical implementation of the mathematical model are compared with experimental data, showing good agreement and supporting the validity of the proposed model. Finally, the model succeeds in simulating a challenging case of free-flow electrophoresis in paper, involving capillary flow and electrophoretic transport developed in a 2D geometry.     

Quantitative EPMA of element depth distribution

A new model for the ionization depth distribution function has been proposed. Within the framework of this model full electron flux is considered to be divided into two fluxes propagating in forward and backward directions through a sample. The intensities of these fluxes can be derived on the basis of simple assumptions of electron-solid interactions. The approach can be effectively applied to a system with an arbitrary form of depth concentration profile. The obtained results are in reasonable agreement with Monte Carlo simulations and experimental results. Some mathematical techniques have been presented for quantitative analysis of thin films on substrates and element depth distribution.     

Modeling of neutron activation process with Americium Beryllium source. Application to the activation of fluorspar samples

This paper shows the mathematical models which represent the phenomena that occur in a neutron activation process. These phenomena are, on the one hand, the neutron flux decreases with the distance between the neutron source and the sample, and on the other hand, the attenuation of the gamma rays originating from the sample activated on its way to the detector position. The development of the mathematical model has been divided into two parts. Firstly, the phenomena are shown separately. Secondly, the phenomena are shown together. Finally, this model is fitted to the neutron activation of a fluorspar sample, and the influence of the two phenomena as defined above can be seen.     

Chemometrics-Based Process Analytical Technology (PAT) Tools: Applications and Adaptation in Pharmaceutical and Biopharmaceutical Industries

Process analytical technology (PAT) is used to monitor and control critical process parameters in raw materials and in-process products to maintain the critical quality attributes and build quality into the product. Process analytical technology can be successfully implemented in pharmaceutical and biopharmaceutical industries not only to impart quality into the products but also to prevent out-of-specifications and improve the productivity. PAT implementation eliminates the drawbacks of traditional methods which involves excessive sampling and facilitates rapid testing through direct sampling without any destruction of sample. However, to successfully adapt PAT tools into pharmaceutical and biopharmaceutical environment, thorough understanding of the process is needed along with mathematical and statistical tools to analyze large multidimensional spectral data generated by PAT tools. Chemometrics is a chemical discipline which incorporates both statistical and mathematical methods to obtain and analyze relevant information from PAT spectral tools. Applications of commonly used PAT tools in combination with appropriate chemometric method along with their advantages and working principle are discussed. Finally, systematic application of PAT tools in biopharmaceutical environment to control critical process parameters for achieving product quality is diagrammatically represented.     

分辨伏安分析重叠峰的研究

研究了一种处理伏安(极谱)重叠峰的数学模型。将几类具峰状的极谱电流公式归纳成一般的关系式,提出了一个通用的拟合函数,经非线性最小二乘法处理,可得到重叠组份的蜂高、峰电位和半峰宽等参数。本法适用于示差脉冲极谱、交流极谱、方波极谱、一阶导数卷积伏安法及其反向溶出伏安重叠峰的分离。已用于示差脉冲极谱和交流极谱重叠峰的分辨,得到满意结果。     

UNIFIED THEORETICAL MOMENT EXPRESSIONS FOR ELUTION CHROMATOGRAPHY AND FRONTAL CHROMATOGRAPHY

The unified theoretical moment expressions for elution chromatography and frontal chromatography when the sorption process is described by a linear model were derived. The moment expressions derived by previous authors can be obtained from these unified theoretical moment expressions. In this paper, a mathematical analysis has been carried out so as to set up a unified theoretical basis for elution and frontal chromatography.     

Change of migration time and separation window accompanied by field-enhanced sample stacking in capillary zone electrophoresis.

When field-enhanced sample stacking was used in capillary zone electrophoresis (CZE) analysis of cations, the decrease of migration time and the reduction of separation window was observed with increase of sample plug length. A simple equation expressing the migration velocity in the stacking process was derived to explain the above phenomenon. From experiments and theoretical consideration, we confirmed that this effect was caused by the higher potential gradient and larger eletroosmotic flow (EOF) mobility at the sample plug than those at the supporting electrolyte. A mathematical model appropriate for the computer simulation of such a system was studied considering the experimental results, and it was concluded that electroosmotic velocity (v(eof)) should be introduced to the equation of continuity as a constant.     

Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties

The ISO 98:1995 Guide to the expression of uncertainty in measurement (GUM) presents important application limitations. For its improvement, different supplements are being developed that will progressively enter into effect. The first of these supplements describes an alternative method for calculating uncertainties, the Monte Carlo method (MCM), which is not restricted to the conditions of the method described in the GUM: the linearity of the model and the application of the central limit theorem. MCM requires computer calculation systems for generating pseudo-random numbers and for evaluating the model a large number of times. There are software applications that have been specifically developed for calculating uncertainties, some of which include MCM; but they do not allow the user to control all factors in the process, particularly the result stabilization criteria. On the contrary, its implementation in a mathematical program for general purposes such as MATLAB, enables total control over the process, is simple and benefits from its calculation speed. This article details programming in MATLAB for the implementation of the adaptive MCM method.     

油/水/表面活性剂所组成分散体系的数学模型

对分散体系的研究,大多采用经验或半经验的方式。例如,表面活性剂的亲水、亲油性平衡值(Hydiophihc-Lipophilic Balance,HLB值),其不确定性使得人们很难利用HLB值来决定某一具体的表面活性剂的实用性;尽管Delichatsios等在研究动力学条件对分散结果的影响时提供了很有价值的关系式,但这类关系式却无法反映动力学条件和表面活性剂在分散体系形成中的关系及重要性,类似的问题在分散体系的研究中相当普遍,且很难满足人们的实际需要,本文尝试在前人研究的基础上,利用分散体系研究中比较成熟的基本概念,用数学方法建立由各量化数学参数所组成的数学模型。     

Interrelationships between generalized Tikhonov regularization,generalized net analyte signal,and generalized least squares for desensitizing a multivariate calibration to interferences

Orthogonal pre‐processing (orthogonal projection) of spectral data is a common approach to generate analyte‐specific information for use in multivariate calibration. The goal of this pre‐processing is to remove from each spectrum the respective sample interferent contributions (spectral interferences from overlap, scatter, noise, etc.). Two approaches to accomplish orthogonal pre‐processing are net analyte signal (NAS) and generalized least squares (GLS). Developed in this paper is the mathematical relationship between NAS and GLS. It is also realized that orthogonal NAS pre‐processing can remove too much analyte signal and that the degree of interferent correction can be regulated. Similar to GLS, the degree of correction is accomplished by using a regularization (tuning) parameter to form generalized NAS (GNAS). Also developed in this paper is an alternative to GNAS and GLS based on generalized Tikhonov regularization (GTR). The mathematical relationships between GTR, GNAS, and GLS are derived. A result is the ability to express the model vector as the sum of two contributions: the orthogonal NAS contribution and a non‐NAS contribution from the interferent components. Thus, rather than the usual situation of sequentially pre‐processing data by either GNAS or GLS followed by model building with the pre‐processed data, the methods of GTR, GNAS, and GLS are expressed as direct computations of model vectors allowing concurrent pre‐processing and model building to occur. Simultaneous pre‐processing and model forming are shown to be natural to the GTR process. Two near‐infrared spectroscopic data sets are studied to compare the theoretical relationships between GTR, GNAS, and GLS. One data set covers basic calibration, and the other data set is for calibration maintenance. Filter factor representation is key to developing the interprocess relationships. Copyright © 2013 John Wiley & Sons, Ltd.     

Liquid-supported membranes in chromium(VI) optical sensing: transport modelling

Flat sheet liquid-supported membranes (FSLSM) containing Aliquat 336 as a carrier have been evaluated as sample interface in an optical sensor for Cr(VI) monitoring. A model describing the transport mechanism of Cr(VI) through the membrane is reported. The model considers a diffusion process through a feed aqueous diffusion layer, a fast interfacial chemical reaction and a diffusion of ALQHCrO₄ and (ALQ)₂CrO₄ species through the membrane (Aliquat 336, ALQ). The mathematical equations describing the transport rate are derived and they correlate the membrane permeability coefficient to diffusional and equilibrium parameters as well as to the chemical composition of the system, i.e. extractant concentration in the membrane phase and acidity in the feed phase. The experimental data are explained by the derived equations and the diffusion resistances to mass transfer are evaluated. The influence of other experimental parameters, such as stirring speed in the feed phase and nature of the diluent and stripping agent on the transport is also discussed. Experiments with optical detection demonstrate the suitability of liquid-supported membranes (LSM) containing ALQ as interfaces for optical sensing.     

A Closed‐Loop Control Strategy for Producing Nitrile Rubber of Uniform Chemical Composition in a Semibatch Reactor: A Simulation Study

To improve the quality of industrial nitrile rubbers, the copolymer chemical composition, p_A(t), should ideally be kept constant along the reaction. This work proposes a closed‐loop control strategy for the semibatch operation of the reactor with the aim of regulating p_A(t) within a reduced range of variability. The proposed strategy is evaluated by simulating a mathematical model of the process. To this effect, a simplified mathematical model of the reaction is first derived and then utilized to obtain a suboptimal control law and a soft‐sensor that estimates the polymerization rates. The suboptimal control law is compensated by adding a term proportional to errors in p_A(t). The simulated example considers the production of the low‐composition AJLT grade, with the copolymerization reaction represented by a detailed mathematical model adjusted to an industrial plant. Due to the high performance of the soft‐sensor, the simulation results suggest that the proposed closed‐loop strategy is efficient to adequately regulate p_A(t) in spite of structural and parametric uncertainties, while other quality variables remained practically unaffected.     

Charge/discharge of an electrochemical supercapacitor electrode pore; non-uniqueness of mathematical models

A thermodynamic analysis has been done to enhance understanding of the relation between various mathematical models for electrochemical supercapacitor pores. For the same capacitive charge/discharge experiment a variety of one-dimensional mathematical model equations concerning the transport of ions and double layer charge/discharge along the pore are shown to be indistinguishable. Some of those indistinguishable equations could be interpreted as derived from diffusional mechanisms while others appear as derived from migrational mechanisms. Ohmic resistivities and diffusivities obtained in such case are not contradicting results but characterize identical physical processes. The results are valid as long as the assumptions of irreversible thermodynamics of local equilibrium along the pore and of linearization of the flux equations hold.     

气-固流化床反应器内双流体力学模型及其验证 Ⅱ.单组分两维射流床内流场特性分析

由以质量、动量和能量三大守恒定律为基础的湍流两相流理论出发,建立了描述气固流化床内两相流动的数学模型;在微型计算机上编写了相应的数值计算和图形处理程序;为了验证模型的可靠性,本文着手模拟与分析了单组分颗粒体系两维射流流化床内气、固相速度场、空隙度和压力场随时间、空间变化规律;得到了与前人实验结果相吻合的结论。     

Non-linear regression methods in NIRS quantitative analysis

Due to its speed and precision, near-infrared reflectance spectroscopy (NIRS) has become a widely used analytical technique in many industries. It offers, moreover, a number of other advantages which make it ideal for meeting current demands in terms of control and traceability: low cost per sample analysed; little or no need for sample preparation; ability to analyse a wide range of products and parameters; a high degree of reproducibility and repeatability. NIRS can be built into in-line processes, and - since no reagents are required - produces no waste. However, the major drawback to the use of NIRS for its most traditional application (the generation of prediction equations) is that it is a secondary method, and as such needs to be calibrated using a conventional reference method. For quantitative applications, calibration involves ascertaining the optimum mathematical relationship between spectral data and data provided by the reference method. The model may be fairly complex, since the NIRS spectrum is highly variable and contains physical/chemical information for the sample which may be redundant. As a result, multivariate calibration is required, based on a set of absorption values from several wavelengths. Since the relationship to be modelled is often non-linear, classical regression methods are unsuitable, and more complex strategies and algorithms must be sought in order to model this non-linearity. This overview addresses the most widely used non-linear algorithms in the management of NIRS data.     

Mixed-mode electrokinetic chromatography of aromatic bases with two pseudo-stationary phases and pH control

The electrokinetic chromatographic (EKC) separation of a series of aromatic bases was achieved utilising an electrolyte system comprising an anionic soluble polymer (polyvinylsulfonic acid, PVS) and a neutral beta-cyclodextrin (beta-CD) as pseudo-stationary phases. The separation mechanism was based on a combination of electrophoresis, ion-exchange interactions with PVS, and hydrophobic interactions with beta-CD. The extent of each chromatographic interaction was independently variable, allowing for control of the separation selectivity of the system. The ion-exchange and the hydrophobic interactions could be varied by changing the PVS and the beta-CD concentrations, respectively. Additionally, mobilities of the bases could be controlled by varying pH, due to their large range of pKa values. The separation system was very robust with reproducibility of migration times being <2% RSD. The two-dimensional parameter space defined by the two variables, [beta-CD] and %PVS, was modelled using a physical model derived from first principles. This model gave very good correlation between predicted and observed mobilities (r2=0.999) for the 13 aromatic bases and parameters derived from the model agreed with the expected ion-exchange and hydrophobic character of each analyte. The complexity of the mathematical model was increased to include pH and this three-dimensional system was modelled successfully using an artificial neural network (ANN). Optimisation of both the two-dimensional and three-dimensional systems was achieved using the normalised resolution product and minimum resolution criteria. An example of using the ANN to predict conditions needed to obtain a separation with a desired migration order between two of the analytes is also shown.     

Simulation of the effects of complex- formation equilibria in electrophoresis: I. mathematical model

Simul 5 Complex is a one-dimensional dynamic simulation software designed for electrophoresis, and it is based on a numerical solution of the governing equations, which include electromigration, diffusion and acid-base equilibria. A new mathematical model has been derived and implemented that extends the simulation capabilities of the program by complexation equilibria. The simulation can be set up with any number of constituents (analytes), which are complexed by one complex-forming agent (ligand). The complexation stoichiometry is 1:1, which is typical for systems containing cyclodextrins as the ligand. Both the analytes and the ligand can have multiple dissociation states. Simul 5 Complex with the complexation mode runs under Windows and can be freely downloaded from our web page http://natur.cuni.cz/gas. The article has two separate parts. Here, the mathematical model is derived and tested by simulating the published results obtained by several methods used for the determination of complexation equilibrium constants: affinity capillary electrophoresis, vacancy affinity capillary electrophoresis, Hummel-Dreyer method, vacancy peak method, frontal analysis, and frontal analysis continuous capillary electrophoresis. In the second part of the paper, the agreement of the simulated and the experimental data is shown and discussed.