Scientific Programming

Volume 2016, Article ID 3279423, 15 pages

http://dx.doi.org/10.1155/2016/3279423

## Modeling and Optimization of the Drug Extraction Production Process

^{1}College of Information Science and Engineering, Northeastern University, Shenyang, Liaoning 110004, China^{2}State Key Laboratory of Synthetical Automation for Process Industries, Northeastern University, Shenyang 110004, China

Received 17 June 2016; Revised 31 August 2016; Accepted 14 September 2016

Academic Editor: Chengyan Yue

Copyright © 2016 Dakuo He et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

#### Abstract

Optimized control of the drug extraction production process (DEPP) aims to reduce production costs and improve economic benefit while meeting quality requirements. However, optimization of DEPP is hampered by model uncertainty. Thus, in this paper, a strategy that considers model uncertainty is proposed. Mechanistic modeling of DEPP is first discussed in the context of previous work. The predictive model used for optimization is then developed by simplifying the mechanism. Optimization for a single extraction process is first implemented, but this is found to lead to serious wastage of herbs. Hence, the optimization of a multiextraction process is then conducted. To manage the uncertainty in the model, a data-driven iterative learning control method is introduced to improve the economic benefit by adjusting the operating variables. Finally, fuzzy parameter adjustment is adopted to enhance the convergence rate of the algorithm. The effectiveness of the proposed modeling and optimization strategy is validated through a series of simulations.

#### 1. Introduction

Drug extraction, or drug leaching, is one of the most significant operations in the pharmaceutical industry. As the basic and primary process of drug production, it has been widely applied to many medicinal plants [1–7]. In the drug extraction production process (DEPP), a solvent or chemical reagent that offers high solubility for the effective constituent (EC) in the herbs and poor solubility for constituents that need not be extracted is applied to solid herbs. The EC then dissolves out of the herb organization and into the solvent or chemical reagent [8]. The extracted EC is finally used in various types of drugs, such as granules, tablets, and capsules, in subsequent pharmaceutical processes.

The disadvantages of this production process include low extraction yield, wastage of materials, and high energy consumption. Modeling and process optimization, which aim to increase the extraction yield and minimize production costs while meeting specific quality requirements, are therefore particularly significant in both theoretical research and practical applications.

The optimization of drug extraction process has received increasing attention. For example, Alam et al. [9] studied the optimization of the extraction parameters of embelin from* Embelia ribes* through ultrasound-assisted extraction with a Box–Behnken design. Bochi et al. [10] optimized the extraction conditions and anthocyanin yields in experiments with high proportions of water. Chen et al. [11] applied an orthogonal experiment to optimize the extraction conditions of polysaccharides from* Ornithogalum caudatum* Ait. Chen et al. [12] used the response surface methodology to optimize the experimental conditions for ultrasonic-assisted extraction of functional components from sugar beet molasses. Bae et al. [13] successfully developed and validated a simple qualitative and quantitative method for the simultaneous determination of 15 phenolic compounds and caffeine from teas and then optimized the extraction process using the response surface methodology based on a central composite design. In addition to these innovations, many other scholars have made tremendous contributions to the theoretical and practical optimization of DEPP [3, 14–16]. However, many of these reports focus on optimizing the extraction conditions using experimental design or simulation techniques. To the best of the authors’ knowledge, the optimization of DEPP in terms of improving the economic benefit of the whole production process has rarely been reported in the literature. The present work develops a mechanism model for DEPP based on some previous efforts and then proposes an optimization strategy to resolve practical problems such as the production efficiency and production costs.

To implement this optimization, a mechanism model of DEPP should be developed. Such mechanistic modeling plays several significant roles: first, the modeling process will analyze the mechanism of the drug extraction process, confirm its operating variables and quality indicators, and analyze the relationship between them; second, an appropriate model can be used to simulate the actual production process to generate the required data and analyze the optimization results. As an actual simulator, the mechanism model should be able to link the extraction efficiency of the EC and volatile oil—the quality indicators—with the operating variables (steam flow at the bottom and side of the extraction tank and the extraction time).

The mechanistic modeling of DEPP mainly consists of modeling the following components: extraction tank, mass transfer process of EC, volatile oil recycling, and efficiency of the oil-water separator. A mathematical model of the extraction tank that describes the changes in temperature and liquid level over time has been developed [17]. As the principle and mechanism of the mass transfer process in drug extraction are very similar to those of metal leaching, mechanistic models of metal leaching [3, 18–22] can be used as references in developing a mass transfer model for the EC. Additionally, Han et al. derived a diffusion rate equation for volatile oils, allowing a mechanistic model of volatile oil recovery to be developed [23]. Finally, the efficiency of the oil-water separator is introduced to describe the separation efficiency of oil droplets with a certain diameter [24]. The above mechanistic models are combined to simulate the whole DEPP, and the rationality and validity of this approach are verified through a series of simulations. The innovation and contribution of the DEPP model presented in this paper can be summarized as follows. First, we extend a modeling approach for the leaching process to model the mass transfer process of ECs. Second, we present a combined mechanistic modeling framework for the overall DEPP by integrating four discrete components described in previous studies.

In addition to a mechanistic model, a predictive model is also necessary for such optimization. In this work, the established mechanism is simplified to serve as a predictive model. The economic benefit per unit time is considered as the optimization objective, while the steam flow at the bottom and side of the extraction tank and the extraction time are treated as decision variables. The optimization model is then established under certain quality constraints. Several classical optimization algorithms, such as particle swarm optimization (PSO) [25, 26], differential evolution (DE) [27], and artificial bee colony (ABC) [28], are adopted to solve this optimization problem. Comparing these algorithms, it is concluded that PSO achieves the best performance in determining the optimal solution. Thus, a PSO algorithm is used to solve this optimization problem and obtain the optimal economic benefit and corresponding parameters, including optimal quality indicators and operating variables. The present work first considers the optimization of a single extraction process. However, the extraction efficiency of the EC in this case is very low, leading to serious wastage of herb materials. The optimization control for multiextraction is therefore investigated. In the multiextraction process, the extraction frequency is defined as the number of times that the herbs are subjected to the extraction process. However, the optimal extraction frequency in terms of economic benefit is unknown. Thus, the extraction frequency is treated as one of the decision variables when establishing the optimization problem. Note that the extraction frequency is an integer in this problem.

The optimal economic benefit of the multiextraction process is based on the predictive model, whereas the actual optimal economic benefit can be calculated by plugging the best operating variables into the mechanism model. There are some discrepancies between the predicted and actual values of the optimal economic benefit. In practice, however, it is unlikely that the actual production process can be modeled accurately (or even approximately) with a process model [29, 30]. Process optimization is hampered by such model uncertainty, and so the “optimal” value given by the model may not necessarily mean “optimal for the process” [31].

Iterative learning control (ILC) is highly effective in controlling systems with repetitive operations that precisely follow a desired target trajectory. It has been widely applied in repetitive industrial processes because of its perfect learning ability from the repetitive tracking task [32–34]. Recently, data-driven ILC methods have been proposed to deal with complicated practical systems [35–37]. The control scheme is data-driven because there is no explicit model information or training process, and only the measured input and output data are used for the controller design, analysis, and implementation [36]. As one such method, data-driven optimal terminal ILC (DDOTILC) works under the principle that the control law is only updated using the terminal output tracking error [35]. In this work, DDOTILC is applied to implement iterative optimization control for DEPP in order to overcome the model uncertainty via the online adjustment of the operating variables. The fuzzy adaptive adjustment of parameters in DDOTILC is then implemented to enhance the convergence rate. Using this approach, the model uncertainty can be reduced and the economic benefit improved by adjusting the operating variables.

#### 2. Principle and Production Technology of the Drug Extraction Process

##### 2.1. Principle of the Drug Extraction Process

###### 2.1.1. Mass Transfer Theory of Effective Constituent

Drug extraction is one kind of solid-liquid extraction. Thus, the mass transfer principle and computing method follow the solid-liquid extraction system model shown in Figure 1. It is assumed that the herb particles are composed of solute (EC) and inert carriers (herb residues), so the solid-liquid extraction system is composed of solute, solvent, and inert solid. Additionally, there will be a gas-liquid film at the interface between the solid particles and liquid phase. It is generally acknowledged that this mass transfer process can be divided into the five steps described in Figure 1 [3, 8]:(1)The diffusion of solvent into the herb particle surface(2)The permeation of solvent from the herb surface to the interior(3)The dissolution of the EC inside the herb particles(4)The diffusion of EC from inside the herb particles to the surface (internal diffusion)(5)The diffusion of EC from the herb particle surface to the solvent across the gas-liquid film (external diffusion).