Journal of Engineering

Volume 2016 (2016), Article ID 4358282, 7 pages

http://dx.doi.org/10.1155/2016/4358282

## Partial Control of a Continuous Bioreactor: Application to an Anaerobic System for Heavy Metal Removal

^{1}Chemical & Biochemical Engineering Division, Tecnológico de Estudios Superiores de Ecatepec, Avenida Tecnologico S/N, Valle de Anahuac, 55210 Ecatepec de Morelos, MEX, Mexico^{2}Escuela Superior de Apan, Universidad Autónoma del Estado de Hidalgo, Carretera Apan-Calpulalpan, Km 8, Chimalpa Tlalayote S/N, Colonia Chamilpa, 43900 Apan, HGO, Mexico^{3}Biotechnology and Bioengineering Department, CINVESTAV-IPN, Avenida Instituto Politécnico Nacional 2508, San Pedro Zacatenco, 07360 Mexico City, MEX, Mexico

Received 23 November 2015; Revised 21 April 2016; Accepted 5 May 2016

Academic Editor: Jong M. Park

Copyright © 2016 M. I. Neria-González 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

This work presents a control strategy for a continuous bioreactor for heavy metal removal. For this aim, regulation of the sulfate concentration, which is considered the measured and controlled state variable, allowed diminishing the cadmium concentration in the bioreactor, where the corresponding controller was designed via nonlinear bounded function. Furthermore, a nonlinear controllability analysis was done, which proved the closed-loop instability of the inner or uncontrolled dynamics of the bioreactor. A mathematical model, experimentally corroborated for cadmium removal, was employed as a benchmark for the proposed controller. Numerical experiments clearly illustrated the successful implementation of this methodology; therefore, cadmium removal amounted to more than 99%, when the initial cadmium concentration was up to 170 mg/L in continuous operating mode.

#### 1. Introduction

Attention to bioremediation processes has greatly increased during the last decade. Anaerobic reduction has been used as a means for treating a variety of sulfate-containing industrial water generated from various industrial activities, such as food processing, pulp and paper industries, mining and mineral processing, scrubbing of flue gases, and petrochemical industries [1]. Moreover, the existing sulfate can be reduced to hydrogen sulfide resulting in unfavorable ecological effects. Therefore, the use of biological sulfate reduction (BSR) is an attractive alternative or supplement for the simultaneous removal of heavy metals and sulfate from wastewaters. In BSR, the produced sulfide forms insoluble precipitates with the metal ions; the extremely low solubility of the formed sulfide metal (bioprecipitation) allows for the removal of heavy metals from the wastewater [2, 3].

To achieve the full biological potential of cells, optimal environmental conditions for cell growth and product formation must be maintained in the bioreactor, at least, regarding the most important key parameters. The wide use of anaerobic sulfate-reducing bioreactors has been addressing the necessity of robust, flexible, and efficient operation modes, where the corresponding control strategies play key roles. The anaerobic sulfate-reducing systems are affected by many factors, including temperature, retention time, pH, and chemical composition of the wastewater [4, 5]. Much emphasis has been placed on the control of continuous and fed-batch bioreactors because of their traditional prevalence in industry; however, if production of cell mass or product is to be optimized, then continuous operation is desirable for the development of bioprocess engineering. Unforeseen disturbances in a continuous bioreactor may result in a failure in the reactor’s operation, which requires a new start-up procedure.

The key objective of a continuous bioreactor control system is usually washout; this can be avoided by closing one feedback loop and controlling cell mass or substrate concentrations. Besides, to optimize the reaction and maintain the quality of the product, it could be essential to keep biomass, substrate, and some products at desired values [6, 7]. To this date, PID-type controllers are the most applied in the process industries. However, because of (i) rapid development in biotechnology, (ii) the computational capabilities of controllers, (iii) the industrial demands, (iv) process optimization in upscaling, and (v) complexity of biosystems, control actions have had to be increased, so the challenge is to implement advanced control algorithms [8, 9].

A number of papers, dealing with the new controller design under the framework of gain scheduling, have been published in the open literature dealing with predictive, optimal, and nonlinear control theories [10, 11]. Unfortunately, because of their mathematical complexity, most of them cannot be applied to industrial plants. In order to solve this problem, control engineers have had to design* ad hoc* control schemes to be able to deal with demanding operating conditions. For example, Aguilar et al. [12] have proposed novel approaches to design nonlinear PI- and PID-type controllers using more sophisticated techniques that allow developing new friendly tuning rules for the controller’s gains and assuring semiglobal robust performance. Another successful control approach is related to sliding mode, which shows some robust properties against model uncertainties and external disturbances when the system reaches the named sliding surface; however, the chattering problem can induce, in the worst case, system’s instabilities. A way to avoid the above chattering is the use of high order sliding-mode controllers, which have been proposed to provide smoothness performance to the corresponding output injection and improve the closed-loop system behavior; however, the theoretical frame to prove closed-loop convergence is complex [13]. Under this frame, a class of sigmoid functions has been proposed to substitute the discontinuous terms of the sliding-mode controllers [14]. In order to solve the problems described, in this paper, a class of nonlinear controller with bounded output feedback is proposed to provide stabilization for a class of continuous sulfate-reducing bioreactor. This model was employed as a benchmark system to implement a nonlinear controller, where the corresponding feedback is related to bound sigmoid functions. Furthermore, a nonlinear controllability analysis was done. Bioreactor regulation was achieved via sulfate concentration, which is considered as the measured and controlled state variable; this allowed diminishing the cadmium concentration in the bioreactor. Besides, a theoretical frame of the closed-loop stability was provided, which ensured loop stability.

#### 2. Materials and Methods

The presented model was based on a previous work of López-Pérez et al. [15]. The strain* Desulfovibrio alaskensis* 6SR was used [16]. Inoculation and analysis procedures and media used have been described elsewhere [17–19]. The proposed model considers the inhibitory effect of cadmium and H_{2}S on microbial growth. Furthermore, the model includes four processes: (1) carbon source consumption, (2) microbial sulfate reduction, (3) biofilm formation, and (4) cadmium removal. The mathematical model describes the kinetics of cadmium removal in batch systems. A straightforward estimate of acetate production with lactate consumption was obtained by the combination of the Moser-Boulton models and biomass concentration, according to (1) and (2). The Levenspiel inhibition model was modified to describe the reduction of sulfate; the classical growth with the reduction of sulfate to H_{2}S is described by (3)–(5). The mass balance, describing the biofilm formation, is given by (6). The mass balance describing the removal of cadmium is specified by a modified Levenspiel-Haldane model [20] (see (7)). Therefore, the mathematical model of the bioreactor can be expressed by lactate mass balance as follows: acetate mass balance as follows: sulfate mass balance as follows: biomass balance as follows: sulfide mass balance as follows: biofilm mass balance as follows: cadmium in liquid form mass balance as follows:Here, , , and are the exponential terms of the Luong model; is the exponential term for lactate concentration; and are the exponential terms of the Moser model; is the dilution rate; is the mortality constant; is the initial cadmium concentration; is the saturation coefficient; and is the inhibition constant for Haldane; is the yield constant; is the Monod saturation constant for sulfate (); is the inhibition constant for nondissipated hydrogen sulfide (H_{2}S); is the inhibition parameter of lactate; is the inhibition parameter of acetate; is the inhibition constant for cadmium; is the lactate/biomass yield coefficient; is the acetate/biomass yield coefficient.

#### 3. Controller Design

This methodology allows regulating to a desired set point; therefore, regulation is achieved via sulfate concentration, which is considered the measured and controlled state variable; this allows diminishing the cadmium concentration in the bioreactor, where the corresponding feedback is related to the given dilution rate (input flow) (see Figure 1).