Modeling nonlinear stochastic kinetic system and stochastic optimal control of microbial bioconversion process in batch culture

In this paper, we analyze a stochastic model representing batch fermentation in the process of glycerol bio-dissimilation to 1,3-propanediol by klebsiella pneumoniae. The stochasticity in the model is introduced by parameter perturbation which is a standard technique in stochastic population modelling. Thus, based on the nonlinear deterministic dynamical system of glycerol bioconversion to 1,3-propanediol in batch culture, we present the stochastic version of the batch fermentation process driven by a five-dimensional Brownian motion and Lipschitz coefficients, which is suitable for the factual fermentation. Subsequently, we study the existence and uniqueness of solutions for the stochastic system as well as the boundedness and Markov property of solutions. Moveover a stochastic optimal control model is constructed and the sufficient and necessary conditions for optimality are proved via dynamic programming principle. Finally we present computer simulation for the stochastic system by using Stochastic Euler–Maruyama scheme. Compared with the results from the deterministic system, numerical results reveal the peculiar role of stochasticity in the dynamical responses of the batch culture

Optimal 1,3-propanediol production: Exploring the trade-off between process yield and feeding rate variation

This paper proposes a new optimal control model for the production of 1,3-propanediol (1,3-PD) viamicrobial fed-batch fermentation. The proposed model is governed by a nonlinear multi stage dynamic system with two modes: feeding mode, in which glycerol and alkali substrates are added continuously to the fermentor; and batch mode, in which no substrates are added to the fermentor. The non-standard objective function incorporates both the final 1,3-PD yield and the cost of changing the input feeding rate, which is the control variable for the fed-batch fermentation process. Continuous state inequality constraints are imposed to ensure that the concentrations of biomass, glycerol, and reaction products lie within specified limits. Using the constraint transcription method, we approximate the continuous state inequality constraints by a conventional inequality constraint to yield an approximate parameter optimization problem. We then develop a combined particle swarm and gradient-based optimization algorithm to solve this approximate problem. The paper concludes with simulation results

A linear optimal feedback control for producing 1,3-propanediol via microbial fermentation

In this paper, we consider a multistage feedback control strategy for the production of 1,3-propanediol(1,3-PD) in microbial fermentation. The feedback control strategy is widely used in industry, and to the best of our knowledge, this is the first time it is applied to 1,3-PD. The feedback control law is assumed to be linear of the concentrations of biomass and glycerol, and the coefficients in the controller are continuous. A multistage feedback control law is obtained by using the control parameterization method on the coefficient functions. Then, the optimal control problem can be transformed into an optimal parameter selection problem. The time horizon is partitioned adaptively. The corresponding gradients are derived, and finally, our numerical results indicate that the strategy is flexible and efficient

Modelling and parameter identification for a two-stage fractional dynamical system in microbial batch process

In this paper, we consider mathematical modelling and parameter identification problem in bioconversion of glycerol to 1,3-propanediol by Klebsiella pneumoniae. In view of the dynamic behavior with memory and heredity and experimental results in batch culture, a two-stage fractional dynamical system with unknown fractional orders and unknown kinetic parameters is proposed to describe the fermentation process. For this system, some important properties of the solution are discussed. Then, taking the weighted least-squares error between the computational values and the experimental data as the performance index, a parameter identification model subject to continuous state inequality constraints is presented. An exact penalty method is introduced to transform the parameter identification problem into the one only with box constraints. On this basis, we develop a parallel Particle Swarm Optimization algorithm to find the optimal fractional orders and kinetic parameters. Finally, numerical results show that the model can reasonably describe the batch fermentation process, as well as the effectiveness of the developed algorithm. Keywords: fractional dynamical system, parameter identification, parallel optimization

Optimal Control of a Nonlinear Time-Delay System in Batch Fermentation Process

The main control goal in batch process is to get a high yield of products. In this paper, to maximize the yield of 1,3-propanediol (1,3-PD) in bioconversion of glycerol to 1,3-PD, we consider an optimal control problem involving a nonlinear time-delay system. The control variables in this problem include the initial concentrations of biomass and glycerol and the terminal time of the batch process. By a time-scaling transformation, we transcribe the optimal control problem into a new one with fixed terminal time, which yields a new nonlinear system with variable time-delay. The gradients of the cost and constraint functionals with respect to the control variables are derived using the costate method. Then, a gradient-based optimization method is developed to solve the optimal control problem. Numerical results show that the yield of 1,3-PD at the terminal time is increased considerably compared with the experimental data

Optimization of a fed-batch bioreactor for 1,3-propanediol production using hybrid nonlinear optimal control

A nonlinear hybrid system was proposed to describe the fed-batch bioconversion of glycerol to 1,3-propanediol with substrate open loop inputs and pH logic control in previous work [47]. The current work concerns the optimal control of this fed-batch process. We slightly modify the hybrid system to provide a more convenient mathematical description for the optimal control of the fed-batch culture. Taking the feeding instants and the terminal time as decision variables, we formulate an optimal control model with the productivity of 1,3-propanediol as the performance index. Inequality path constraints involved in the optimal control problem are transformed into a group of end-point constraints by introducing an auxiliary hybrid system. The original optimal control problem is associated with a family of approximation problems. The gradients of the cost functional and the end-point constraint functions are derived from the parametric sensitivity system. On this basis, we construct a gradient-based algorithm to solve the approximation problems. Numerical results show that the productivity of 1,3-propanediol can be increased considerably by employing our optimal control policy

Multi-objective optimization of nonlinear switched time-delay systems in fed-batch process

© 2016 Elsevier Inc.Maximization of productivity and minimization of consumption are two top priorities for biotechnological industry. In this paper, we model a fed-batch process as a nonlinear switched time-delay system. Taking the productivity of target product and the consumption rate of substrate as the objective functions, we present a multi-objective optimization problem involving the nonlinear switched time-delay system and subject to continuous state inequality constraints. To solve the multi-objective optimization problem, we first convert the problem into a sequence of single-objective optimization problems by using convex weighted sum and normal boundary intersection methods. A gradient-based single-objective solver incorporating constraint transcription technique is then developed to solve these single-objective optimization problems. Finally, a numerical example is provided to verify the effectiveness of the numerical solution approach. Numerical results show that the normal boundary intersection method in conjunction with the developed single-objective solver is more favourable than the convex weighted sum method

Continuous Biochemical Processing: Investigating Novel Strategies to Produce Sustainable Fuels and Pharmaceuticals

Biochemical processing methods have been targeted as one of the potential renewable strategies for producing commodities currently dominated by the petrochemical industry. To design biochemical systems with the ability to compete with petrochemical facilities, inroads are needed to transition from traditional batch methods to continuous methods. Recent advancements in the areas of process systems and biochemical engineering have provided the tools necessary to study and design these continuous biochemical systems to maximize productivity and substrate utilization while reducing capital and operating costs. The first goal of this thesis is to propose a novel strategy for the continuous biochemical production of pharmaceuticals. The structural complexity of most pharmaceutical compounds makes chemical synthesis a difficult option, facilitating the need for their biological production. To this end, a continuous, multi-feed bioreactor system composed of multiple independently controlled feeds for substrate(s) and media is proposed to freely manipulate the bioreactor dilution rate and substrate concentrations. The optimal feed flow rates are determined through the solution to an optimal control problem where the kinetic models describing the time-variant system states are used as constraints. This new bioreactor paradigm is exemplified through the batch and continuous cultivation of β-carotene, a representative product of the mevalonate pathway, using Saccharomyces cerevisiae strain mutant SM14. The second goal of this thesis is to design continuous, biochemical processes capable of economically producing alternative liquid fuels. The large-scale, continuous production of ethanol via consolidated bioprocessing (CBP) is examined. Optimal process topologies for the CBP technology selected from a superstructure considering multiple biomass feeds, chosen from those available across the United States, and multiple prospective pretreatment technologies. Similarly, the production of butanol via acetone-butanol-ethanol (ABE) fermentation is explored using process intensification to improve process productivity and profitability. To overcome the inhibitory nature of the butanol product, the multi-feed bioreactor paradigm developed for pharmaceutical production is utilized with in situ gas stripping to simultaneously provide dilution effects and selectively remove the volatile ABE components. Optimal control and process synthesis techniques are utilized to determine the benefits of gas stripping and design a butanol production process guaranteed to be profitable

Book of abstracts of the 10th International Chemical and Biological Engineering Conference: CHEMPOR 2008

This book contains the extended abstracts presented at the 10th International Chemical and Biological Engineering Conference - CHEMPOR 2008, held in Braga, Portugal, over 3 days, from the 4th to the 6th of September, 2008. Previous editions took place in Lisboa (1975, 1889, 1998), Braga (1978), Póvoa de Varzim (1981), Coimbra (1985, 2005), Porto (1993), and Aveiro (2001). The conference was jointly organized by the University of Minho, “Ordem dos Engenheiros”, and the IBB - Institute for Biotechnology and Bioengineering with the usual support of the “Sociedade Portuguesa de Química” and, by the first time, of the “Sociedade Portuguesa de Biotecnologia”. Thirty years elapsed since CHEMPOR was held at the University of Minho, organized by T.R. Bott, D. Allen, A. Bridgwater, J.J.B. Romero, L.J.S. Soares and J.D.R.S. Pinheiro. We are fortunate to have Profs. Bott, Soares and Pinheiro in the Honor Committee of this 10th edition, under the high Patronage of his Excellency the President of the Portuguese Republic, Prof. Aníbal Cavaco Silva. The opening ceremony will confer Prof. Bott with a “Long Term Achievement” award acknowledging the important contribution Prof. Bott brought along more than 30 years to the development of the Chemical Engineering science, to the launch of CHEMPOR series and specially to the University of Minho. Prof. Bott’s inaugural lecture will address the importance of effective energy management in processing operations, particularly in the effectiveness of heat recovery and the associated reduction in greenhouse gas emission from combustion processes. The CHEMPOR series traditionally brings together both young and established researchers and end users to discuss recent developments in different areas of Chemical Engineering. The scope of this edition is broadening out by including the Biological Engineering research. One of the major core areas of the conference program is life quality, due to the importance that Chemical and Biological Engineering plays in this area. “Integration of Life Sciences & Engineering” and “Sustainable Process-Product Development through Green Chemistry” are two of the leading themes with papers addressing such important issues. This is complemented with additional leading themes including “Advancing the Chemical and Biological Engineering Fundamentals”, “Multi-Scale and/or Multi-Disciplinary Approach to Process-Product Innovation”, “Systematic Methods and Tools for Managing the Complexity”, and “Educating Chemical and Biological Engineers for Coming Challenges” which define the extended abstracts arrangements along this book. A total of 516 extended abstracts are included in the book, consisting of 7 invited lecturers, 15 keynote, 105 short oral presentations given in 5 parallel sessions, along with 6 slots for viewing 389 poster presentations. Full papers are jointly included in the companion Proceedings in CD-ROM. All papers have been reviewed and we are grateful to the members of scientific and organizing committees for their evaluations. It was an intensive task since 610 submitted abstracts from 45 countries were received. It has been an honor for us to contribute to setting up CHEMPOR 2008 during almost two years. We wish to thank the authors who have contributed to yield a high scientific standard to the program. We are thankful to the sponsors who have contributed decisively to this event. We also extend our gratefulness to all those who, through their dedicated efforts, have assisted us in this task. On behalf of the Scientific and Organizing Committees we wish you that together with an interesting reading, the scientific program and the social moments organized will be memorable for all.Fundação para a Ciência e a Tecnologia (FCT