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

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

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

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

Modeling and control of non-ideally mixed bioreactors

Mixing plays a substantial role in determining the overall performance of a bioreactor. Well mixing in bioreactor, especially for ethanolic fermentation process is important for the homogenization of miscible and immiscible liquids, gas dispersion and suspension of solid particles. Improper mixing will eventually affect the biological and kinetics reactions occurring in the bioreactor and subsequently deteriorate the bioreactor performance. Currently, most modeling and control applications of bioreactors have been devoted to ideally mixed assumption, for simplicity. This is not realistic in practical applications. Furthermore, the strength and accuracy of the bioreactor models reflect their performance and subsequently its control strategy. Therefore, it is vital to consider the imperfect mixing for the control of bioreactor.In this study, a batch, micro-aerobic bioreactor for ethanolic fermentation process will be considered for modeling. Up to date, not much study has been conducted in exploiting the mixing mechanism for controlling this type of bioreactor. Traditionally, only the bioreactor conditions such as temperature and pH are controlled for such a batch bioreactor. Other parameters, such as aeration rate and stirrer speed are not used to control the bioreactor. Thus, it is difficult to improve the bioreactor performance as the bioreactor performance is less sensitive to both temperature and pH than to the mixing mechanism. However, the mixing behaviour of the bioreactor needs to be captured if we are to employ both aeration rate and stirrer speed for the control of such a batch bioreactor.It is known that aeration rate and stirrer speed could significantly affect the biological and kinetics reactions. Therefore, both aeration rate and stirrer speed are suggested in this work as manipulated variables in the modeling of batch bioreactor. Thus, with this approach the ideally mixed assumption will be relaxed.The models proposed will be implemented for control studies. New control strategies will be established for continuous bioreactor, whereby dilution rate and substrate concentration are considered as disturbance variables and both aeration rate and stirrer speed are suggested as manipulated variables. With this approach, the practicability of the proposed models could be investigated.The aims of this research have therefore been as follows: 1. To experimentally study the impact of aeration rate and stirrer speed on the bioreactor performances, i.e. yield and productivity. 2. To develop an integrated bioreactor model to allow us to employ the aeration rate and stirrer speed as manipulated variables for control design. 3. To establish new control strategies for bioreactor without the ideally mixed assumption.A systematic approach has been proposed to develop the non-ideally mixed bioreactor model and to design the control strategy of the lab-scale fermentation process. Three modeling approaches are employed, i.e. data-based, kinetics hybrid and kinetics multi-scale models for the analysis of the impacts of both aeration rate and stirrer speed on the performance of bioreactor. Using the three models, the aeration rate and stirrer speed are also used to analyze the mixing mechanism in the bioreactor.Furthermore, new control strategies are then proposed for the bioreactor. By using the proposed control strategies, the effect of both aeration rate and stirrer speed on the overall performance could be analyzed in the face of disturbances on other process parameters. Furthermore, the stability and achievable performance of the control strategies could be compared for different models. Hence, the proposed control strategies would lead to a better operation of the bioreactor.The study highlighted the following main findings: 1. It is identified that both aeration rate and stirrer speed could affect significantly the overall performance of the bioreactor. Therefore, both aeration rate and stirrer speed rather than temperature and pH could be used as manipulated variables for controlling the bioreactor. The ideally mixed assumption is relaxed where the mixing mechanism of the bioreactor is included in the proposed model.2. The main issue in modeling is the complexity of the microbial reactions and kinetics of the bioreactor performance for the non-ideally mixed behaviour of the bioreactor. Thus, it is important to identify the main reactions and kinetics which actually affect the bioreactor performance. In this study, Monod’s kinetics has been employed with the implementation of both aeration rate and stirrer speed. It is shown that the kinetics multi-scale model demonstrated good predictions of the mixing mechanism of bioreactor. Different conditions of aeration rate and stirrer speed influence the mixing mechanism and thus, contribute to the dynamics and kinetics within the bioreactor. These show that both aeration rate and stirrer speed play important role in studying the non-ideally mixed mechanism of the bioreactor.3. Optimization results, however, suggest that the kinetics hybrid model gives the most comparable values of maximum yield and productivity. Thus, this model is suggested for the determination of the optimum conditions of the bioreactor operation due to its simplicity in model construction, as compared to the kinetics multi-scale model.4. The control strategy of bioreactor using the data-based model does not always produce good performance, especially in the face of large disturbances. This implies that the use of models with ideally mixed assumptions would not always give good overall performance. Therefore, the controllability of the bioreactor performance is further improved with the implementation of the proposed non-ideally mixed bioreactor model. It is observed that both databased and kinetics hybrid models are able to keep the controlled variables in their set-point values by manipulating both aeration rate and stirrer speed for low disturbance changes.Hence, this research contributes on the understanding of mixing phenomena in micro-aerobic fermentation process from which a set of optimal operational conditions and control strategies to enhance its performance are developed

Modeling and optimization of extracellular polysaccharides production by Enterobacter A47

Polysaccharides are gaining increasing attention as potential environmental friendly and sustainable building blocks in many fields of the (bio)chemical industry. The microbial production of polysaccharides is envisioned as a promising path, since higher biomass growth rates are possible and therefore higher productivities may be achieved compared to vegetable or animal polysaccharides sources. This Ph.D. thesis focuses on the modeling and optimization of a particular microbial polysaccharide, namely the production of extracellular polysaccharides (EPS) by the bacterial strain Enterobacter A47. Enterobacter A47 was found to be a metabolically versatile organism in terms of its adaptability to complex media, notably capable of achieving high growth rates in media containing glycerol byproduct from the biodiesel industry. However, the industrial implementation of this production process is still hampered due to a largely unoptimized process. Kinetic rates from the bioreactor operation are heavily dependent on operational parameters such as temperature, pH, stirring and aeration rate. The increase of culture broth viscosity is a common feature of this culture and has a major impact on the overall performance. This fact complicates the mathematical modeling of the process, limiting the possibility to understand, control and optimize productivity. In order to tackle this difficulty, data-driven mathematical methodologies such as Artificial Neural Networks can be employed to incorporate additional process data to complement the known mathematical description of the fermentation kinetics. In this Ph.D. thesis, we have adopted such an hybrid modeling framework that enabled the incorporation of temperature, pH and viscosity effects on the fermentation kinetics in order to improve the dynamical modeling and optimization of the process. A model-based optimization method was implemented that enabled to design bioreactor optimal control strategies in the sense of EPS productivity maximization. It is also critical to understand EPS synthesis at the level of the bacterial metabolism, since the production of EPS is a tightly regulated process. Methods of pathway analysis provide a means to unravel the fundamental pathways and their controls in bioprocesses. In the present Ph.D. thesis, a novel methodology called Principal Elementary Mode Analysis (PEMA) was developed and implemented that enabled to identify which cellular fluxes are activated under different conditions of temperature and pH. It is shown that differences in these two parameters affect the chemical composition of EPS, hence they are critical for the regulation of the product synthesis. In future studies, the knowledge provided by PEMA could foster the development of metabolically meaningful control strategies that target the EPS sugar content and oder product quality parameters

Dynamics Analysis and Prediction of Genetic Regulation in Glycerol Metabolic Network via Structural Kinetic Modelling

Glycerol can be biologically converted to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae. In the synthesis pathway of 1,3-PD, the accumulation of an intermediary metabolite 3-hydroxypropionaldehyde (3-HPA) would cause an irreversible cessation of the dynamic system. Genetic manipulation on the key enzymes which control the formation rate and consumption rate of 3-HPA would decrease the accumulation of 3-HPA, resulting in nonlinear regulation on the dynamic system. The interest of this work is to focus on analyzing the influence of 3-HPA inhibition on the stability of the dynamic system. Due to the lack of intracellular knowledge, structural kinetic modelling is applied. On the basis of statistical account of the dynamical capabilities of the system inthe parameter space,we conclude that, underweak or no inhibition to the reaction of 3-HPAconsumption, the systemismuch easier to obtain a stable state, whereas strong inhibition to its formation is in favor of stabilizing the system. In addition, the existence of Hopf bifurcation in this systemis also verified. The obtained results are helpful for deeply understanding the metabolic and genetic regulations of glycerol fermentation by Klebsiella pneumoniae

Novel strategies for process control based on hybrid semi-parametric mathematical systems

Tese de doutoramento. Engenharia Química. Universidade do Porto. Faculdade de Engenharia. 201

Kinetic models in industrial biotechnology - Improving cell factory performance

An increasing number of industrial bioprocesses capitalize on living cells by using them as cell factories that convert sugars into chemicals. These processes range from the production of bulk chemicals in yeasts and bacteria to the synthesis of therapeutic proteins in mammalian cell lines. One of the tools in the continuous search for improved performance of such production systems is the development and application of mathematical models. To be of value for industrial biotechnology, mathematical models should be able to assist in the rational design of cell factory properties or in the production processes in which they are utilized. Kinetic models are particularly suitable towards this end because they are capable of representing the complex biochemistry of cells in a more complete way compared to most other types of models. They can, at least in principle, be used to in detail understand, predict, and evaluate the effects of adding, removing, or modifying molecular components of a cell factory and for supporting the design of the bioreactor or fermentation process. However, several challenges still remain before kinetic modeling will reach the degree of maturity required for routine application in industry. Here we review the current status of kinetic cell factory modeling. Emphasis is on modeling methodology concepts, including model network structure, kinetic rate expressions, parameter estimation, optimization methods, identifiability analysis, model reduction, and model validation, but several applications of kinetic models for the improvement of cell factories are also discussed