Optimal nonsingular control of fed-batch fermentation

Presented is a new simple method for multidimensional optimization of fed-batch fermentations based on the use of the orthogonal collocation technique. Considered is the problem of determination of optimal programs for fermentor temperature, substrate concentration in feed, feeding profile, and process duration. By reformulation of the state and control variables is obtained a nonsingular form of the optimization problem which has considerable advantage over the singular case since a complicated procedure for determination of switching times for feeding is avoided. The approximation of the state variables by Lagrange polynomials enables simple incorporation of split boundary conditions in the approximation, and the use of orthogonal collocations provides stability for integration of state and costate variables. The interpolation points are selected to obtain highest accuracy for approximation of the objective functional by the Radau-Lobatto formula. The control variables are determined by optimization of the Hamiltonian at the collocation points with the DFP method. Constraints are imposed on state and control variables.The method is applied for a homogeneous model of fermentation with volume, substrate, biomass, and product concentrations as the state variables. Computer study shows considerable simplicity of the method, its high accuracy for low order of approximation, and efficient convergence.     

Feedback optimization of fed-batch fermentation

The problem of feedback optimization of the feed rate for fed-batch fermentation processes is formulated in the framework of singular control theory and switching hypersurfaces. Using four differential balance equations that describe a general class of fedbatch processes and a general objective function to be minimized, it is shown that under certain restrictions the feedback optimization of the feed rate can be realized as a nonlinear function of the state variables, such as the concentrations of cell mass, substrate and product, and the fermentor volume. The restrictions on the initial conditions, the fermentation kinetics and the objective function, that are needed for realization of the feedback optimization, are provided. Fed-batch fermentation models of lysine and alcohol are used to construct switching curves and to illustrate the feedback optimization of the feed flow rates.     

A heuristic approach to fed-batch optimisation of streptokinase fermentation

Previous studies have shown that the rate of formation of streptokinase, a secondary metabolite, in batch fermentation is proportional to the specific growth rate of the biomass, which in turn is inhibited by its substrate and the primary product (lactic acid). These kinetics suggest the suitability of fed-batch operation to increase the yield of streptokinase. A near-optimal feed policy has been calculated by the chemotaxis algorithm, and it shows a substrate feed rate decreasing nonlinearly and vanishing after 11 hours. This is followed by batch fermentation for a further 8 hours, at the end of which 12% more streptokinase is generated than by purely batch fermentation. Further improvements in productivity are possible.List of Symbols k _dh^–1 decay constant for active cells - k _ph^–1 decay constant for streptokinase - K _Igl^–1 inhibition constant for lactic acid - K_S gl^–1 inhibition constant for substrate - M gl^–1 lactic acid concentration - P gl^–1 streptokinase concentration - Q 1h^–1 substrate feed rate - S gl^–1 substrate concentration - S _ingl^–1 inlet concentration of substrate - t h time - t _bh end-point of batch fermentation - t _fh end-point of fed-batch fermentation - V l volume of broth in fermenter - V ₀ l initial value of V (at t=0) - V _ml maximum value of V - X gl^–1 total biomass concentration - X _agl^–1 concentration of active biomass - Y _MX yield coefficient for lactic acid from biomass - Y _PX yield coefficient for streptokinase from biomass - Y _XS yield coefficient for biomass from substrate Greek Letters h^–1 specific growth rate of biomass - _mh^–1 maximum specific growth rate     

A nonsingular optimization approach to the feed rate profile optimization of fedbatch cultures

A new method to calculate the optimal feed rate profile for fedbatch culture is proposed. Instead of the usual singular control approach of taking the feed rate as the control variable, the substrate concentration profile is used as the transformed control variable to avoid the computational difficulty associated with the singular control. Thus, the problem is converted into a nonsingular optimization problem of determining the optimal substrate concentration profile subject to a constraint. The equivalent feed rate profile to match the optimal substrate concentration profile is then generated. With this method the computational difficulty associated with singular controls for high-order systems is circumvented. The proposed method is illustrated by a number of examples.     

On-line control of fed-batch fermentation of dilute-acid hydrolyzates

Dilute-acid hydrolyzates from lignocellulose are, to a varying degree, inhibitory to yeast. In the present work, dilute-acid hydrolyzates from spruce, birch, and forest residue, as well as synthetic model media, were fermented by Saccharomyces cerevisiae in fed-batch cultures. A control strategy based on on-line measurement of carbon dioxide evolution (CER) was used to control the substrate feed rate in a lab scale bioreactor. The control strategy was based solely on the ratio between the relative increase in CER and the relative increase in feed rate. Severely inhibiting hydrolyzates could be fermented without detoxification and the time required for fermentation of moderately inhibiting hydrolyzates was also reduced. The feed rate approached a limiting value for inhibiting media, with a corresponding pseudo steady-state value for CER. However, a slow decrease of CER with time was found for media containing high amounts of 5-hydroxymethyl furfural (HMF). The success of the control strategy is explained by the conversion of furfural and HMF by the yeast during fed-batch operation. The hydrolyzates contained between 1.4 and 5 g/l of furfural and between 2.4 and 6.5 g/l of HMF. A high conversion of furfural was obtained (between 65-95%) at the end of the feeding phase, but the conversion of HMF was considerably lower (between 12-40%).     

Comparative evaluation of various control schemes for fed-batch fermentation

The crucial problem associated with control of fed-batch fermentation process is its time-varying characteristics. A successful controller should be able to deal with this feature in addition to the inherent nonlinear characteristics of the process. In this work, various schemes for controlling the glucose feed rate of fed-batch baker's yeast fermentation were evaluated. The controllers evaluated are fixed-gain proportional-integral (PI), scheduled-gain PI, adaptive neural network and hybrid neural network PI. The difference between the specific carbon dioxide evolution rate and oxygen uptake rate (Q_c-Q_o) was used as the controller variable. The evaluation was carried out by observing the performance of the controllers in dealing with setpoint tracking and disturbance rejection. The results confirm the unsatisfactory performance of the conventional controller where significant oscillation and offsets exist. Among the controllers considered, the hybrid neural network PI controller shows good performance.     

Modeling and advanced control of recombinant Zymomonas mobilis fed-batch fermentation

This work presents the development of an unstructured kinetic model incorporating the differing degrees of product, substrate, and pH inhibition on the kinetic rates of ethanol fermentation by recombinant Zymomonas mobilis CP4:pZB5 for growth on two substrates. Product inhibition was observed to start affecting the specific growth rate at an ethanol concentration of 20 g/L and the specific productivity at about 35-40 g/L. Specific growth rate was also shown to be more sensitive to inhibition by lowered pH as well. A model for the inhibition of two competing substrates' cellular uptake via membrane transport is proposed. Inhibition functions and model parameters were determined by fitting experimental data to the model. The model was utilized in a nonlinear model predictive control (NMPC) algorithm to control the product concentration during fed-batch fermentation to offset the inhibitory effects of product inhibition. Using the optimal feeding policy determined online, the volumetric productivity of ethanol was improved 16.6% relative to the equivalent batch operation when the final ethanol concentration was reached.     

On-line adaptive control of a fed-batch fermentation of Saccharomyces cerevisiae

The feasibility of applying an adaptive control technique to a fermentation process is investigated. The nonlinear, time-variant parameters of a fermentation process were estimated on-line as a series of linearized describing matrices. The matrices were used to update a suboptimal feedback law which controlled the process in real time over the linear region. Experiments were performed on a small-scale fully instrumented fermenter with the online, real-time adaptive control package. Results are presented for both single- and multivariable control, and indicate successful control of yeast cell growth.     

Experimental optimization of a real time fed-batch fermentation process using Markov decision process

This article describes a methodology that implements a Markov decision process (MDP) optimization technique in a real time fed-batch experiment. Biological systems can be better modeled under the stochastic framework and MDP is shown to be a suitable technique for their optimization. A nonlinear input/output model is used to calculate the probability transitions. All elements of the MDP are identified according to physical parameters. Finally, this study compares the results obtained when optimizing ethanol production using the infinite horizon problem, with total expected discount policy, to previous experimental results aimed at optimizing ethanol production using a recombinant Escherichia coli fed-batch cultivation. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 317-327, 1997.     

分批补料对木糖发酵生产乙醇的影响

以树干毕赤酵母为发酵菌种,纯木糖为发酵底物,通过分批补料来提高糖利用率以及乙醇得率。结果表明,在24h内,最佳初始木糖浓度为80g/L,在28h的发酵周期中,可以将木糖浓度提高至90g/L,在32h发酵周期内可以将木糖浓度提高至100g/L。通过分批补料,乙醇浓度得到明显提高。当总糖浓度分别为80g/L、90g/L时,24h发酵周期内,分批补料次数以1次为宜,乙醇浓度分别达30.95g/L、32.60g/L,相比于不补料即一次性投料,乙醇浓度分别提高了9.36%、9.18%。总糖浓度100g/L,28h发酵周期内,补料2次效果最佳,乙醇浓度达37.49g/L,比一次性投料下提高了10.36%,较一次性投料达到相同发酵效果缩短了4h。     

Optimized pulse-feeding fed-batch fermentation for enhanced lignin to polyhydroxyalkanoate transformation

With an anticipated growth of Bio-Circular-Green economy, the amount of lignin generated as by-product from biorefineries is increasing. Hence, lignin valorising strategies become a very interesting option to improve economic viability of the biorefineries. This study revealed the development of bioprocesses for upgrading lignin into bioplastic. Specifically, a novel strain of Pseudomonas fulva has been applied for microbial bioconversion of organosolv lignin to fermentative polyhydroxyalkanoate (PHA) production. Fed-batch fermentation of lignin-to-PHA with pulse-feeding approach was optimized using Design of Experiment. Effects of C:N ratio and feeding profiles on PHA accumulation in P. fulva were investigated to determine optimal operation. Under optimized fed-batch, the PHA concentration of 195.2 ± 6.6 mg/L could be reached and the PHA content was more than 2 folds enhancement compared to batch process. Type of PHA produced was also characterized for chemical composition via GC–MS analysis. The established lignin to PHA conversion could provide platform for developing integrated lignin bioprocessing to promote cost-effective biorefineries.     

Simple control of fed-batch processes for recombinant protein production with E. coli

A very simple but effective process control technique is proposed that leads to a high batch-to-batch reproducibility with respect to biomass concentration as well as the specific biomass growth rate profiles in E. coli fermentations performed during recombinant protein production. It makes use of the well-established temperature controllers in currently used fermenters, but takes its information from the difference between the controlled culture temperature T (cult) and the temperature T (coolin) of the coolant fed to the fermenter's cooling jacket as adjusted by the fermenter temperature controller. For process control purposes this measured difference is corrected regarding stirrer influences and cumulated before it is used as a new process control variable. As a spin-off of this control, it becomes possible to estimate online the oxygen mass transfer rates and the corresponding k(L)a values during the real cultivation process.     

Production of pullulan by a fed-batch fermentation

Summary In pullulan production from sucrose byAureobasidium pullulans, a sugar concentration higher than 5% (w/v) inhibited cell growth and the production of exopolysaccharide. By a fed-batch fermentation, the inhibitory effects of the high sugar concentration were overcome and 58.0 g/1 of exopolysaccharide were obtained from 10% sucrose.Abbreviations m, n relationship parameters for the growth and non-growth associated product formation - X, Xmax biomass and maximum biomass concentration (g cell/1) - P product concentration (g exopolysaccharide/1) - specific growth rate of cell (hr^–1)     

Process monitoring of an industrial fed-batch fermentation

Market demand places great emphasis in industry on product quality. Consequently, process monitoring and control have become important aspects of systems engineering. In this article we detail the results of a 2-year study focusing on the development of a condition monitoring system for a fed-batch fermentation system operated by Biochemie Gmbh in Austria. We also demonstrate the suitability and limitations of current state of the art technologies in this field and suggest novel modifications and configurations to improve their suitability for application to a fed-batch fermentation system.     

Segregation to non-dividing cells in recombinant Escherichia coli fed-batch fermentation processes

In Escherichia coli fermentation processes, a drastic drop in viable cell count as measured by the number of colony forming units per ml (c.f.u. ml(-1)) is often observed. This phenomenon was investigated in a process for the production of the recombinant fusion protein, promegapoietin (PMP). After induction, the number of c.f.u. ml(-1) dropped to approximately 10% of its maximum though the biomass concentration continued to increase. Flow cytometric analysis of viability and intracellular concentration of PMP showed that almost all cells were alive and contributed to the production. Thus, the drop in the number of c.f.u. ml(-1) probably reflects a loss of cell division capability rather than cell death.     

Repeated fed-batch fermentation using biosensor online control for citric acid production by Yarrowia lipolytica

Biosensor-controlled substrate feeding was used in a citric acid production process with the yeast strain Yarrowia lipolytica H222 with glucose as the carbon source. The application of an online glucose biosensor measurement facilitated the performance of long-time repeated fed-batch process with automated bioprocess control. Ten cycles of repeated fed-batch fermentation were carried out in order to validate both the stability of the microorganism for citric acid production and the robustness of the glucose biosensor in a long-time experiment. In the course of this fermentation with a duration of 553 h, a slight loss of productivity from 1.4 g/(L×h) to 1.1 g/(L×h) and of selectivity for citric acid from 91% to 88% was observed. The glucose biosensor provided 6,227 measurements without any loss of activity.