An on-line physiological state recognition system for the lysine fermentation process based on a metabolic reaction model

A metabolic reaction model was developed for the lysine fermentation process by Corynebacterium glutamicum AJ-3462 to estimate the physiological state of the cells-that is, the growth and production activity, and the flux distribution of metabolites-from on-line measurable rates only. First, the extended Kalman filter was applied to eliminate noise in the measured rates. Then, using the metabolic reaction model, the lysine production rate and flux distribution were calculated. The estimation results allowed the physiological state of lysine production to be recognized, and an appropriate measure corresponding to the estimated state, such as intermittent addition of glucose and/or leucine, to be taken to maintain a high level of lysine productivity in batch culture. Finally, application of the recognition system enabled lysine to be produced from glucose at a higher yield than that from glucose- or leucine-limited exponential fed-batch cultures. (c) 1997 John Wiley & Sons, Inc. Biotechnol Bioeng 55: 170-181, 1997.     

Online nonlinear sequential Bayesian estimation of a biological wastewater treatment process

Online estimation of unknown state variables is a key component in the accurate modelling of biological wastewater treatment processes due to a lack of reliable online measurement systems. The extended Kalman filter (EKF) algorithm has been widely applied for wastewater treatment processes. However, the series approximations in the EKF algorithm are not valid, because biological wastewater treatment processes are highly nonlinear with a time-varying characteristic. This work proposes an alternative online estimation approach using the sequential Monte Carlo (SMC) methods for recursive online state estimation of a biological sequencing batch reactor for wastewater treatment. SMC is an algorithm that makes it possible to recursively construct the posterior probability density of the state variables, with respect to all available measurements, through a random exploration of the states by entities called ‘particle’. In this work, the simplified and modified Activated Sludge Model No. 3 with nonlinear biological kinetic models is used as a process model and formulated in a dynamic state-space model applied to the SMC method. The performance of the SMC method for online state estimation applied to a biological sequencing batch reactor with online and offline measured data is encouraging. The results indicate that the SMC method could emerge as a powerful tool for solving online state and parameter estimation problems without any model linearization or restrictive assumptions pertaining to the type of nonlinear models for biological wastewater treatment processes.     

Estimation of specific growth rate from cell density measurements

For modelling purposes it is of great importance to derive the specific growth rate as a function of time from biomass measurements. Traditional methods such as exponential or polynomial fitting do not give satisfactory results nor do these methods take the noise characteristics of the biomass measurements into account. Standard recursive techniques, such as Kalman filtering, use only the data up to the time under consideration and are dependent of a good initial estimation. This paper describes a technique based on combining subsequent backward and forward extended Kalman filtering to give a smoothing estimator for the specific growth rate. The estimator does not need an initial value and is shown to have a single tuning parameter. The applicability of the estimator is demonstrated on batch and fed-batch cultivations of two organisms: Bordetella pertussis and Neisseria meningitidis.     

A maximum production strategy of lysine based on a simplified model derived from a metabolic reaction network

The aim of this study is to develop a strategy for maximum production of a target product with a simplified model derived from a metabolic reaction network through an example of lysine production. Based on the model, a search for the optimal specific growth rate profile was conducted among the available conditions of batch fermentation based on the derived model, when the total fermentation time was fixed. The optimal specific growth rate was obtained as a boundary control: initially, the specific growth rate was maintained at a maximum value and was subsequently switched to a critical value giving the maximum specific production rate. To make the specific growth rate follow this optimal profile as accurately as possible in batch mode, first, an appropriate initial concentration of leucine was employed in the experiment. Second, the feeding strategy of leucine was further studied. The specific growth rate profile with feeding was closer to the optimal one and the amount of lysine produced at the final stage of fermentation was increased about twofold, compared to that in the batch fermentation. Finally, the strategy was summarized as an algorithm for general use of this method.     

Multirate state and parameter estimation in an antibiotic fermentation with delayed measurements

This article discusses issues related to estimation and monitoring of fermentation processes that exhibit endogenous metabolism and time-varying maintenance activity. Such culture-related activities hamper the use of traditional, software sensor-based algorithms, such as the extended kalman filter (EKF). In the approach presented here, the individual effects of the endogenous decay and the true maintenance processes have been lumped to represent a modified maintenance coefficient, m(c). Model equations that relate measurable process outputs, such as the carbon dioxide evolution rate (CER) and biomass, to the observable process parameters (such as net specific growth rate and the modified maintenance coefficient) are proposed. These model equations are used in an estimator that can formally accommodate delayed, infrequent measurements of the culture states (such as the biomass) as well as frequent, culture-related secondary measurements (such as the CER). The resulting multirate software sensor-based estimation strategy is used to monitor biomass profiles as well as profiles of critical fermentation parameters, such as the specific growth for a fed-batch fermentation of Streptomyces clavuligerus. (c) 1994 John Wiley & Sons, Inc.     

Robust and reliable estimation via recursive nonlinear dynamic data reconciliation based on cubature Kalman filter

Since measurements of process variables are subject to measurements errors as well as process variability, data reconciliation is the procedure of optimally adjusting measured date so that the adjusted values obey the conservation laws and constraints. Thus, data reconciliation for dynamic systems is fundamental and important for control, fault detection, and system optimization. Attempts to successfully implement estimators are often hindered by serve process nonlinearities, complicated state constraints, and un-measurable perturbations. As a constrained minimization problem, the dynamic data reconciliation is dynamically carried out to product smoothed estimates with variances from the original data. Many algorithms are proposed to solve such state estimation such as the extended Kalman filter (EKF), the unscented Kalman filter, and the cubature Kalman filter (CKF). In this paper, we investigate the use of CKF algorithm in comparative with the EKF to solve the nonlinear dynamic data reconciliation problem. First we give a broad overview of the recursive nonlinear data dynamic reconciliation (RNDDR) scheme, then present an extension to the CKF algorithm, and finally address the issue of how to solve the constraints in the CKF approach. The CCRNDDR method is proposed by applying the RNDDR in the CKF algorithm to handle nonlinearity and algebraic constraints and bounds. As the sampling idea is incorporated into the RNDDR framework, more accurate estimates can obtained via the recursive nature of the estimation procedure. The performance of the CKF approach is compared with EKF and RNDDR on nonlinear process systems with constraints. The conclusion is that with an error optimization solution of the correction step, the reformulated CKF shows high performance on the selection of nonlinear constrained process systems. Simulation results show the CCRNDDR is an efficient, accurate and stable method for real-time state estimation for nonlinear dynamic processes.     

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.     

Modelling oscillatory behavior in batch fermentations

A batch fermentation is modelled with constant and variable yeild terms. It is shown that the model cannot exhibit oscillations if a constant yield term is used. Oscillations in the cell concentration, but not in the limiting substrate concentration, can be simulated if a variable yield function of the limiting substrate is used. Conditions, for which the variable yield needs to satisfy in order to generate oscillations in the cell concentration, are discussed. The primary condition is that the yield must become zero at the same time that the specific growth rate does. Experimental results exhibiting oscillatory behavior are presented and compared with the proposed model.     

State estimation of a Uricase production process with Candida Utilis

The present work discusses the implementation of a Kalman filtering procedure in a state estimation of a batch Uricase production process with Candida Utilis. An unstructured model of the process is used for the estimation procedure. The observability is thoroughly investigated and a Kalman filter is applied afterwards as a powerful and precise state estimation tool. The estimates in all cases of observability are presented, compared and discussed.     

Optimal production of glutathione by controlling the specific growth rate of yeast in fed-batch culture

The optimal of the specific growth rate was obtained with simple mathematical model in a yeast fed-batch cultures. The model was based on the mass balance around the fed-batch system and the relationship between the specific growth rate, mu, and the specific production rate of glutathione, rho(G). The optimal profile of mu was calculated as a bang-bang type, That is mu, should start from the maximum value, mu(max) and should be kept at mu(max); then mu should be switched to mu(c), which gives a maximum value of rho(G). It was proven from the maximum principle that switching was needed only once, with the switching time from mu(max) to mu(c) depending on the final required glutathione content. Finally, this ideal profile of mu for the maximum production of glutathione was realized by manipulating the substrates feed rate in the fed-batch culture. Using the extended Kalman filter and a programmed-controller/feedback-compensator (PF) system, mu could be controlled at the optimal profile obtained. As a result, the maximum production of glutathione was accomplished fairly successfully. However, further improvement in the controller performance for mu is desired. The control strategy employed here can be applied to other batch reaction processes.     

General characteristics of optimal feed rate profiles for various fed-batch fermentation processes

General Characteristics of the optimal feed rate profiles have been deduced for various fed-batch fermentation processes by analyzing singular controls and singular arcs. The optimal control sequences depend on the shapes of the specific growth and product formation rates, mu andpi, and the initial conditions. For fed-batch processes described by four mass balance equations, the most general optimal control sequence consists of a period of maximum feed rate, a period of minimum feed rate (a batch period), a period of singular feed rate (variable and intermediate), and a batch period. Degenerate sequences in which one or more periods are missing can result with a particular set of initial conditions. If the fermentation time is not critical, the singular control maximizes the net yield of product and only when the time is also important, it balances a trade off between the yield of product and the specific growth rate which dictates the fermentation time. With the sequence of optimal control known, the optimal feed rate profile determination is reduced to a problem of determining switching times.     

Reaction rate reconstruction from biomass concentration measurement in bioreactors using modified second-order sliding mode algorithms

This paper deals with the estimation of unknown signals in bioreactors using sliding observers. Particular attention is drawn to estimate the specific growth rate of microorganisms from measurement of biomass concentration. In a recent article, notions of high-order sliding modes have been used to derive a growth rate observer for batch processes. In this paper we generalize and refine these preliminary results. We develop a new observer with a different error structure to cope with other types of processes. Furthermore, we show that these observers are equivalent, under coordinate transformations and time scaling, to the classical super-twisting differentiator algorithm, thus inheriting all its distinctive features. The new observers' family achieves convergence to time-varying unknown signals in finite time, and presents the best attainable estimation error order in the presence of noise. In addition, the observers are robust to modeling and parameter uncertainties since they are based on minimal assumptions on bioprocess dynamics. In addition, they have interesting applications in fault detection and monitoring. The observers performance in batch, fed-batch and continuous bioreactors is assessed by experimental data obtained from the fermentation of Saccharomyces Cerevisiae on glucose.     

Stoichiometry of carbohydrate fermentation and microbial growth efficiency in a continous culture of mixed rumen bacteria

Summary A population of mixed rumen bacteria was maintained in a chemostat at four different dilution rates, with glocose as the growth limiting carbon and energy substrate. Increasing the dilution rate shifted the proportions of end products: methane decreased and propionate increased. Fermentation and hydrogen balances were calculated from the fermentation end products. Values were similar to earlier ones from batch incubations of rumen contents. This suggests that theoretical overall reaction schemes for carbohydrate fermentation in the rumen, proposed earlier, are also valid in continuous culture.A positive correlation between dilution rate and microbial growth efficiency (gN_inc./kg OM_f was observed, confirming earlier work.Apparently conflicting results of chemostat work and recent in vivo experiments are discussed.     

Phenol degradation by Ralstonia eutropha: colorimetric determination of 2-hydroxymuconate semialdehyde accumulation to control feed strategy in fed-batch fermentations.

Phenol biodegradation by Ralstonia eutropha was modeled in different culture modes to assess phenol feeding in biotechnological depollution processes. The substrate-inhibited growth of R. eutropha was described by the Haldane equation with a Ks of 2 mg/L, a Ki of 350 mg/L and a mumax of 0.41 h(-1). Furthermore, growth in several culture modes was characterized by the appearance of a yellow color, due to production of a metabolic intermediate of the phenol catabolic pathway, 2-hydroxymuconic semialdehyde (2-hms) which was directly correlated to the growth rate and/or the phenol-degradation rate, because these two parameters are coupled (as seen by the constant growth yield of 0.68 g biomass/g phenol whatever the phenol concentration). This correlation between color appearance and metabolic activity was used to develop a control procedure for optimal phenol degradation. A mass-balance equation modeling approach combined with a filtering step using an extended Kalman filter enabled state variables of the biological system to be simulated. A PI controller, using the estimation of the phenol concentration provided by the modeling step, was then built to maintain the phenol concentration at a constant set-point of 0.1 g/L which corresponded to a constant specific growth rate of 0.3 h(-1), close to the maximal specific growth value of the strain. This monitoring strategy, validated for two fed-batch cultures, could lead, in self-cycling fermentation systems, to a productivity of more than 19 kg of phenol consumed/m(3)/d which is the highest value reported to date in the literature. This system of monitoring metabolic activity also protected the bacterial culture against toxicity problems due to the transient accumulation of phenol.     

Fermentation kinetics of spent sulfite liquor by Saccharomyces cerevisiae

The growth kinetics of the yeast Saccharomyces cerevisiae and the production rate of ethanol have been studied in batch fermentation under anaerobic conditions in a 20-L fermentor. Two substrates were used in fermentation trials: a synthetic mixture of three fermentable sugars, D-glucose, D-mannose, and D-galactose, and a low-yield liquor originating from a bisulfite cooking process. The Monod model adequately described the system in relation to the specific growth rate mu(x) and the specific product formation rate mu(P). Different fermentation parameters (growth rate, substrate utilization, and product formation) were determined for the synthetic mixture and the bisulfite liquor. It was observed that the specific growth rate is much lower in spent sulfite liquor than in a synthetic medium. However, the specific product formation rate remains the same in both media.     

Joint estimation in batch culture by using unscented kalman filter

The disturbances caused by uncertain factors are inevitable in microbial fermentation. In this paper, we study the joint estimation problem for state and parameter in the bio-dissimulation process of glycerol to 1,3-PD in batch culture. Based on the nonlinear stochastic dynamic system model, we establish the corresponding iteration equations of Joint Unscented Kalman Filter (UKF) by referring to the Extended Kalman Filter (EKF), which is generally applied in microbial fermentation. Through numerical computation, both the state estimations and the uncertain model parameter estimations are obtained. Furthermore, the results of different parameter identification methods are compared. The results show that Joint UKF is more feasible for the process of controlling the glycerol fermentation.     

Profile control of the specific growth rate in fed-batch experiments

Summary The aim of this paper is to apply a computer control scheme to a laboratory scale fermentor so that the specific growth rate in a baker's yeast fed-batch culture, which cannot be measured directly, will follow as accurately as possible the desired profile specified in advance. Using an extended Kalman filter and programmed controller/feedback compensator (PF) system proposed previously, profile control of the specific growth rate () was achieved experimentally in a baker's yeast fed-batch culture. Also, bang-bang type profile control of minimized the proportion of budding cells, which have a strong correlation with the fermentative activity in bread-making.     

Using the Kalman filter and dynamic models to assess the changing HIV/AIDS epidemic

Many factors, including therapy and behavioral changes, have modified the course of the HIV/AIDS epidemic in recent years. To include these modifications in HIV/AIDS models, in the absence of appropriate external data sources, changes over time in the parameters can be incorporated by a recursive estimation technique such as the Kalman filter. The Kalman filter accounts for stochastic fluctuations in both the model and the data and provides a means to assess any parameter modifications included in new observations. The Kalman filter approach was applied to a simple differential model to describe the observed HIV/AIDS epidemic in the homo/bisexual male community in Paris (France). This approach gave quantitative information on the time-evolution of some parameters of major epidemiological significance (average transmission rate, mean incubation rate, and basic reproduction rate), which appears quite consistent with the recent epidemiological literature.     

An adaptive state estimator for detecting contaminants in bioreactors

An algorithm is presented for detecting the appearance of contaminants during batch or fed-batch fermentations, using only presently available on-line measurements. Its adaptive nature enables it to rely on almost no prior knowledge of the real process. The necessary on-line measurements are total biomass and its production rate; it is also shown how a physical variable such as oxygen uptake can be used alone instead. The algorithm's properties are studied theoretically and through simulations. These were confirmed by on-line experimental results, obtained with a Yeast culture, both pure and contaminated by a Bacteria. The algorithm does not detect contaminants when none are there, and it also provides a convergent estimate of a pure culture's specific growth rate. Contaminated cultures are recognized by the algorithm, and this detection can be made more or less conservative. After detection, the various estimates may diverge, due to general observability difficulties, though this divergence can itself be monitored. Moreover, the algorithm is easy to tune and its qualitative behavior is quite insensitive to its adjustable parameters. A practical criterion and scheme for implementation are proposed. The generality of the approach, which far exceeds the experimental system used, is finally discussed.