Stable adaptive algorithm for simultaneous estimation of time-varying parameters and state variables in aerobic bioprocesses

The application of modern model based control algorithms in the bioprocesses is hampered by the lack of accurate and cheap on-line sensors, capable of providing on-line measurements of the main process variables and parameters. In this paper, a new approach for estimation of immeasurable time-varying parameters and state variable is presented for a class of aerobic bioprocesses using only on-line measurements of the oxygen uptake rate. The approach consists in the design of a new parameter estimator of biomass growth rate and yield coefficient for oxygen consumption on the basis of the theory of adaptive estimation. The dynamical equation of the measurable reaction rate, oxygen uptake rate, is presented as a linear one with respect to the biomass growth rate and the yield coefficient for oxygen consumption. In this way, the structure of the proposed estimator becomes linear time-varying one. After some mathematical transformations, that structure is presented in a form, allowing to be derived the stability conditions using some theoretical results concerning the stability of adaptive observers. The estimates of the yield coefficient for oxygen consumption, the biomass concentration and specific growth rate are obtained then on the basis of the generated estimates using well known kinetic models of bioprocesses. With respect to previous similar approaches, the new estimation algorithm gives stable estimates not only of immeasurable state variable and reaction rates but likewise of an yield coefficient. The behavior of the proposed estimator is studied under inexact initial conditions, step changes of dilution rate and in the presence of measurement noise by simulations using a process model, which belongs to the investigated class of bioprocesses.     

State and parameter estimation of microalgal photobioreactor cultures based on local irradiance measurement

Local photosynthetic photon flux fluence rate (PPFFR) determined by a submersible 4pi quantum micro-sensor was used in developing a versatile on-line state estimator for stirred-tank microalgal photobioreactor cultures. A marine micro-alga Dunaliella salina was used as a model organism in this study. On-line state estimation was realized using the extended Kalman filter (EKF), based on a state model of the photobioreactor and on-line local PPFFR measurement. The dynamic state model for the photobioreactor was derived based on mass-balance equations of the relevant states. The measurement equation was established based on an empirical correlation between the microalgal biomass concentration and the local PPFFR measured at a fixed point inside the photobioreactor. An internal model approach was used to estimate the specific growth rate without the need of state-based kinetic expression. The estimator was proven to be capable of estimating biomass concentration and specific growth rate, as well as phosphate and dissolved oxygen concentrations in a photobioreactor illuminated with either fixed or time-varying incident radiation. The quantum sensor was shown to be robust and able to quickly respond to dynamic changes in local PPFFR. In addition, the quantum sensor outputs were not affected by bubble aeration or agitation within the typical operating range. The strong filtering capacity of EKF gives the state estimator superior performance compared to direct calculation from the empirical biomass/local PPFFR correlation. This state estimation system makes use of inexpensive and reliable sensor hardware to report key process dynamics of microalgal photobioreactor cultures on-line, enabling improved operation of such a process.     

Nonlinear estimation of specific growth rate for aerobic fermentation processes

The specific growth rate of the biomass, a very important parameter of almost every fermentation process, cannot be measured directly or estimated from related variables, as the concentrations of biomass, substrates, or products, due to the lack of reliable and cheap sensors. In this article a stable adaptive estimator of the specific growth rate is designed for those aerobic processes where the measurement of the oxygen uptake rate is available on-line. This particular approach can be applied also for other reaction rates if the model of the process satisfies some very general assumptions, which make the dynamics of the measured reaction rate a nonlinear function only of two unknown parameters, the specific growth rate and its time derivative. With respect to a previous similar approach, the new estimator has one additional parameter and a different nonlinear structure. From the analysis of the dynamics of the estimation error, a tuning criterion is derived, by which the two different algorithms can be compared under similar conditions. Simulation results show a good performance of both estimators for various kind of processes and disturbances. (c) 1995 John Wiley & Sons, Inc.     

On-line estimation of the specific growth rate based on viable biomass measurements: experimental validation

The application of model based control techniques to biotechnological processes is often hampered due to the lack of reliable on-line sensors. This problem can be tackled by the application of software sensors, in which the available hardware measurements are combined with the model equations. The resulting estimates serve as additional measurements useful for process monitoring and control. In this paper, an observer based estimator for the specific growth rate based on on-line viable biomass measurements is studied. Several fed-batch experiments with baker's yeast in a stirred tank bioreactor illustrate the design, tuning, and implementation from a practical point of view. The main contributions of this paper are to illustrate (i) the implementation and validation of the presented algorithm in real-time, (ii) the use of an advanced on-line biomass measurement, and (iii) the design and tuning of the algorithm from a practical point of view. Real-time knowledge of the specific growth rate is important because it yields information on the viability of the cells and it can be used in real-time feedback control algorithms.     

Structured modeling and state estimation in a fermentation process: Lipase production by Candida rugosa

A simple structured mathematical model coupled with a methodology of state and parameter estimation is developed for lipase production by Candida rugosa in batch fermentation. The model describes the system according to the following qualitative observations and hypothesis: Lipase production is induced by extracellular oleic acid present in the medium. The acid is transported into the cell where it is consumed, transformed, and stored. Lipase is excreted to the medium where it is distributed between the available oil-water interphase and aqueous phase. Cell growth is modulated by the intracellular substrate concentration. Model parameters have been determined and the whole model validated against experiments not used in their determination. The estimation problem consists in the estimation of three state variables (biomass, intra- and extracellular substrate) and two kinetic parameters by using only the on-line measurement provided by exhaust gas analysis. The presented estimation strategy divides the complex problem into three subproblems that can be solved by stable algorithms. The estimation of biomass (X) and the specific growth rate (mu), is achieved by a recursive prediction error algorithm using the on-line measurement of the carbon dioxide evolution rate. mu is then used to perform an estimation of intracellular substrate and the other kinetic parameter related to substrate transport (A) by an adaptive observer. Extracellular substrate is then evaluated by means of the estimated values of intracellular substrate and biomass through the material balance of the reactor. Simulation and experimental tests showed good performance of the developed estimator, which appears suitable to be used for process control and monitoring. (c) 1995 John Wiley & Sons, Inc.     

Estimation of multiple biomass growth rates and biomass concentration in a class of bioprocesses

In this paper, an approach to the estimation of multiple biomass growth rates and biomass concentration is proposed for a class of aerobic bioprocesses characterized by on-line measurements of dissolved oxygen and carbon dioxide concentrations, as well as off-line measurements of biomass concentration. The approach is based on adaptive observer theory and includes two steps. In the first step, an adaptive estimator of two out of three biomass growth rates is designed. In the second step, the third biomass growth rate and the biomass concentration are estimated, using two different adaptive estimators. One of them is based on on-line measurements of dissolved oxygen concentration and off-line measurement of biomass concentrations, while the other needs only on-line measurements of the carbon dioxide concentration. Simulations demonstrated good performance of the proposed estimators under continuous and batch-fed conditions.     

On-line estimation of biological variables during pH controlled lactic acid fermentations

Indirect measurement of lactose, galactose, lactic acid, and biomass concentration from on-line sodium hydroxide weight measurements have been obtained for pure and mixed batch cultures of Streptococcus salivarius ssp. thermophilus 404 and Lactobacillus delbrueckii subsp. bulgaricus 398 conducted at controlled pH and temperature. Linear correlations were established between the equivalent sodium hydroxide concentration and the lactose (substrate), galactose and lactic acid (products) concentrations while nonlinear relationships were developed between biomass and lactic acid concentrations. These nonlinear relationships took into account the inhibitory effect of lactic acid on growth and acidification. The indirect measurements of biomass concentration were introduced into a nonlinear estimator of the state variables and of the specific growth and lactic acid production rates. Good agreement was found between estimated and measured biomass concentrations (error index ranging from 10.8% to 12.6%). The results showed the feasibility of on-line estimation of biomass concentration and of the specific kinetics from NaOH addition weight measurements and its applicability for monitoring lactic acid fermentations. Using off-line measurements of L(+) and D(-) lactic acid concentrations, the evolution of the concentration of each strain in mixed cultures was obtained from the relationships proposed for the mixed cultures. (c) 1994 John Wiley & Sons, Inc.     

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.     

Real-time monitoring and control of microbial bioprocesses with focus on the specific growth rate: current state and perspectives

Understanding the growth characteristics of microorganisms is an essential step in bioprocessing, not only because product formation may be growth-associated but also because they might influence cell physiology and thereby product quality. The specific growth rate, a key variable of many bioprocesses, cannot be measured directly and relies on the estimation through other measurable variables such as biomass, substrate, or product concentrations. Techniques for real-time estimation of the specific growth rate in microbial fed-batch cultures are discussed in the present paper. The advantages and limitations of different models and various monitoring techniques are discussed, highlighting the importance of the specific growth rate in the development of fast, reliable, and robust processes for the production of high-value products such as recombinant proteins.     

On-line estimation of biodegradation in an unsaturated soil

The objective of this study was to develop a model-based estimator of biodegradation in unsaturated soil. This would allow real-time assessment of the efficiency of treatment bioprocesses, such as bioventilation and biopile, and eventually permit optimization through the implementation of control strategies. Based on a reduced-order model, an asymptotic observer was designed to estimate on-line the contaminant concentration, using carbon dioxide measurement. Two observer-based estimators were built to approximate: (1) the specific microbial growth rate; and (2) the biocontact kinetics representing the soil resistance to contaminant biodegradation. State observers and parameter estimators were confronted with the experimental results of biodegradation in microcosms. Hexadecane was used as the model compound, representing petroleum hydrocarbons. Three water contents, corresponding to 20%, 50% and 80% of the water-holding capacity, were tested. The asymptotic observer is able to predict hexadecane depletion with an error on the overall time trajectories of 13%, 8% and 4% for the dry, intermediate and wet soils, respectively, which is acceptable given that all the biokinetic parameters were identified from a biodegradation experiment in liquid phase. The observer-based estimator of the specific microbial growth rate, based on the CO₂ measurement, was successfully calibrated using the off-line measurements of hexadecane as validation data, and allowed estimation of the time when biodegradation switched from a microbial to a biocontact limitation. The biocontact kinetics was also identified on-line, using an estimator based on the hexadecane not in biocontact. These results are very encouraging with respect to the potential for on-line assessment of the performance of treatment bioprocesses in unsaturated soils.     

On-line estimation of the maximum specific growth rate of nitrifiers in activated sludge systems.

The on-line estimation of the maximum specific growth rate of autotrophic biomass is addressed in this article. A general nitrification process model, which is valid for any realistic flow pattern, is used to develop the estimation algorithm. Depending on the measurements available, two estimation equations are derived. While both require measuring the nitrification activity of the activated sludge, one requires the additional measurement of the nitrifiable nitrogen concentrations at the two ends of the bioreactor, and the other requires the nitrate nitrogen concentrations at the same locations. The algorithm also requires some stoichiometric and kinetic parameters. However, sensitivity analysis shows that the estimate is insensitive to the parameters other than the autotrophic decay rate. Compared to the existing algorithms, the algorithm developed in this article does not rely on the assumption of ideal flow pattern in the plant and does not require an error-prone estimate of the autotrophic biomass concentration. Experimental and simulation studies show that the algorithm performs well and is robust to influent variations and accidental sludge losses.     

Adaptive on-line model for aerobic Saccharomyces cerevisiae fermentation

In order to study and control fermentation processes, indirect on-tine measurements and mathematical models can be used. In this article we present a mathematical on-line model for fermentation processes. The model is based on atom and partial mass balances as well as on equations describing the acid-base system. The model is brought into an adaptive form by including transport equations for mass transfer and unstructured expressions for the fermentation kinetics. The state of the process, i.e., the concentrations of biomass, substrate, and products, can be estimated on-line using the balance part of the model completed with measurement equations for the input and output flows of the process. Adaptivity is realized by means of on-line estimation of parameters in the transport and kinetic expressions using recursive regression analysis. These expressions can thus be used in the model as valid equations enabling prediction of the process. This makes model-based automation of the process and testing of the validity of the measurement variables possible. The model and the on-line principles are applied to a 3.5-L laboratory tormentor in which Saccharomyces cerevisiae is cultivated. The experimental results show that the model-based estimation of the state and the predictions of the process correlate closely with high-performance liquid chromatography (HPLC) analyses. (c) 1995 John Wiley & Sons, Inc.     

Nonlinear predictive control for maximization of CO2 bio-fixation by microalgae in a photobioreactor

In the framework of environment preservation, microalgae biotechnology appears as a promising alternative for CO₂ mitigation. Advanced control strategies can be further developed to maximize biomass productivity, by maintaining these microorganisms in bioreactors at optimal operating conditions. This article proposes the implementation of Nonlinear Predictive Control combined with an on-line estimation of the biomass concentration, using dissolved carbon dioxide concentration measurements. First, optimal culture conditions are determined so that biomass productivity is maximized. To cope with the lack of on-line biomass concentration measurements, an interval observer for biomass concentration estimation is built and described. This estimator provides a stable accurate interval for the state trajectory and is further included in a nonlinear model predictive control framework that regulates the biomass concentration at its optimal value. The proposed methodology is applied to cultures of the microalgae Chlorella vulgaris in a laboratory-scale continuous photobioreactor. Performance and robustness of the proposed control strategy are assessed through experimental results.     

Monitoring of fed-batch <Emphasis Type="Italic">E. coli</Emphasis> fermentations with software sensors

Accurate monitoring and control of industrial bioprocess requires the knowledge of a great number of variables, being some of them not measurable with standard devices. To overcome this difficulty, software sensors can be used for on-line estimation of those variables and, therefore, its development is of paramount importance. An Asymptotic Observer was used for monitoring Escherichia coli fed-batch fermentations. Its performance was evaluated using simulated and experimental data. The results obtained showed that the observer was able to predict the biomass concentration profiles showing, however, less satisfactory results regarding the estimation of glucose and acetate concentrations. In comparison with the results obtained with an Extended Kalman Observer, the performance of the Asymptotic Observer in the fermentation monitoring was slightly better.     

Generally applicable fed-batch culture concept based on the detection of metabolic state by on-line balancing

In many microorganisms, flux limitations in oxidative metabolism lead to the formation of overflow metabolites even under fully aerobic conditions. This can be avoided if the specific growth rate is controlled at a low enough value. This is usually accomplished by controlling the substrate feeding profile in a fed-batch process. The present work proposes a control concept which is based on the on-line detection of metabolic state by on-line calculation of mass and elemental balances. The advantages of this method are: 1) the check of measurement consistency based on all of the available measurements, 2) the minimum requirement of a priori knowledge of metabolism, and 3) the exclusive use of simple and established on-line techniques which do not require direct measurement of the metabolite in question. The control concept has been linked to a simple adaptive controller and applied to fed-batch cultures of S. cerevisiae and E. coli, organisms which express different overflow metabolites, ethanol and acetic acid, respectively. Oxidative and oxidoreductive states of S. cerevisiae and E. coli cultures were detected with high precision. As demonstrated by the formation of acetic acid in E. coli cultures, metabolic states could be correctly distinguished for systems for which traditional methods, such as respiratory quotient (RQ), are insensitive. Hence, it could be shown that the control concept allowed avoidance of overflow metabolite formation and operation at maximum oxidative biomass productivity and oxidative conversion of substrate into biomass. Based on mass and elemental balances, the proposed method additionally provides a richness of additional information, such as yield coefficients and estimation of concentrations and specific conversion rates. These data certainly help the operator to additionally evaluate the state of the process on-line.     

Evaluation of on-line viable biomass measurements during fermentations of Candida utilis

In this article the suitability of the Biomass Monitor for on-line measurement of viable biomass is thoroughly evaluated during aerobic fermentations of Candida utilis. Successively a number of specifications of the measuring device are discussed for the studied biological system. The optimal measurement frequency for the given experimental conditions is determined. Furthermore, reliable calibrations of the capacitance readings versus well-known off-line analysis of dry weight and plate counts of the yeast have been established. In addition, the impact of varying fermentation conditions such as stirrer speed and air flow rate together with the influence of the oxygen concentration and conductance of the medium on the capacitance signal have been studied and quantified when a significant influence was observed. It is illustrated that knowledge of the viable biomass during fermentations is very useful in the estimation of the specific growth rate of the organism.     

An artificial neural network for biomass estimation from automatic pH control signal

This study developed an artificial neural network (ANN) to estimate the growth of microorganisms during a fermentation process. The ANN relies solely on the cumulative consumption of alkali and the buffer capacity, which were measured on-line from the on/off control signal and pH values through automatic pH control. The two input variables were monitored on-line from a series of different batch cultivations and used to train the ANN to estimate biomass. The ANN was refined by optimizing the network structure and by adopting various algorithms for its training. The software estimator successfully generated growth profiles that showed good agreement with the measured biomass of separate batch cultures carried out between at 25 and 35_C.     

Product formation kinetics in genetically modified <Emphasis Type="Italic">E. coli </Emphasis>bacteria: inclusion body formation

A data-driven model is presented that can serve two important purposes. First, the specific growth rate and the specific product formation rate are determined as a function of time and thus the dependency of the specific product formation rate from the specific biomass growth rate. The results appear in form of trained artificial neural networks from which concrete values can easily be computed. The second purpose is using these results for online estimation of current values for the most important state variables of the fermentation process. One only needs online data of the total carbon dioxide production rate (tCPR) produced and an initial value x of the biomass, i.e., the size of the inoculum, for model evaluation. Hence, given the inoculum size and online values of tCPR, the model can directly be employed as a softsensor for the actual value of the biomass, the product mass as well as the specific biomass growth rate and the specific product formation rate. In this paper the method is applied to fermentation experiments on the laboratory scale with an E. coli strain producing a recombinant protein that appears in form of inclusion bodies within the cells’ cytoplasm.     

Multi-rate nonlinear state and parameter estimation in a bioreactor

This paper concerns real-time, multi-rate, nonlinear state and parameter estimation in a pilot-scale biochemical reactor in which cultivation of mouse-mouse hybridoma cells takes place. A multi-rate estimator is designed and implemented to estimate specific growth rate and concentrations of viable cells, total cells, glucose, glutamine, and monoclonal antibodies (MAb) in the reactor. These are estimated from frequent measurement (inferred values) of oxygen uptake rate (OUR) and infrequent and delayed measurements of the concentrations of viable cells, total cells, glucose, glutamine, and MAb. The infrequent measurements are available every 2 to 17 h with a time delay of 0.08 to 2.00 h, and OUR is inferred from dissolved oxygen concentration measurements that are available very 0.17 h. For each of the process variables, its infrequent measurement data and the profile of its estimate are presented to show the performance of the multi-rate estimator.     

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.