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.     

Feedback stabilization of fed-batch bioreactors: non-monotonic growth kinetics

This paper deals with the design of a feedback controller for fed-batch microbial conversion processes that forces the substrate concentration C(S) to a desired setpoint, starting from an arbitrary (initial) substrate concentration when non-monotonic growth kinetics apply. This problem is representative for a lot of industrial fermentation processes, with the baker's yeast fermentation as a well-known example. It is assumed that the specific growth rate mu is function of the substrate concentration only. A first approach exploits the availability of on-line measurements of both the substrate and biomass concentration. A second approach is merely based on on-line measurements of the biomass concentration, which provide an estimate for the specific growth rate. After a reformulation of the substrate concentration setpoint into a specific growth rate setpoint, it is demonstrated that the fed-batch process can still be stabilized around any desired operating point along the non-monotonic kinetics.     

The tuning of a model-based estimator for the specific growth rate of Candida utilis

Control of microbial conversion processes is frequently inhibited by the infeasibility of measuring important process variables. In order to circumvent this lack of measurements, an accurate or valuable and conveniently measurable on-line hardware measurement can be combined with the balance equations describing the process to obtain estimates of less easily measurable variables. In this article the on-line estimation of the specific growth rate of Candida utilis is evaluated. The observer-based estimator requires a hardware measurement of the biomass during fermentations in conjuction with a model of the process; therefore the Biomass Monitor, giving an on-line measurement of viable biomass, is used in the bioreactor experiments described. The optimal tuning of the estimation for the experimental conditions is described and several alternative adaptations of the design of the estimator are presented. The influence of implemented time intervals for discretization of the estimator on the reliability of the estimated growth rate values is discussed. Additionally, the necessary choice of an initial value of the estimated specific growth rate has proven to be of great importance in practice.     

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.     

Nonlinear observation of specific growth rate in aerobic fermentation processes

Simple nonlinear observers for the on-line estimation of the specific growth rate from presently attainable real-time measurements are presented. The proposed observers do not assume or require any model for the specific growth rate and they are very successful in accurately estimating this parameter. Moreover, they are very easy to implement and to calibrate. Indeed, due to the particular structure of their gain, their tuning is reduced to the calibration of a single parameter. Simulation results obtained under different operating conditions are given in order to highlight the performances of the proposed estimators.     

On the applicability of adaptive bioprocess state estimators

This article presents an industrial case study, examining the application of a novel adaptive biomass estimator to an industrial microfungi production process. It is our intention that this contribution should focus upon the implementation issues of the algorithm, in preference to a rigorous theoretical development. The novel algorithm adopted is developed from Adaptive Inferential Estimation studies of Guilandoust and co-workers. The technique utilizes input-output process measurements obtained at different frequencies, thereby providing more frequent estimates of biomass concentration than are otherwise available from off-line laboratory analyses. The algorithm is particularly suited to the biotechnology industry, as it is capable of utilizing irregular assay measurements with varying delays.Although this article demonstrates the encouraging industrial implications of the adaptive algorithm, like all adaptive techniques currently developed, it is restricted by the inability to perform robust on-line system identification. The ultimate selection of a "suboptimal" "fixed parameter" algorithm for on-line implementation, is therefore directly attributable to these inadequacies. Aspects of data acquisition, data pretreatment, and data quality are critical for real process applications, and while some practical approaches are adopted here, many important implementation problems remain unresolved. (c) 1993 John Wiley & Sons, Inc.     

A predictive and feedback control algorithm maintains a constant glucose concentration in fed-batch fermentations.

A combined predictive and feedback control algorithm based on measurements of the concentration of glucose on-line has been developed to control fed-batch fermentations of Escherichia coli. The predictive control algorithm was based on the on-line calculation of glucose demand by the culture and plotting a linear regression to the next datum point to obtain a predicted glucose demand. This provided a predictive "coarse" control for the glucose-based nutrient feed. A direct feedback control using a proportional controller, based on glucose measurements every 2 min, fine-tuned the feed rate. These combined control schemes were used to maintain glucose concentrations in fed-batch fermentations as tight as 0.49 +/- 0.04 g/liter during growth of E. coli to high cell densities.     

A predictive and feedback control algorithm maintains a constant glucose concentration in fed-batch fermentations

A combined predictive and feedback control algorithm based on measurements of the concentration of glucose on-line has been developed to control fed-batch fermentations of Escherichia coli. The predictive control algorithm was based on the on-line calculation of glucose demand by the culture and plotting a linear regression to the next datum point to obtain a predicted glucose demand. This provided a predictive "coarse" control for the glucose-based nutrient feed. A direct feedback control using a proportional controller, based on glucose measurements every 2 min, fine-tuned the feed rate. These combined control schemes were used to maintain glucose concentrations in fed-batch fermentations as tight as 0.49 +/- 0.04 g/liter during growth of E. coli to high cell densities.     

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.     

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.     

The kinetics of Lagenidium giganteum growth in liquid and solid cultures

AIMS: Production of the mosquito biolarvacide Lagenidium giganteum in solid culture has been proposed as an economic alternative to production in liquid culture because of observations of improved shelf life and efficacy upon storage. Understanding the differences between these production systems and estimating growth rate in solid culture are important for commercialization. In order to address these needs a logistic model was developed to describe the growth kinetics of L. giganteum produced in solid and liquid cultures. METHODS AND RESULTS: Kinetic parameters in the logistic model were estimated by nonlinear regression of CO2 evolution rate (CER) and biomass data from solid and liquid cultivation experiments. Lagenidium giganteum biomass was measured using DNA extracted directly from samples. The logistic model was fit to experimental biomass and CER data with low standard errors for parameter estimates. The model was validated in two independent experiments by examining prediction of biomass using on-line CER measurements. CONCLUSIONS: There were significant differences between maximum biomass density, maintenance coefficients, and specific growth rates for liquid and solid cultures. The maximum biomass density (mg dw ml-1) was 11 times greater for solid cultivation compared with liquid cultivation of L. giganteum; however, the maintenance coefficient (mg CO2 h-1 (mg dw)-1) was six times greater for liquid cultivation than in solid cultivation. The specific growth rate at 30 degrees C was approximately 30% greater in liquid cultivation compared with solid cultivation. Slower depletion of substrate and lower endogenous metabolism may explain the longer shelf life of L. giganteum produced in solid culture. SIGNIFICANCE AND IMPACT OF THE STUDY: A simple logistic model was developed which allows real-time estimation of L. giganteum biomass from on-line CER measurements. Parameter estimates for liquid and solid cultivation models also elucidated observations of longer shelf life for production in solid culture.     

Real-time monitoring and automatic density control of large-scale microalgal cultures using near infrared (NIR) optical density sensors

Signals from near infrared (NIR) light transmittance sensors were used for both real-time monitoring of algal biomass density in growing mass cultures (200l tubular biofences), and also as feedback in a system that controlled the density of the culture by automatic injection of fresh growth medium. When operated in a semi-continuous production mode between predefined density values, diurnal growth patterns were recorded on-line that provided information on the dynamics of the microalgal cultures with respect to environmental conditions. The bioreactor system was also programmed to operate in constant biomass density mode, thereby maintaining the culture at the optimal population density (OPD), and sustaining high biomass production levels. The system has potential for operating a dynamic density set point for microalgal cultures where the optimal population density varies as a function of ambient growing conditions.     

Online automatic tuning and control for fed-batch cultivation

Performance of controllers applied in biotechnological production is often below expectation. Online automatic tuning has the capability to improve control performance by adjusting control parameters. This work presents automatic tuning approaches for model reference specific growth rate control during fed-batch cultivation. The approaches are direct methods that use the error between observed specific growth rate and its set point; systematic perturbations of the cultivation are not necessary. Two automatic tuning methods proved to be efficient, in which the adaptation rate is based on a combination of the error, squared error and integral error. These methods are relatively simple and robust against disturbances, parameter uncertainties, and initialization errors. Application of the specific growth rate controller yields a stable system. The controller and automatic tuning methods are qualified by simulations and laboratory experiments with Bordetella pertussis.     

On-line soft sensing in upstream bioprocessing

This review provides an overview and a critical discussion of novel possibilities of applying soft sensors for on-line monitoring and control of industrial bioprocesses. Focus is on bio-product formation in the upstream process but also the integration with other parts of the process is addressed. The term soft sensor is used for the combination of analytical hardware data (from sensors, analytical devices, instruments and actuators) with mathematical models that create new real-time information about the process. In particular, the review assesses these possibilities from an industrial perspective, including sensor performance, information value and production economy. The capabilities of existing analytical on-line techniques are scrutinized in view of their usefulness in soft sensor setups and in relation to typical needs in bioprocessing in general. The review concludes with specific recommendations for further development of soft sensors for the monitoring and control of upstream bioprocessing.     

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.     

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.     

An algorithmic approach to constructing the on-line estimation system for the specific growth rate

The objective of this article is to propose an algorithm for the on-line estimation of the specific growth rate in a batch or a fed-batch fermentation process. The algorithm shows the practical procedure for the estimation method utilizing the macroscopic balance and the extended Kalman filter. A number of studies of the on line estimation have been presented. However, there are few studies discussing about the selection of the observed variables and for the tuning of some parameters of the extended Kalman filter, such as covariance matrix and initial values of the state.The beginning of this article is devoted to explain the selection of the observed variable. This information is very important in terms of the practical know-how for using technique. It is discovered that the condition number is a practically useful and valid criterion for number is a practically useful and valid criterion for choosing the variable to be observed.Next, when the extended Kalman filter in applied to the online estimation of the specific growth rate, which is directly unmeasurable, criteria for judging the validity of the estimated value from the observed data are proposed. Based on the proposed criterial, the system equation of the specific growth rate is selected and initial value of the state variable and covariance matrix of the system noises are adjusted. From many experiments, it is certified that the specific growth rate in the batch or fed -batch fermentation can be estimated accurately by means of the algorithm proposed here. In these experiments, that is, when the cell concentration is measured directly, the extended Kalman filter using the convariance matrix with a constant element can estimate more accurately values of the specific growth rate than the adaptive extended Kalman filter does.     

Reconfigurable control system design for fault diagnosis and accommodation

The growing demand in system reliability and survivability under failures has urged ever-increasing research effort on the development of fault diagnosis and accommodation. In this paper, the on-line fault tolerant control problem for dynamic systems under unanticipated failures is investigated from a realistic point of view without any specific assumption on the type of system dynamical structure or failure scenarios. The sufficient conditions for system on-line stability under catastrophic failures have been derived using the discrete-time Lyapunov stability theory. Based upon the existing control theory and the modern computational intelligence techniques, an on-line fault accommodation control strategy is proposed to deal with the desired trajectory-tracking problems for systems suffering from various unknown and unanticipated catastrophic component failures. Theoretical analysis indicates that the control problem of interest can be solved on-line without a complete realization of the unknown failure dynamics provided an on-line estimator satisfies certain conditions. Through the on-line estimator, effective control signals to accommodate the dynamic failures can be computed using only the partially available information of the faults. Several on-line simulation studies have been presented to demonstrate the effectiveness of the proposed strategy. To investigate the feasibility of using the developed technique for unanticipated fault accommodation in hardware under the real-time environment, an on-line fault tolerant control test bed has been constructed to validate the proposed technology. Both on-line simulations and the real-time experiment show encouraging results and promising futures of on-line real-time fault tolerant control based solely upon insufficient information of the system dynamics and the failure dynamics.     

A simple model-based control for Pichia pastoris allows a more efficient heterologous protein production bioprocess

A predictive control algorithm coupled with a PI feedback controller has been satisfactorily implemented in the heterologous Rhizopus oryzae lipase production by Pichia pastoris methanol utilization slow (Mut(s)) phenotype. This control algorithm has allowed the study of the effect of methanol concentration, ranging from 0.5 to 1.75 g/L, on heterologous protein production. The maximal lipolytic activity (490 UA/mL), specific yield (11,236 UA/g(biomass)), productivity (4,901 UA/L . h), and specific productivity (112 UA/g(biomass)h were reached for a methanol concentration of 1 g/L. These parameters are almost double than those obtained with a manual control at a similar methanol set-point. The study of the specific growth, consumption, and production rates showed different patterns for these rates depending on the methanol concentration set-point. Results obtained have shown the need of implementing a robust control scheme when reproducible quality and productivity are sought. It has been demonstrated that the model-based control proposed here is a very efficient, robust, and easy-to-implement strategy from an industrial application point of view.     

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.