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.     

Unstable steady state operations of substrate inhibited cultures by dissolved oxygen control

Microorganism kinetic growth characterized by substrate inhibition was investigated by means of a continuous stirred tank reactor equipped with a feedback controller of the medium feeding flow rate. The aerobic growth of Pseudomonas sp. OX1 with phenol as carbon/energy source was adopted as a case study to test a new control strategy using dissolved oxygen concentration as a state variable. The controller was successful in steadily operating bioconversion under intrinsically unstable conditions. A simple model of the controlled system was proposed to set the feedback controller. The specific growth rate of Pseudomonas sp. OX1 was successfully described by means of the Haldane model. The regression of the experimental data yielded μ(M)=0.26 h(-1), K(Ph)=5×10(-3)g/L and K(I)=0.2g/L. The biomass-to-substrate fractional yield as a function of the specific growth rate did not change moving from substrate-inhibited to substrate-deficient state. The data was modelled according to the Pirt model: m=1.7×10(-2)g/(gh), Y(X/Ph)(Th)=1.3g/g. The specific growth rates calculated for batch and continuous growth were compared.     

Unstable steady state operations of substrate inhibited cultures by dissolved oxygen control

Microorganism kinetic growth characterized by substrate inhibition was investigated by means of a continuous stirred tank reactor equipped with a feedback controller of the medium feeding flow rate. The aerobic growth of Pseudomonas sp. OX1 with phenol as carbon/energy source was adopted as a case study to test a new control strategy using dissolved oxygen concentration as a state variable. The controller was successful in steadily operating bioconversion under intrinsically unstable conditions. A simple model of the controlled system was proposed to set the feedback controller.The specific growth rate of Pseudomonas sp. OX1 was successfully described by means of the Haldane model. The regression of the experimental data yielded μ_M = 0.26 h⁻¹, K_Ph = 5 × 10⁻³ g/L and K_I = 0.2 g/L. The biomass-to-substrate fractional yield as a function of the specific growth rate did not change moving from substrate-inhibited to substrate-deficient state. The data was modelled according to the Pirt model: m = 1.7 × 10⁻² g/(g h), . The specific growth rates calculated for batch and continuous growth were compared.     

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.     

A method for the control of the dissolved oxygen tension in microbial cultures

A method for the control of dissolved oxygen tension in growing microbial cultures is described. The apparatus consists of a motor-driven air sparge pipe which may be lowered or raised to give a variable point of entry of the air stream into the culture liquid and hence a variable gas dispersion and gas–liquid contact time. Control of the sparge pipe position is by means of a feedback control loop consisting of a dissolved oxygen probe, an on/off controller, and a reversing electric motor which drives the sparge pipe. The difficulty presented by the relatively slow response of the oxygen probe has been overcome by incorporating an adjustable rate of control action.     

Bioreactor state estimation and control

Advanced control methods have been effectively employed for industrial chemical processing for decades. Only recently, however, have model-based strategies been implemented for biological processes. Some notable advances include the enhancement of metabolic flux models to describe the dynamic behavior observed in biochemical reactors. The combination of more than one type of model in a hybrid form was shown to perform well for bioprocess control applications.     

Progress in monitoring, modeling and control of bioprocesses during the last 20 years

The paper gives a review on the recent development of bioprocess engineering. It includes monitoring of product formation processes by flow injection analysis, various types of chromatographic and spectroscopic methods as well as by biosensors. The evaluation of mycelial morphology and physiology by digital image analysis is discussed also. It deals with advanced control of indirectly evaluated process variables by means of state estimation/observer, with the use of structured and hybrid models, expert systems and pattern recognition for process optimization and gives a short report on the state of the art of metabolic flux analysis and metabolic engineering.     

An energy cost minimizing strategy for fermentation dissolved oxygen control

A cost-minimizing mathematical model for on-line control of dissolved oxygen using agitation speed and aeration rate was developed. In pilot scale monensin fermentation using Streptomyces cinnamonensis, this algortihm provided stable control of dissolved oxygen at 40%, reducing energy usage 27.8%. The agitation and aeration profiles provided by the algorithm respresent the pathway of least energy cost for control at the desired dissolved oxygen level. Other observed advantages of bivariable control were reduction of foaming, evaporation, and gas holdup. Reduced maintenance of compressors and agitator motors could also be expected due to decreased load. Monensin productivity equivalent to fermentation with constant agitation and aeration was not obtained, however, with potency reduced 14.8% with the dissolved oxygen control strategy.List of Symbols A m² cross sectional area of fermentor - A ₁, A ₂, A ₃, A ₄ constants of polynomial fit to Calderbank's equations - BP N/m² gauge back pressure - C _ag $/W/s cost of electrical power - C _Q $/m³ cost of compressed air - CE mol/m³/s carbon dioxide evolution rate - D m impeller diameter - DO, DO _meas, DO _sp % dissolved oxyen saturation at any time, measured, and setpoint respectively - h m height of liquid in fermentor - H N/m²/mmol Henry's constant for oxygen in water - H _av average gas holdup in fermentor - k _L a, k _L a _meas, k _L k _sp s^–1 oxygen mass transfer coefficient at any time, measured, and setpoint respectively - N, N _sp s^–1 agitation speed at any time and setpoint respectively - N _a, N _{a, sp} aeration number at any time and setpoint respectively - N _i total number of impellers - N _p impeller power number - N _s number of impellers into which air is directly sparged - OU, OU _meas mol/m³/s Oxygen uptake rate at any time and measured respectively - P W ungassed agitation power - P _g, P _g,meas, P _g,sp W gassed agitation power at any time, measured, and set point respectively - Q, Q _meas, Q _sp m³/s aeration rate at any time, measured, and setpoint respectively - T K fermentation temperature - u _g m/s linear gas velocity - V m³ fermentation liquid volume - mole fraction of oxygen in fermentation off-gas - calculation constant - motor efficiency - $/s sum of agitation and aeration costs - kg/m³ liquid density     

Adaptive control of dissolved oxygen concentration in a bioreactor

A new adaptive DO (dissolved oxygen) concentration control algorithm considering DO electrode dynamics with response time delay has been developed. A system model with two time-varying parameters was used to relate the DO concentration with two control variables: air flow rate and agitation speed. Parameters of this model were estimated on-line using a regularized constant trace recursive least-squares method. An extended Kalman filter was used to remove the effect of noises from the DO concentration measurements and thus to improve control performance. A discrete one-step ahead control scheme was adopted to determine control actions based on the parameter estimation results. Experimental results showed that the new adaptive DO concentration control algorithm performed better than other algorithms tested, a PID controller and adaptive algorithms without the DO electrode dynamics.     

Long-term continuous monitoring of dissolved oxygen in cell culture medium for perfused bioreactors using optical oxygen sensors

For long-term growth of mammalian cells in perfused bioreactors, it is essential to monitor the concentration of dissolved oxygen (DO) present in the culture medium to ascertain the health of the cells. An optical oxygen sensor based on dynamic fluorescent quenching was developed for long-term continuous measurement of DO for NASA-designed rotating perfused bioreactors. Tris(4,7-diphenyl-1,10-phenanthroline) ruthenium(II) chloride is employed as the fluorescent dye indicator. A pulsed, blue LED was chosen as the excitation light source. The sensor can be sterilized using an autoclave. The sensors were tested in a perfused rotating bioreactor supporting a BHK-21 (baby hamster kidney) cell culture over one 28-day, one 43-day, and one 180-day cell runs. The sensors were initially calibrated in sterile phosphate-buffered saline (PBS) against a blood-gas analyzer (BGA), and then used continuously during the entire cell culture without recalibration. In the 180-day cell run, two oxygen sensors were employed; one interfaced at the outlet of the bioreactor and the other at the inlet of the bioreactor. The DO concentrations determined by both sensors were compared with those sampled and measured regularly with the BGA reference. The sensor outputs were found to correlate well with the BGA data throughout the experiment using a single calibration, where the DO of the culture medium varied between 25 and 60 mm Hg at the bioreactor outlet and 80-116 mm Hg at the bioreactor inlet. During all 180 days of culture, the precision and the bias were +/-5.1 mm Hg and -3.8 mm Hg at the bioreactor outlet, and +/- 19 mm Hg and -18 mm Hg at inlet. The sensor dynamic range is between 0 and 200 mm Hg and the response time is less than 1 minute. The resolution of the sensor is 0.1 mm Hg at 50 mm Hg, and 0.25 mm Hg at 130 mm Hg.     

An algorithm for adaptive control of dissolved oxygen concentration in batch culture

An effective automatic control algorithm for set-point control of dissolved oxygen concentration in batch culture has been developed. Adaptation of PI controller to the variable state of batch culture is based on analytically obtained functional relations between the controller parameters and the state variables: oxygen uptake rate, stirring speed, and saturation value of dissolved oxygen concentration, which are measured or estimated on-line. Results of experimental investigation of the adaptive control system are presented.     

A hierarchical modeling framework for multiple observer transect surveys

Ecologists often use multiple observer transect surveys to census animal populations. In addition to animal counts, these surveys produce sequences of detections and non-detections for each observer. When combined with additional data (i.e. covariates such as distance from the transect line), these sequences provide the additional information to estimate absolute abundance when detectability on the transect line is less than one. Although existing analysis approaches for such data have proven extremely useful, they have some limitations. For instance, it is difficult to extrapolate from observed areas to unobserved areas unless a rigorous sampling design is adhered to; it is also difficult to share information across spatial and temporal domains or to accommodate habitat-abundance relationships. In this paper, we introduce a hierarchical modeling framework for multiple observer line transects that removes these limitations. In particular, abundance intensities can be modeled as a function of habitat covariates, making it easier to extrapolate to unsampled areas. Our approach relies on a complete data representation of the state space, where unobserved animals and their covariates are modeled using a reversible jump Markov chain Monte Carlo algorithm. Observer detections are modeled via a bivariate normal distribution on the probit scale, with dependence induced by a distance-dependent correlation parameter. We illustrate performance of our approach with simulated data and on a known population of golf tees. In both cases, we show that our hierarchical modeling approach yields accurate inference about abundance and related parameters. In addition, we obtain accurate inference about population-level covariates (e.g. group size). We recommend that ecologists consider using hierarchical models when analyzing multiple-observer transect data, especially when it is difficult to rigorously follow pre-specified sampling designs. We provide a new R package, hierarchicalDS, to facilitate the building and fitting of these models.     

Making sense of parameter estimation and model simulation in bioprocesses

Most articles that report fitted parameters for kinetic models do not include meaningful statistical information. This study demonstrates the importance of reporting a complete statistical analysis and shows a methodology to perform it, using functionalities implemented in computational tools. As an example, alginate production is studied in a batch stirred-tank fermenter and modeled using the kinetic model proposed by Klimek and Ollis (1980). The model parameters and their 95% confidence intervals are estimated by nonlinear regression. The significance of the parameters value is checked using a hypothesis test. The uncertainty of the parameters is propagated to the output model variables through prediction intervals, showing that the kinetic model of Klimek and Ollis (1980) can simulate with high certainty the dynamic of the alginate production process. Finally, the results obtained in other studies are compared to show how the lack of statistical analysis can hold back a deeper understanding about bioprocesses.     

Feedforward-feedback control of dissolved oxygen concentration in a predenitrification system

As the largest single energy-consuming component in most biological wastewater treatment systems, aeration control is of great interest from the point of view of saving energy and improving wastewater treatment plant efficiency. In this paper, three different strategies, including conventional constant dissolved oxygen (DO) set-point control, cascade DO set-point control, and feedforward-feedback DO set-point control were evaluated using the denitrification layout of the IWA simulation benchmark. Simulation studies showed that the feedforward-feedback DO set-point control strategy was better than the other control strategies at meeting the effluent standards and reducing operational costs. The control strategy works primarily by feedforward control based on an ammonium sensor located at the head of the aerobic process. It has an important advantage over effluent measurements in that there is no (or only a very short) time delay for information; feedforward control was combined with slow feedback control to compensate for model approximations. The feedforward-feedback DO control was implemented in a lab-scale wastewater treatment plant for a period of 60 days. Compared to operation with constant DO concentration, the required airflow could be reduced by up to 8–15% by employing the feedforward-feedback DO-control strategy, and the effluent ammonia concentration could be reduced by up to 15–25%. This control strategy can be expected to be accepted by the operating personnel in wastewater treatment plants.     

A dissolved oxygen budget model for Lake Erie in summer

SUMMARY.

• 1 In this paper we extend a vertical mixing model of Lake Erie with an oxygen budget model. The model was tested against data gathered in the summers of 1979 and 1980 with good results, showing that it is capable of simulating vertical distributions of temperature and dissolved oxygen over relatively short time periods.
• 2 The results underline the importance of turbulent mixing in distributing oxygen throughout the water column in the Central Basin of the lake. In addition, the results indicate that production and respiration processes dominate the budget under the influence of low wind speeds, while surface fluxes dominate during periods of high wind.
• 3 Bottom mixing delays the onset of anoxic conditions at the sediment/water interface by distributing the sediment demand over the 5–6 m depth of the bottom mixed layer.

     

A simple and rapid method for monitoring dissolved oxygen in water with a submersible microbial fuel cell (SBMFC)

A submersible microbial fuel cell (SBMFC) was developed as a biosensor for in situ and real time monitoring of dissolved oxygen (DO) in environmental waters. Domestic wastewater was utilized as a sole fuel for powering the sensor. The sensor performance was firstly examined with tap water at varying DO levels. With an external resistance of 1000?, the current density produced by the sensor (5.6±0.5-462.2±0.5mA/m(2)) increased linearly with DO level up to 8.8±0.3mg/L (regression coefficient, R(2)=0.9912), while the maximum response time for each measurement was less than 4min. The current density showed different response to DO levels when different external resistances were applied, but a linear relationship was always observed. Investigation of the sensor performance at different substrate concentrations indicates that the organic matter contained in the domestic wastewater was sufficient to power the sensing activities. The sensor ability was further explored under different environmental conditions (e.g. pH, temperature, conductivity, and alternative electron acceptor), and the results indicated that a calibration would be required before field application. Lastly, the sensor was tested with different environmental waters and the results showed no significant difference (p>0.05) with that measured by DO meter. The simple, compact SBMFC sensor showed promising potential for direct, inexpensive and rapid DO monitoring in various environmental waters.     

赤霉素发酵溶氧优化调控研究

为了解溶氧对赤霉素发酵过程影响以及相应工艺优化,采用不同溶氧条件下藤仓赤霉菌Gibberella fujikuroi分批发酵生产赤霉素的过程进行菌丝浓度、残糖浓度和GA3产物浓度检测,并微分运算得出比生长速率与比产物合成速率随发酵时间变化,分析了溶氧对比生长速率与比产物合成速率以及得率的影响,进而提出Gibberella fujikuroi发酵高产的溶氧控制策略:在发酵初始阶段(0–50h)控制溶氧30%左右,以维持较高的菌体生长速率;发酵中后期(50–184h),溶氧控制在15%,以获取菌丝持续较高的GA3合成速率能力。采用这一优化溶氧控制策略,发酵过程中最大菌丝浓度19.24g/L、最终赤霉素浓度2 180mg/L和平均比产物合成速率0.616mg/(g·h),比未优化前发酵分别提高了8.33%、13.25%和4.58%,表明所采取的分阶段溶氧控制策略对促进GA3生产有效。