A contribution to optimal control of fed-batch biochemical processes

The problem of looking for high efficient modern control strategies in fermentation technology is very urgent, nowdays. Particular attention should be paid to the processes in fed-batch mode. Both, optimal feedforward and feedback control approaches are suggested. A contribution is considered to have been made in the feedback control where continuous and discrete versions are treated as well. The control laws are carried out by a variation calculus problem and a polynomial pole placement synthesis solution, respectively. All the algorithms result in an optimal substrate feed rate profile. On the basis of recursive least squares identification of the model coefficients an adaptive discrete-time control strategy is proposed. Some satisfying simulation results are dealt with.     

Adaptive pole placement control algorithm for DO-control in beta-lactamase production

The dissolved oxygen (DO) is an important variable in aerobic fermentations and affects the cell growth and product formation. Dissolved oxygen control is difficult in batch fermentations because of the time-varying conditions, time delays, and the probe dynamics. Modeling of the various patterns of biological activity in fermentations and their impact on the DO process dynamics is essential to both achieve a satisfactory control and to track the aforementioned patterns. An adaptive pole placement algorithm with time-delay compensation was used for controlling the DO, coupled with system identification using recursively estimated autoregressive models with exogeneous inputs (ARX). The flow rate of O2 in a constant flow rate gas inlet mixture is used as the manipulated variable. Supervision and coordination techniques are applied to improve the control performance. The control performance is affected by the accuracy of the model prediction and the selected time delay. The effect of DO level on the productivity of beta-lactamase using Bacillus subtilis under oxygen-limited conditions is investigated. Beta-lactamase stability is improved under prolonged growth conditions with low DO levels.     

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.     

A new method for the adaptive determination of optimum pH and temperature

An adaptive control algorithm for the on-line determination of optimal temperature or pH for biomass production in a continuous fermentor is presented. The algorithm requires no prior information and uses a dynamic Hammerstein model to identify parameters and to estimate an optimal steady-state control value. A check of the estimated performance measure second derivative is included to ensure that the target extremum is an optimum. The process is driven towards this optimum with a variable step size that depends on the quality of the on-line identified model. Numerical simulations are performed on a dynamic chemostat model that incorporates a metabolic time delay. The algorithm successfully finds the optimum temperature or pH values and maintains the reactor at the optimum steady state.     

Efficient nonlinear predictive control of a biochemical reactor using neural models

This paper describes the application of artificial neural networks to modelling and control of a continuous fermentor. A computationally efficient nonlinear model predictive control (MPC) algorithm with nonlinear prediction and linearisation (MPC-NPL) which needs solving on-line a quadratic programming problem is developed. It is demonstrated that the algorithm results in closed-loop control performance similar to that obtained in nonlinear MPC, which hinges on full on-line non-convex optimisation. The computational complexity of the MPC-NPL algorithm is shown, control accuracy and robustness are also demonstrated in the case of noisy measurements and disturbances affecting the process.     

An adaptive control algorithm for fed-batch culture

The implementation of adaptive control for a fed-batch culture in order to maximize the output of product based on a self-adjusting model is discussed in the present work. Optimization methods were applied to the generalized mathematical model of a fed-batch fermentation process to determine control algorithms that could be used for on-line process control. The efficiency of the proposed adaptive algorithms was investigated by simulating a model system. The model of amylotytic enzyme fermentation that was proposed by the authors was taken from a real process. Dynamic modelling has shown that the main problem of realization is connected with the on-line identification of the adaptive model's parameters. To avoid this problem, we have introduced special limitations on the parameters' time variations that increased the convergence of the identification algorithm. The results of the investigation have shown the efficiency of the proposed adaptive algorithms, and the results of this work should be investigated for real process control.     

Optimal feeding strategies by adaptive mesh selection for fed-batch bioprocesses

The objective of this contribution is the design of optimal feeding strategies for fed-batch bioprocesses, where complex dynamic models with input and state constraints are present. For the solution of this dynamic optimization problem a transformation to a finite dimensional optimization problem is made using piecewise linear control profiles. The optimization of these profiles is performed by a sequential approach, that includes an ODE solver for the solution of the model ODE's. Further an adaptive mesh selection algorithm was investigated for an appropriate discretization of the control profiles. The implementation of the resulting optimal feeding profiles is shown for a process example, namely the production of nikkomycin by Streptomyces tendae. This implementation uses a hierarchical process control framework, that consists of components for process monitoring, state estimation, and trajectory control.     

Computer control of pH and DO in a laboratory fermenter using a neural network technique

In this contribution, the advantages of the artificial neural network approach to the identification and control of a laboratory-scale biochemical reactor are demonstrated. It is very important to be able to maintain the levels of two process variables, pH and dissolved oxygen (DO) concentration, over the course of fermentation in biosystems control. A PC-supported, fully automated, multi-task control system has been designed and built by the authors. Forward and inverse neural process models are used to identify and control both the pH and the DO concentration in a fermenter containing a Saccharomyces cerevisiae based-culture. The models are trained off-line, using a modified back-propagation algorithm based on conjugate gradients. The inverse neural controller is augmented by a new adaptive term that results in a system with robust performance. Experimental results have confirmed that the regulatory and tracking performances of the control system proposed are good.     

Comparison of five clustering algorithms to classify phytoplankton from flow cytometry data.

BACKGROUND: Artificial neural networks (ANNs) have been shown to be valuable in the analysis of analytical flow cytometric (AFC) data in aquatic ecology. Automated extraction of clusters is an important first stage in deriving ANN training data from field samples, but AFC data pose a number of challenges for many types of clustering algorithm. The fuzzy k-means algorithm recently has been extended to address nonspherical clusters with the use of scatter matrices. Four variants were proposed, each optimizing a different measure of clustering "goodness." METHODS: With AFC data obtained from marine phytoplankton species in culture, the four fuzzy k-means algorithm variants were compared with each other and with another multivariate clustering algorithm based on critical distances currently used in flow cytometry. RESULTS: One of the algorithm variants (adaptive distances, also known as the Gustafson--Kessel algorithm) was found to be robust and reliable, whereas the others showed various problems. CONCLUSIONS: The adaptive distances algorithm was superior in use to the clustering algorithms against which it was tested, but the problem of automatic determination of the number of clusters remains to be addressed.     

Ein adaptives und lernfähiges System für diskrete stochastische Prozesse. I

Summary An algorithm is given for an adaptive and learning system which controls any given unknown objective system while learning its stochastic behaviour by observing its reactions to control inputs. The algorithm consists of two subalgorithms; one for estimating the stochastic transition structure of the objective system with regard to some kinds of a priori information, and the other for determining the optimal control input to each state of the objective system on the basis of its estimated transition structure. This combined algorithm has shown to serve as an adaptive and learning system. This paper concerns with the decision algorithm of control inputs, and the subsequent with the estimation algorithm of transition structure.     

Modeling and multi-criteria optimization of an industrial process for continuous lactic acid production

The key feature of this paper is the optimization of an industrial process for continuous production of lactic acid. For this, a two-stage fermentor process integrated with cell recycling has been mathematically modeled and optimized for overall productivity, conversion, and yield simultaneously. Non-dominated sorting genetic algorithm (NSGA-II) was applied to solve the constrained multi-objective optimization problem as it is capable of finding multiple Pareto-optimal solutions in a single run, thereby avoiding the need to use a single-objective optimization several times. Compared with traditional methods, NSGA-II could find most of the solutions in the true Pareto-front and its simulation is also very direct and convenient. The effects of operating variables on the optimal solutions are discussed in detail. It was observed that we can make higher profit with an acceptable compromise in a two-stage system with greater efficiency.     

Oxygen transfer modeling and simulations for an industrial continuous airlift fermentor

This article deals with the modeling of the oxygen transfer in an industrial airlift fermentor used for lactic yeast production on whey substrates. The purpose of this study was to improve the understanding of the interactions among the various parameters that govern the oxygen transfer phenomena in this type of fermentor. The reliability of the proposed model is demonstrated. The results of the investigations have been put into practice on the industrial scale and have contributed to monitor better the fermentation process. The model was also used to develop new ways of industrial fermentor design.     

Rechnergestützte Führung von fermentationsprozessen teil III

In the second part of the publication [1] the application of an adaptive algorithm for the adaptation of the static optimum was orientated on a specific problem. In this third part the indirect determination of the productivity from the nitrogen balance used in the adaptive algorithm is supplied, and control algorithms founded on the nitrogen balance are given in order to complete the algorithm.     

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.     

Extremum seeking scheme for continuous fermentation processes described by an unstructured fermentation model

This paper examines the problem of maximising the productivity of a class of fermentation processes described by an unstructured fermentation process model. For a given dilution rate, an extremum seeking adaptive control has been used to maximise the productivity of a fermentation process. The concept behinds the extremum seeking method is to iteratively adjust the feed substrate rate in order to steer the process to yield a maximum productivity. The main advantage of the extremum seeking adaptive control is it does not require any structural information of the modeling uncertainty.     

The component retrieval problem in printed circuit board assembly

Minimization of the makespan of a printed circuit board assembly process is a complex problem. Decisions involved in this problem concern the specification of the order in which components are to be placed on the board and the assignment of component types to the feeder slots of the placement machine. If some component types are assigned to multiple feeder slots, an additional problem emerges: for each placement on the board, one must select the feeder slot from which the required component is to be retrieved. In this paper, we consider this component retrieval problem for placement machines of the Fuji CP type. We explain why simple forward dynamic programming schemes cannot provide a solution to this problem, invalidating the correctness of an algorithm proposed by Bard, Clayton, and Feo (1994). We then present a polynomial algorithm that solves the problem to optimality. The analysis of the component retrieval problem is facilitated by its reformulation as a PERT/CPM problem with design aspects: finding the minimal makespan of the assembly process amounts to identifying a design for which the longest path in the induced PERT/CPM network is shortest. The complexity of this network problem is analyzed, and we prove that the polynomial solvability of the component retrieval problem is caused by the specific structure it inflicts on the arc lengths of the network: in the absence of this structure, the network problem is shown to be NP-hard.     

Using highly efficient nonlinear experimental design methods for optimization of Lactococcus lactis fermentation in chemically defined media

Optimization of fermentation media and processes is a difficult task due to the potential for high dimensionality and nonlinearity. Here we develop and evaluate variations on two novel and highly efficient methods for experimental fermentation optimization. The first approach is based on using a truncated genetic algorithm with a developing neural network model to choose the best experiments to run. The second approach uses information theory, along with Bayesian regularized neural network models, for experiment selection. To evaluate these methods experimentally, we used them to develop a new chemically defined medium for Lactococcus lactis IL1403, along with an optimal temperature and initial pH, to achieve maximum cell growth. The media consisted of 19 defined components or groups of components. The optimization results show that the maximum cell growth from the optimal process of each novel method is generally comparable to or higher than that achieved using a traditional statistical experimental design method, but these optima are reached in about half of the experiments (73–94 vs. 161, depending on the variants of methods). The optimal chemically defined media developed in this work are rich media that can support high cell density growth 3.5–4 times higher than the best reported synthetic medium and 72% higher than a commonly used complex medium (M17) at optimization scale. The best chemically defined medium found using the method was evaluated and compared with other defined or complex media at flask‐ and fermentor‐scales. © 2009 American Institute of Chemical Engineers Biotechnol. Prog., 2009     

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.     

Reconstruction for 3D PET Based on Total Variation Constrained Direct Fourier Method

This paper presents a total variation (TV) regularized reconstruction algorithm for 3D positron emission tomography (PET). The proposed method first employs the Fourier rebinning algorithm (FORE), rebinning the 3D data into a stack of ordinary 2D data sets as sinogram data. Then, the resulted 2D sinogram are ready to be reconstructed by conventional 2D reconstruction algorithms. Given the locally piece-wise constant nature of PET images, we introduce the total variation (TV) based reconstruction schemes. More specifically, we formulate the 2D PET reconstruction problem as an optimization problem, whose objective function consists of TV norm of the reconstructed image and the data fidelity term measuring the consistency between the reconstructed image and sinogram. To solve the resulting minimization problem, we apply an efficient methods called the Bregman operator splitting algorithm with variable step size (BOSVS). Experiments based on Monte Carlo simulated data and real data are conducted as validations. The experiment results show that the proposed method produces higher accuracy than conventional direct Fourier (DF) (bias in BOSVS is 70% of ones in DF, variance of BOSVS is 80% of ones in DF).     

Optimal temperature control for batch beer fermentation

Optimal control theory was applied to the process of batch beer fermentation. The performance functional considered was a weighted sum of maximum ethanol production and minimum time. Calculations were based on the model of Engasser et al. modified to include temperature effects. Model parameters were determined from isothermal batch fermentations. The fermentor cooling duty was the single available control. Temperature state variable constraints as well as control variable constraints were considered. The optimal control law is shown to be bang-bang control with the existence of a singular arc corresponding to isothermal operation at the maximum temperature constraint. An iterative algorithm is presented for computing appropriate switching times using a penalty-function-augmented performance functional.