Jan Peter Axelsson

Probing control of fed-batch cultivations: analysis and tuning

Production of various proteins can today be made using genetically modified Escherichia coli bacteria. In cultivations of E. coli it is important to avoid accumulation of the by-product acetate. Formation of acetate occurs when the specific glucose uptake exceeds a critical value and can be avoided by a proper feeding strategy. A difficulty is that the critical glucose uptake often is poorly known and even time varying. We here analyze an approach for control of glucose feeding that enables feeding at the critical glucose uptake without prior information. The key idea is to superimpose a probing signal to the feed rate in order to obtain information used to determine if the feed rate should be increased or decreased. The main contribution of this paper is to derive guidelines for tuning of the probing controller. A sufficient condition for stability is presented. By introducing proportional and proportional¯integral control action it is possible to improve performance with an unchanged stability guarantee. This also gives a possibility to maintain a minimum specified distance to the critical glucose uptake where acetate formation starts. (Less)

A Probing Feeding Strategy for Escherichia coli Cultures

A strain-independent feeding strategy for fed-batch cultures of Escherichia coli is presented. By superimposing short pulses in the glucose feed rate, on-line detection of acetate formation can be made using a standard dissolved oxygen sensor. A simple feedback algorithm is then used to adjust the feed rate to avoid acetate formation. The feasibility of the strategy is demonstrated by both simulation and experiments.

On the Role of Adaptive Controllers in Fed-Batch Yeast Production

Abstract The substrate control problem of fed-batch yeast production is analysed. It is based on broth ethanol measurement as indicator of over- or under-feeding. The main reason for control is to track the drastic growth in feed demand during a cultivation. Uncertainity in this growth is considered the main disturbance, and variation in process dynamics is regarded of minor importance. The discussion focuses on the low-frequency aspects of the control design. The limitation of conventional PID control is analysed. It is found that the integral part, while maintaining stability, cannot be made strong enough to compensate for the exponential increase in the feed demand. Introduction of a basic dosage scheme may result in a smaller disturbance and smaller ethanol errors, while an observer of the exponential load gives a further improvement of the ethanol control. An error in the initial estimate of the feed demand is eliminated, and influence from variation in the growth rate parameter is reduced. The strength of the disturbance rejection increases with the closed loop bandwidth. A longer sensor response time would call for a lower bandwidth. A moderate phase advance can be obtained by derivative action. However, tuning of the derivative part of the regulators is found difficult and quite sensitive to the process parameters. The limited time for tuning during a cultivation makes straight forward application of auto-tuners or self-tuners of minor value. A self-tuner would require some added excitation and need special care for the load disturbance. The analysis of simple regulators suggests adaptivity of the internal disturbance model.

A pulse technique for control of fed-batch fermentations

A strategy for control of substrate feed rate in fed-batch fermentations is presented. The main idea is to make pulses in the feed rate and to evaluate the response in the dissolved oxygen signal. This gives an indirect measurement of the substrate demand that is used for feedback control of the feed rate. Experimental data is used to develop a model of a fermentation process. The model is used to derive simple tuning rules that require little process specific information. Several simulation experiments show the feasibility of the presented strategy.

Substrate Control of Biotechnical Fedbatch Processes. Robustness and the Role of Adaptivity

Abstract Results from experiments on laboratory scale fedbatch processes are presented as well as analysis and design of the control system. The main reason for control is to track the drastic growth in feed demand during a cultivation. Variations in the amount and quality of the inocculum makes precalculated dosage schemes of limited value to obtain reproducible cultivation conditions. Two processes have been studied on a laboratory scale, production of bakers’ yeast, and production of the enzyme salicylate hydroxylase using a strain of bacteria. Direct measurement was used to monitor the feed demand. A regulator structure is proposed based on an observer for the exponentially growing feed demand. It can be viewed as a modified PID regulator around a dosage scheme, but it is less sensitive to errors in the dosage scheme than conventional PID control. The a priori knowledge of the feed profile is further relaxed by introduction of adaptation of the growth rate parameter. The obtained non-linear control system has a simple structure and stability is garanteed for a wide range of initial values using the technique of Liapunov function. The linearized system is analysed in the frequency domain and the adaptation is shown to have negligible influence on the loop phase margin. The adaptive regulator is tested in simulation against real feed profiles and shows good results.

Characterizing the Substrate Control Problem of Ethanol Monitored Fed-Batch Yeast Production

Abstract The substrate control problem of fed-batch yeast production is investigated. The control principle is based on the fact that the yeast produces ethanol in case of over-feeding and consumes ethanol in case of under-feeding. A mathematical model is derived for the ethanol dynamics in a fed-batch reactor. The transfer function has one fix and one time-varying part. Several closed-loop identification experiments were done on laboratory scale, to validate the model at different cell concentrations. Interpretation of the data from these experiments are discussed in some detail. Data was fitted to time invariant linear models of different orders. It was possible to follow process variations under a cultivation. A wider experience from many ethanol controlled cultivations are also summarized. The most apparent difference between ethanol-controlled cultivations are deviations in the exponential feed rate profile. This is considered the main reason for control. The sensor time delay and dynamics impose a limitation on the control performance. However, the results from identification promise good possibilities for dead time compensation. Further, the structure of the time-variable, more uncertain part, can be described by a first order system, and this fact might be useful in control design. Differences in process dynamics between cultivations are also reported and the implications for tuning are discussed.

Stability Issues in Fedbatch Fermentation

Abstract We make a brief review of a quantitative model to describe recombinant yeast in fed-batch reactors and present a detailed study of the dynamical behaviour of a simplified cell growth model which nevertheless shares many properties with the full original model. The phase-diagram of the cell-glucose subsystem is thoroughly analyzed and the problems associated with the sensitivity of the system trajectories in connection to the ethanol levels present in the broth are discussed.

Control design for a bilinear system reachable sets and exact linearization

A bilinear system model of a continuous tank reactor from a biotechnology application (F. Mandenius et al., 1987) is studied. The concentrations of the substrate sugar and the product ethanol were measured on-line and utilized to control the flow-rate through the fermenter. The system can be integrated analytically making it possible to describe the reachable sets. Limited controllability is found on a line in the state space. These reachable set expressions are used to obtain a time-optimal controller that for large disturbances implies reversed control action as compared to linear control. Transformations used when applying exact linearization are described. The lack of controllability, also obtained using the Lie brackets of differential geometry, shows up as singularities in the transformations.<<ETX>>

Computer Control of Sucrose Concentration in a Fermentor with Continuous Flow

Abstract Fermentation in a 5 l continuous flow reactor with immobilized yeast cells is controlled. Substrate concentration (sucrose) is continuously measured with an enzyme thermistor. The control variable is flowrate through the reactor. The performance limiting factor of the system is a timedelay in the measurement signal. A bilinear process model is formulated and used for design of a regulator. The regulator consists of a Kalman filter with the bilinear model and linear state feedback. Implementat ion is done on a PDP11/03 computer. Programs are written in PASCAL extended with a realtime kernel. This regulator is compared with a conventional PID-regulator. The regulators are tested using simulation and experiments are done on the real process. It is shown that the enzyme thermistor signal permits a proper computer control of the fermentation.