Andrea Holmberg

On the practical identifiability of microbial growth models incorporating Michaelis-Menten type nonlinearities

Abstract The reason for difficulties in obtaining unique estimates of the parameters μ m and K s of the Michaelis-Menten equation are analysed for a microbial batch growth process. With the aid of simulation studies in which the influences of different types of noise on the parameter estimates are compared, it is shown that, although theoretically identifiable in the deterministic case with ideal measurements, the parameters cannot in general be correctly determined from noisy measurements. The difficulties are further illuminated by estimation examples using real data. It certain situations, in which the value of the ratio K s / s o is high or in which only few and noisy measurements are available, the linear approximation of the Michaelis-Menten equation gives a better fit. The practical difficulties in obtaining correct values of the model parameters do not limit the applicability of the Michaelis-Menten model, which in most cases explains the bacterial growth behavior excellently. Rather, they underline the fact that care must be taken when utilizing parameter estimates for biological interpretations.

Procedures for parameter and state estimation of microbial growth process models

Practical problems concerning parameter and state estimation of microbial growth processes, with application to batch and continuous fermentation processes and to the activated sludge wastewater treatment process are discussed. Besides the usual aggregated single substrate-single organism mass balance model with Michaelis-Menten growth dynamics, an alternative model, in which the biomass concentration is divided into age classes, is introduced. A method in which the parameters were adjusted manually with sensitivity functions was used for parameter estimation. With the aid of some examples it was shown that the Michaelis-Menten model is not practically identifiable. A recursive state-estimation algorithm for control and supervision purposes was developed and its application in combination with both the aggregated and the age distribution model was demonstrated.

Modelling of the activated sludge process for microprocessor-based state estimation and control

Abstract A simple dynamic model of the activated sludge process including the volatile suspended solids (VSS) concentration in the aeration basin, the VSS or suspended solids (SS) concentration in the recycle flow and the SS concentration in the effluent was obtained by simplifying a comprehensive model using empirically verified assumptions. The model can be used for on-line estimation of the influent BOD-load and the effluent BOD, in combination with a recursive algorithm for oxygen uptake rate (OUR) and k L a estimation requiring only dissolved oxygen and air flow rate measurements. The estimation procedure has been implemented and tested at a real plant using a microprocessor. Control of the activated sludge process is discussed and concluded to be a hierarchical two-level problem. The upper level control actions are aimed at bringing the process to an optimal state of operation. For this purpose verbally formulated control laws are used. On the lower level the control task is to maintain the process in the optimal state.

Microprocessor-based estimation of oxygen utilization in the activated sludge wastewater treatment process

Abstract Three time-recursive algorithms for estimating the oxygen utilization rate in the activated sludge wastewater treatment process have been compared. On-line estimation of the oxygen utilization rate is a prerequisite for the indirect estimation of the state variables. The algorithms were implemented using a microprocessor at a real wastewater treatment plant in Suomenoja in Finland. Each algorithm was in operation for a period of at least one week. On the basis of results obtained during this experiment a single method was chosen, which was in fact a combination of those studied.

A Microprocessor-based Estimation and Control System for the Activated Sludge Process

Abstract A method for estimating the concentrations of sludge and biochemical oxygen demand, BOD, in activated sludge plants was developed and implemented at a real plant using a microprocessor. The estimator utilizes the oxygen utilization rate (OUR), which is obtained recursively from dissolved oxygen and air flow measurements.

Application of Control Engineering to Fermentation Processes

Abstract The paper deals with applications of control engineering methods to fermentation processes. The progress, difficulties and role of control engineering in this quite new field are discussed according to the authors’ experience and opinions. A brief survey on dynamic analysis and modelling of fermentations is presented. Reasonable objectives in control and optimization are considered. As a case example computer control of a newly developed fungal protein process is considered.

Modelling and Control of a Protein Fermentation Process Utilizing the Spent Sulphite Liquor

Abstract The paper introduces results obtained in a system engineering study on the Pekilo-process. In this process single-cell protein is produced from the spent sulphite liquor by fermenting a species of microfungi (Paecilomyces varioti). Besides protein production the process serves also as a waste treatment unit by reducing the organic content of the spent liquor. The results are mainly related to modelling, optimization and process control. The Pekilo-process and related equipment are described. A detailed fermentor model is presented and its experimental identification, validity and applications are discussed. Optimization and process control are considered and illustrated with simulations.

Experiences on Parameter and State Estimation of Microbial Growth Processes

Abstract This paper reports the study of some special problems arlslng in parameter and state estimation of microbial growth processes. Because of the special features of such processes, purpose-oriented methods were found to be most suitable for both parameter and state estimation. A method in which the parameters were adjusted manually with the help of sensitivity functions was us~d for parameter estimation. A recursive state-estimation algorithm for control purposes was developed, in which special attention is paid to the utilization of the age distribution dynamics of biomass for biomass growth estimation.

OPTIMISATION OF BIOTECHNICAL PROCESSES UTILISING INTEGRATED METHODS FOR EXPERIMENTAL AND SAMPLING DESIGN

Abstract The importance of optimal experimental design and data analysis in biotechnical research and development is addressed. An example of applying the response surface method (RSM) for optimisation of constant parameters in static models is given. A new method for applying experimental design to dynamic processes is introduced. The method is applied to determine the sampling instants and the initial concentration of substrate, which give the maximum accuracy for parameter estimation, for a batch fermentation process described by the Monod model.

Multivariate Process Modelling Applied to Lysine Production

Abstract A multivariate technique (projection to latent structures, PLS) was used for modelling the production of an amino acid, lysine. Lysine fermentations were divided into three growth phases. Separate PLS-models were constructed for each of these phases. We demonstrate that sequential PLS-models can be used for fed-batch fermentation modelling.