AICME II abstracts

Control and optimization in ecological problems

Hybrid modelling of microbial population dynamics for control purposes: an example of anaerobic wastewater treatment. Nelly Noykova1 and Petya Koprinkova2 . As a rule, biotechnological processes involve mixed cultures, which are responsible for a large amount of biochemical reactions. A mathematical description of the theoretical mass and energy balances leads to nonlinear ODE models. The inclusion of all available biochemical information often results in huge mathematical models. For example the recently created ADM1 model for anaerobic digestion (Batstone et al., 2002) includes 32 state variables. This model is increasingly complex and intrinsically unverifiable, which makes its application for practical purposes non-feasible. For practical control and optimization purposes simpler models are still needed. But even the simplest second order Monod models can cause some identifiability problems in the case when not all state variables are measurable. An additional requirement for the models, created for on-line control, is to obtain the model predictions as fast as possible. The goal of this work is to investigate the hybrid modelling approach, where the deterministic ODEs modelling is combined with neural network approach. Firstly the classical Monod type model is investigated. Identifiability analyses and parameter estimation are based on the available information from the measured variable(s). The estimated model is assumed as a ”true” description of the investigated processes. 1 Department of Mathematical Sciences, University of Turku, FIN-20014, Turku, FINLAND (e-mail: [email protected]). 2 Institute of Control and System Research - BAS, Block 2, Acad. G. Bonchev St. 1113 Sofia, Bulgaria (e-mail: ).

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Control and optimization in ecological problems

AICME II abstracts

After that neural network modelling approach is applied in order to obtain on-line estimates of the non-observed process variables. Thus our hybrid approach combine the advantage of including the most important biochemical information, and in the same time produce much faster results for the estimates of non-observed state variables. This makes the hybrid model very suitable for control purposes. In our anaerobic wastewater treatment example we assume both substrate and microorganism concentrations as nonmeasurable. The only measurable variable is the biogas production rate. Our results from this very realistic case show that the hybrid modelling approach works well and could be applied for control purposes. Our future work is oriented to more complicated models, which involve more biochemical information.

References [1] Batstone DJ, Keller J, Angelidaki I, Kalyuzhnyi SV, Pavlostathis SG, Rozzi A, Sanders WTM, Siergist H, Vavilin VA. 2002. Anaerobic Digestion Model No. 1. IWA Scientific and Technical Report No.13, IWA Publishing, UK. [2] Koprinkova P, Patarinska T, Popova S. 2002. Biomass and growth rate estimation by neural networks. Proc. of Nat. Conf. Automatic and Informatics, 5-6 Nov. 2002, Sofia ,pp.69-72. [3] Noykova N. Modelling and identification of microbial population dynamics in wastewater treatment, University of Turku, Institute for Applied Mathematics, Thesis E9 , 2002. [4] Petrova, M., Koprinkova, P., Patarinska, T. 1997. Neural Network Model of Fermentation Processes. Microorganisms Cultivation Model. Biopr. Eng. 16 (3): 145-149.

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