PIECEWISE CONTINUOUS CONTROL OF AN ANAEROBIC DIGESTION PROCESS Afzal Chamroo, Christian Vasseur, Nicolaï Christov Laboratoire d’Automatique, Génie Informatique & Signal Université des Sciences et Technologies de Lille, 59655 Villeneuve d’Ascq Cedex, France afzal.chamroo@ed.univ-lille1.fr, christian.vasseur@univ-lille1.fr, nicolai.christov@univ-lille1.fr Abstract - The paper deals with a new approach for computer-based control of a methane fermentation process in stirred tank bioreactors. The process is described by a non-linear mathematical model based on one-stage reaction scheme. The process con- trol is realized using a piecewise continuous regulator which enables tracking of a variable set point trajectory and overperforms the existing anaerobic digestion control schemes. Computer simulation examples illustrate the performance of the proposed ap- proach. Keywords – Anaerobic digestion, Non-linear systems, Piecewise continuous regulator. INTRODUCTION During the last two decades the anaerobic digestion (meth- ane fermentation) has been widely used in the biological wastewater treatment and depolution of highly concentrated wastes from animal farms and agroindustries [1]. Anaerobic processes result in the production of a biogas, an important energy source that can replace fossil fuel sources and thus contribute to the greenhouse gas reduction. Anaerobic digestion processes are very complex and their efficient control is still an open problem. Due to the very limited on-line information, the process control is usually reduced to the regulation of the biogas production rate (energy supply) or of the concentration of polluting organic matter (depolution control) at a desired value in presence of disturbances [2]. In this case, however, the classical linear regulators do not have good performances because of the strongly non-linear input-output process characteristics [3]. More sophisticated linearizing controllers have been pro- posed in [2, 4, 5 ], but due to some implementation difficul- ties they haven’t found practical application. In this paper a new control scheme for anaerobic digestion processes is proposed, based on the piecewise continuous regulator developed in [6, 7, 8 ]. The proposed control scheme can be efficiently implemented and overperforms the existing anaerobic digestion controllers both in distur- bance rejection and set point tracking. MATHEMATICAL MODEL OF THE PROCESS Consider the model of anaerobic digestion in a stirred tank bioreactor, based on a one-stage reaction scheme [2, 4, 5 ] : 1 0 2 ( i dX X DX dt dS k X DS S dt Q k X =μ − =− μ + − = μ ) (1) with max S S k S μ μ= + where is the biomass concentration (mg/l), X μ - the specific growth-rate of the methane producing bacteria (1/day), - the dilution rate (1/day), - the concentra- tion of the soluble organic (mg/l), - influent organic pollutant concentration (mg/l), Q - the biogas flow rate (liter biogas for liter of the medium per day), and , , and D S 0i S 1 k 2 k S k max μ are coefficients. To avoid the washout of microorganisms, the variations of and are limited in some admissible ranges: D 0i S min max max 0 0 0 0 , i i i D D S S S ≤ ≤ ≤ ≤ . For a laboratory-scale bioreactor the following estimates of the model parameters , , and have been obtained [5] : 1 k 2 k S k max μ (2) 1 2 max ˆ ˆ ˆ ˆ 6.7, 16.8, 2.3, 0.35. S k k k = = = μ = The non linear mathematical model (1) together with the parameter values (2) are used to simulate the anaerobic digestion control system by means of a computer. PIECEWISE CONTINUOUS CONTROL In [6,7] a class of hybrid systems called Piecewise Con- tinuous Systems (PCS) has been introduced. These systems, characterized by autonomous switchings and controlled impulses can be used as regulators: Piecewise Continuous Controllers (PCC). PCC are easily implemented on digital calculators and allow set point tracking by the plant’s state. Though the standard PCC requires a linear model of the plant to be controlled, it is shown in [8] that an adaptation of the PCC gives rise to a particular regulator that allows control without knowledge of the plant’s model, thus suit- able for some time-varying or non linear plants. Piecewise Continuous Controller The behavior of a PCC can be summarized as follows: • The state ˆ () n t λ ∈Σ of the PCC is switched to forced values at regular intervals of period . The corresponding switching set is represented by e t { } ., 0,1,2,... e S kt k = = .