Neli Dimitrova

Nonlinear Stabilizing Control of an Uncertain Bioprocess Model

Nonlinear Stabilizing Control of an Uncertain Bioprocess Model In this paper we consider a nonlinear model of a biological wastewater treatment process, based on two microbial populations and two substrates. The model, described by a four-dimensional dynamic system, is known to be practically verified and reliable. First we study the equilibrium points of the open-loop system, their stability and local bifurcations with respect to the control variable. Further we propose a feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point. A numerical extremum seeking algorithm is designed to stabilize the dynamics towards the maximum methane output flow rate in the presence of coefficient uncertainties. Computer simulations in Maple are reported to illustrate the theoretical results.

On the asymptotic stabilization of an uncertain bioprocess model

We study a nonlinear model of a biological digestion process, involving two microbial populations and two substrates and producing biogas (methane). A feedback control law for asymptotic stabilization of the closed-loop system is proposed. An extremum seeking algorithm is applied to stabilize the system towards the maximum methane flow rate.

New result on the model-based biological control of the chemostat

Abstract We investigate a known competition model of the chemostat with general (nonmonotone) response functions and distinct removal rates. Based on the competitive exclusion principle, Rapaport and Harmand (2008) [13] established the concept of the so called biological control. The proof of the latter result is based on a theorem of Li (1998) [11]. Here we first propose a modification of Li’s theorem and then present an extension of the biological control concept.

Verified Computation of Fast Decreasing Polynomials

In this paper the problem of verified numerical computation of algebraic fast decreasing polynomials approximating the Dirac delta function is considered. We find the smallest degree of the polynomials and give precise estimates for this degree. It is shown that the computer algebra system Maple does not always graph such polynomials reliably because of evaluating the expressions in usual floating-point arithmetic. We propose a procedure for verified computation of the polynomials and use it to produce their correct graphic presentation in Maple.

Model-based optimization of biogas production in an anaerobic biodegradation process

In this paper we consider a four-dimensional bioreactor model, describing an anaerobic digestion process of wastewater treatment and biogas production. We propose a simple and practically realizable approach for global asymptotic stabilization of the model and for maximizing the biogas flow rate; the latter is achieved by using a numerical extremum seeking algorithm.

Nonlinear Adaptive Control of a Bioprocess Model with Unknown Kinetics

In this paper we consider a nonlinear model of an anaerobic wastewater treatment process, in which biodegradable organic is decomposed to produce methane. The model, described by a four-dimensional dynamic system, is known to be practically validated and reliable.We propose a feedback control law for asymptotic stabilization of the closed-loop system towards a fixed operating point. Moreover, a model-based numerical extremum seeking algorithm is applied to stabilize the control system towards an equilibrium point with maximal methane flow rate. The robustness of the feedback control is demonstrated by assuming uncertainties in the growth rate functions. Computer simulations are reported to illustrate the theoretical results.

Über die Distributivgesetze der erweiterten Intervallarithmetik

ZusammenfassungDie vorliegende Arbeit befaßt sich mit weiteren Zusammenhängen zwischen den Rechenoperationen der erweiterten Intervallarithmetik; man vgl. etwa [3], [4], [5]. Insbesondere werden die Distributivgesetze zwischen den Operationen dieser Arithmetik untersucht. Für Ausdrücke der Gestalt(A−B) C, (A+B)/C, (A−B)/C u. a. werden gleichwertige angegeben. Als Spezialfall davon erhält man Distributivgesetze der wohlbekannten Intervallarithmetik. Die Intervalle werden durch ihre Mittelpunkte und Halbängen dargestellt.AbstractFurther relations between the operations in the extended interval arithmetic are discussed in this paper. In particular, the distributive laws in the extended arithmetic are considered, that is it is shown how to present expressions of the form(A−B) C, (A+B)/C, (A−B)/C etc. in an equivalent form. As a special case the well-known distributive laws for the usual interval operations are obtained.

OUTPUT FEEDBACK STABILIZATION OF AN ANAEROBIC DIGESTION MODEL

We study a nonlinear model of a biological wastewater treatment process, involving two microbial populations and two substrates and producing biogas (methane). A nonadaptive feedback control law for asymptotic stabilization of the closed-loop system towards a previously chosen operating point is proposed. An extremum seeking algorithm is applied to stabilize the system dynamics towards the maximum methane flow rate. Computer simulations are reported to illustrate the robustness of the feedback under model uncertainties.

Stability analysis of a bioreactor model for biodegradation of xenobiotics

We consider an ecological model for biodegradation of toxic substances in aquatic and atmospheric biotic systems. The model, which is described by a nonlinear system of four ordinary differential equations, is known to be experimentally validated. We compute the equilibrium points of the model and study their asymptotic stability. Basic properties of the solutions like uniform boundedness and uniform persistence are established. Global asymptotic results are also developed. Numerical simulation results are presented to demonstrate the theoretical studies.

Nonlinear Adaptive Control of an UncertainWastewater Treatment Model

A nonlinear model of an anaerobic digester wastewater treatment process is considered. Assuming that the model parameters are unknown but bounded, the asymptotic stabilizability of the control system is studied and a new adaptive stabilizing feedback control law is proposed. Computer simulations are also presented to illustrate the theoretical results.