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In this work we analyze the transient behavior of the dynamics of multiple species competing in a chemostat for a single resource, presenting slow/fast characteristics. We prove that coexistence among a subset of species, with growth functions close to each other, can last for a substantially long time. For these cases, we also show that the proportion of non-dominant species can be increasing before decreasing, under certain conditions on the initial distribution.

This paper deals with the control of a multistage continuous fermenter (MSCF) used for the study of wine fermentation. The control design is facing three main difficulties: 1) system nonlinearity; 2) lack of online measurement of the controlled variable (sugar concentration); and 3) positive constraints on the control inputs (inlet flow rates of each tank) coming from the cascade structure of the system. A control strategy has been proposed, which accounts for these specificities. It is based on an input–output linearization control law coupled with an antiwindup technique and a state observer (the Kalman filter). The strategy has been tested and validated first on numerical simulations and then applied to the real process. The experiments gave satisfactory results that open up new perspectives on the use of the MSCF. [ABSTRACT FROM AUTHOR]

This paper deals with the design of a robust sliding mode-based extremum-seeking controller aimed at the online optimization of a class of uncertain reaction systems. The design methodology is based on an input-output linearizing method with variable-structure feedback, such that the closed-loop system converges to a neighborhood of the optimal set point with sliding mode motion. In contrast with previous extremum-seeking control algorithms, the control scheme includes a dynamic modelling-error estimator to compensate for unknown terms related with model uncertainties and unmeasured disturbances. The proposed online optimization scheme does not make use of a dither signal or a gradient-based optimization algorithm. Practical stabilizability for the closed-loop system around to the unknown optimal set point is analyzed. Numerical experiments for two nonlinear processes illustrate the effectiveness of the proposed robust control scheme. Copyright © 2017 John Wiley & Sons, Ltd. [ABSTRACT FROM AUTHOR]

This paper proposes an alternative extremum seeking control design technique for the solution of real-time optimization control problems. The technique considers a proportional-integral approach that minimizes the impact of a time-scale separation on the transient performance of the extremum-seeking controller. It is assumed that the equations describing the dynamics of the nonlinear system and the cost function to be minimized are unknown and that the objective function is measured. The dynamics are assumed to be of relative degree one with respect to the objective function. Two simulation examples are presented to demonstrate the effectiveness of the proposed technique. [ABSTRACT FROM AUTHOR]

In this work, we proposed a novel hybrid fuzzy-sliding mode observer designed in such a manner that it can be utilized to estimate various parameters by simply using the related process model, without redesigning the structure of the whole observer. The performances and effectiveness of this hybrid observer are shown through numerical simulation based on a case study involving an ethylene polymerization process to estimate the ethylene and butene concentrations in the reactor as well as the melt flow index. It can be concluded that the proposed hybrid observer provides fast estimation with a high rate of accuracy even in the presence of disturbances and noise in the model. This hybrid observer is also compared with the sliding mode, extended Luenberger and proportional sliding mode observers to highlight its effectiveness and advantages over these observers. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a thermodynamically stable evolution criterion for homogeneous multi-component mixtures with chemical transformation is proposed. The approach is motivated and governed by physical considerations strongly related to the second law of the thermodynamics. More precisely we show that there exists some potential function directly defined on the space of the extensive and/or intensive variables for any transformation, and that meets the evolution criterion without any restriction on the chemical reaction kinetics. As a consequence the irreversibility degree or passivity of the mixture under mass transfer and transport phenomena is explicitly expressed. Some numerical simulations for a homogeneous binary mixture with chemical reaction under multiplicity are given to validate our theoretical developments. [Copyright &y& Elsevier]

Abstract: In this paper, we present an adaptive extremum seeking control scheme for fed-batch bioreactors with Haldane kinetics. The proposed adaptive extremum seeking approach utilizes the structure information of the process kinetics to derive a seeking algorithm that drives the system states to the desired setpoints that maximize the biomass production. It assumes that only the substrate concentration is available for on-line measurement. Lyapunov stability is used in the design of the extremum seeking controller structure and the development of the parameter learning laws. The performance of the approach is illustrated via numerical simulations. [Copyright &y& Elsevier]

A preface for the journal "Mathematical and Computer Modelling of Dynamical Systems," vol. 14, no.1, February 2008, issue 1, is presented.