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This paper addresses the problem of observer-based stabilization of discrete-time linear systems in presence of parameter uncertainties and ℓ2-bounded disturbances. We propose a new variant of the classical two-step LMI approach. In the first step, we use a slack variable technique to solve the optimization problem resulting from stabilization by a static state feedback. In the second step, a part...
In this paper, a step by step algorithm is given to design functional unknown input observer for nonlinear discrete time systems under the Polytopic Takagi-Sugeno framework (also known as multiple models systems). Applying the Lyapunov theory and the ℒ2 attenuation, Linear Matrix Inequalities (LMI)s conditions are deduced which are solved for feasibility to obtain observer design matrices. To reject...
In this note, we design an invariant observer for a two step (acidogenesis-methanogenesis) mass balance non linear model, in order to estimate simultaneously all bacteria and substrate concentrations found in the anaerobic digestion process. The particularity of the designed observer is the use of only the methane flow rate which is cheap to measure and commonly measured online even at industrial...
In this paper, we propose to control the quantity and quality of the produced biogas from the anaerobic digestion of organic matter, digested in either a continuous stirred tank reactor or a fixed bed digester. This is motivated by the aim of providing the power grid with a stable amount of energy despite fluctuations in the treated waste concentration and composition. Therefore, we apply the linearizing...
In this paper we consider the control of the methane flow rate in biogas production using a continuous stirred tank reactor or a fixed bed digester. The goal is to regulate the methane flow rate in order to match an energy demand in spite of variations in the waste concentrations. For this purpose, a two step (acidogenesis-methanogenesis) nonlinear mass balance model is considered. Due to the costs...
The complexity of modeling the anaerobic digestion process meets the difficulty to describe and analyze them mathematically. This paper sets the fundamentals for further fully automatic modelling and analysis of biogas systems. Hence, a simplified mathematical model for the anaerobic digestion process of organic matter, in a continuous stirred tank reactor is proposed. With the aim of upgrading the...
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