Nonlinear modelling of a synchronized chemostat with impulsive state feedback control

Pang

Discrete Dynamics in Nature and Society

et al. 2015

The rhizosphere microbe plays an important role in removing the pollutant generated from industrial and agricultural production. To investigate the dynamics of the microbial degradation, a nonlinear mathematical model of the rhizosphere microbial degradation is proposed based on impulsive state feedback control. The sufficient conditions for existence of the positive order-1 or order-2 periodic solution are obtained by using the geometrical theory of the semicontinuous dynamical system. We show the impulsive control system tends to an order-1 periodic solution or order-2 periodic solution if the control measures are achieved during the process of the microbial degradation. Furthermore, mathematical results are justified by some numerical simulations.

Section: Model Description and Preliminariesmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Impulsive State Feedback Control of the Rhizosphere Microbial Degradation in the Wetland Plant

Pang

Discrete Dynamics in Nature and Society

et al. 2015

“…Under these conditions, microorganisms are at the declining multiplication period because of the low substrate concentration. When substrate concentration is high, microorganisms are in the logarithmic growth phase, and substrate is degraded at maximum velocity that is described as zero-order reaction relation; in this situation, there is no relation between substrate concentration and substrate biodegradation rate (Monod, 1949;Sun et al, 2010).…”

Section: Derivation Of Mathematical Models 231 Derivation Of Nh 3 -mentioning

confidence: 99%

NH3-N degradation dynamics and calculating model of filtration bed height in Constructed Soil Rapid Infiltration

Zhang

Liu

2011

Chin. Geogr. Sci.

The research on Constructed Soil Rapid Infiltration (CSRI) system is in its infancy at home and abroad. There are several details about the mechanism and application of CSRI system needed to be further studied. A major limitation in the current research is the absence of degradation dynamics of pollutants, and the height of filtration bed in CSRI system currently determined by empirical judgment lacks accuracy and logicality. To solve these two problems, the soil column of CSRI system was utilized to treat domestic wastewater, meanwhile, the NH 3 -N degradation dynamics were studied according to the Monod equation, the research of Mann A T and the NH 3 -N degradation law. Then the mathematical model of filtration bed height was built based on NH 3 -N degradation dynamics equation in the soil column. It has been proven that within a limited range this model can calculate the appropriate height of filtration bed accurately in order to optimize technological parameters of hydraulic load and the concentration of influent NH 3 -N, improving the effluent quality of CSRI system.

“…In these researches, the authors analyzed the proposed system's dynamic behavior (e.g., the existence and stability of period-1 solution and the existence of period-2 solution) by applying the Poincaré principle and Poincaré-Bendixson theorem of the impulsive differential equation. Recently, in microbioprocess engineering, the dynamic properties of the kinetic models with impulse effects characterized by the universal microorganism growth rate and two different kinds of biomass yield are also analyzed theoretically by Sun et al [37][38][39].…”

Section: Introductionmentioning

confidence: 99%

Theoretical Study and Optimization of the Biochemical Reaction Process by Means of Feedback Control Strategy

Sun

Kasperski

Tian

2012

Journal of Chemistry

Self Cite

The aim of this work is to present a theoretical analysis and optimization of a biochemical reaction process by means of feedback control strategy. To begin with, a mathematical model of the biochemical reaction process with feedback control is formulated. Then, based on the formulated model, the analysis of system's dynamics is presented. The optimization of the bioprocess is carried out, in order to achieve maximal biomass productivity. It is shown that during the optimization, the bioprocess with impulse effects loses the possibility of synchronization and strives for a simple continuous bioprocess. The analytical results presented in the work are validated by numerical simulations for the Tessier kinetics model.