Lansun Chen

Nonlinear modelling of a synchronized chemostat with impulsive state feedback control

Bioreactor control is an active area of research on continuous microorganism cultivation. Control of the substrate concentration in the bioreactor medium is especially necessary because of the substrate inhibition phenomenon. Moreover in order to maintain the dissolved oxygen content in an appropriate range, the biomass concentration should not exceed a set level. To maintain the biomass concentration in the desired range the universal mathematical model of a continuous bioprocess with impulsive state feedback control is formulated in the article. By discussing the dynamic properties of the model including the existence and stability of the periodic solution, the choice of suitable operating conditions for continuous culture systems can be simplified, offering the possibility of establishing general and more systematic operations and control strategies based on the counteraction of the mechanisms underlying the adverse effects of the bioreactor dynamics. The article also presents and discusses aspects of the bioprocess optimization.

Modelling and simulation of a continuous process with feedback control and pulse feeding

Abstract This paper deals with feedback control of a microorganism continuous culture process with pulse dosage supply of substrate and removal of products. By the analysis of the dynamic properties and numerical simulation of the continuous process, the conditions are obtained for the existence and stability of positive period-1 solution of the system. It is also pointed out that there does not exist positive period-2 solution. The results simplify the choice of suitable operating conditions for continuous culture systems. It also gives the complete expression of the period of the positive period-1 solution, which provides the precise feeding period for a regularly continuous culture system to achieve the same stable output as a continuous culture system with feedback control in the same production environment.

Original article: Modelling and qualitative analysis of a predator-prey system with state-dependent impulsive effects

In this work, according to integrated pest management principles, a class of predator-prey system with state-dependent impulsive effects is put forward. In this model, the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. The sufficient conditions for the existence and stability of the semi-trivial periodic solution and the positive order-1 periodic solution are given by the Poincare map and the properties of the Lambert W function. In addition, to verify the feasibility of our main results, the numerical simulations are carried out.

Theoretical approach to modelling and analysis of the bioprocess with product inhibition and impulse effect.

This work presents the first mathematical model of a bioprocess with product inhibition and impulse effect. To begin with, an exemplary mathematical bioprocess model with product inhibition and impulse effect is formulated. Then, according to the model, the analysis of bioprocess stability is presented. The article expresses the product oscillation period, which provides the precise feeding time frame for the regulator bioprocess to achieve an equivalent stable output as that of a bioprocess with impulse effect in the same production environment. Moreover, in this work, the optimization of the production process with respect to the tunable parameters is investigated, and analytical expressions of their optimal values are provided. Numerical simulations using biological data are presented to illustrate the main results.

Nonlinear Modelling and Qualitative Analysis of a Real Chemostat with Pulse Feeding

The control of substrate concentration in the bioreactor medium should be due to the substrate inhibition phenomenon. Moreover, the oxygen demand in a bioreactor should be lower than the dissolved oxygen content. The biomass concentration is one of the most important factors which affect the oxygen demand. In order to maintain the dissolved oxygen content in an appropriate range, the biomass concentration should not exceed a critical level. Based on the design ideas, a mathematical model of a chemostat with Monod-type kinetics and impulsive state feedback control for microorganisms of any biomass yield is proposed in this paper. By the existence criteria of periodic solution of a general planar impulsive autonomous system, the conditions for the existence of period-1 solution of the system are obtained. The results simplify the choice of suitable operating conditions for continuous culture systems. It also points out that the system is not chaotic according to the analysis on the existence of period-2 solution. The results and numerical simulations show that the chemostat system with state impulsive control tends to a stable state or a period solution.

Geometric approach to the stability analysis of the periodic solution in a semi-continuous dynamic system

Integrated pest management (IPM) is a long-term management strategy and has been proved to be more effective in pest control. To well-understand the mechanism and effect of the action of IPM, the geometric theory of the involved semi-continuous dynamic systems is becoming more and more important. In this work, a geometric approach is applied to analyze the stability of the positive order-one periodic solution in semi-continuous dynamic systems. A stability criterion to test the stability of the order-one periodic solution is established. As an application, a stage-structure model involved chemical control is presented to show the efficiency of the proposed method. The sufficient conditions to insure the existence of the periodic solution are provided. In addition, the number and the stability of the periodic solutions are discussed accordingly. The simulations are carried out to verify the results.

Universal modelling and qualitative analysis of an impulsive bioprocess

The work proves that in an impulsive bioprocess the stable oscillation period exists for any microorganisms – i.e. microorganisms of any characteristics of biomass yield and specific growth rate – pointing out the practical and scientific importance of the presented solution. Moreover, universal stability conditions of the impulsive bioprocess are presented. In order to obtain the universality of the solution, a sigmoid function is introduced for description of the biomass yield changes. Further, the universal mathematical model of the impulsive bioprocess is established, tested and discussed. This work shows among others that the impulsive bioprocess extends functionality of a simple continuous bioprocess providing in an easy way to control biomass concentration. The article also introduces a new objective function and then presents and discusses aspects of the impulsive bioprocess multi-criteria optimization. The analytical results presented in the work are validated by numerical simulations.

New Approach to the Nonlinear Analysis of a Chemostat with Impulsive State Feedback Control

Bioreactor control is an important area of research concerning continuous microorganism cultivation. The possible occurrence of the substrate inhibition phenomenon or substrate deficiency engenders the necessity to the control the substrate concentration. Moreover in order to maintain the dissolved oxygen content in an appropriate range, the biomass concentration should not exceed the set out level. To maintain the substrate and biomass concentration in certain desired ranges, a proposal of a new chemostat with pulse state feedback control is presented in the work. Then, a universal mathematical model of the chemostat is formulated, and the dynamic properties of the model including the existence and stability of the periodic solution are discussed. After this, in order to optimize the biomass production, two objective functions are introduced and the optimization is performed. The work shows that the proposed chemostat extends functionality of a chemostat providing in easy way the control of biomass and substrate concentration. The analytical results presented in the work are validated by numerical simulations.

Comment on Existence and stability of periodic solution of a Lotka-Volterra predator-prey model with state dependent impulsive effects [J. Comput. Appl. Math. 224 (2009) 544-555]

In this paper, according to integrated pest management principles, a class of Lotka-Volterra predator-prey model with state dependent impulsive effects is presented. In this model, the control strategies by releasing natural enemies and spraying pesticide at different thresholds are considered. The sufficient conditions for the existence and stability of the positive order-1 periodic solution are given by the Poincare map and the properties of the LambertW function.