| The application of mathematics to biology is an exciting and novel area of research within the discipline of Applied Mathematics. The bioprocess which is described by nonlinear dynamic system model reflects and reveals the complexity and the regularity of the biosystem itself. Re-cently, nonlinear dynamic system theory has developed rapidly with the achievements of com-puter algebra, numerical computing and graphic technology, especially in time-delay system, stochastic system and so on. How to apply nonlinear dynamic system theory to deal with the problems in a biosystem has attracted lots of researchers from different areas, e.g. biochemical science, control science and mathematics.1,3-Propanediol (1,3-PD) is discussed as a bifunc-tional chemical reagent on a large commercial scale, especially as a monomer for polyesters, polyethers and polyurethanes. Compared with chemical synthesis, the bioconversion of1,3-PD is more attractive to industry due to its environmental safe, high region specificity and cheaply renewable feedstock. How to analyze the system phenomena more accurately and optimize the performance of the system with suitable controller become essential works ahead of researchers. Under the support of the National Natural Science Foundations of China, this research can not only enrich the nonlinear dynamic system theory and relative algorithm, but also establish certain theoretical basis for the practical applications. In this dissertation, based on different dynamic models of the continuous fermentation, the global behaviors, stability analysis and controller design of the system are studied. The main contributions are summarized as follows.1. The bioprocess of continuous fermentation is modelled by a stochastic dynamic sys-tem with a bounded Markov diffusion process. The system embodies new characteristics, e.g. control sets, stationarity and ergodicity. Based on multiplicity phenomena, the equilibriums and bifurcations of the deterministic system are analyzed firstly. Considering both of stochastic and deterministic perturbation caused by internal and external disturbance which reflect on the growth rate, global behavior for the stochastic system is analyzed. Based on parallel comput-ing, a improved Control Set Algorithm for computing the control sets for the associated control system is proposed. The probability distributions of relative supports are also computed. The simulation results indicate that these behaviors of the stochastic system can be better descrip-tions of the real bioprocess compared with those of deterministic system. Especially, the global behaviors change under different noise can be rational explanations for the different phenomena which the bioprocess presents under different producing scales and circumstance.2. Based on μ-synthesis theorem, a robust controller in microbial continuous culture is de-signed. By analyzing the structure uncertainty of the system, the transfer function configuration with diagonalizable uncertainty is proposed. To solve the corresponding structured singular val-ue optimization problem, through D-K iteration method, a output feedback controller is designed to assure both of robust stability and robust performance of the closed-loop system simultaneous-ly. The simulation results indicate that the μ-controller might be more feasible for the continuous bioprocess controlling.3. Stability analysis and controller design problem in microbial continuous culture with discrete time delay is studied. Based on the biodynamical model, some properties of its solutions are discussed. And how the time delay affects the stability of the system is investigated. LMIs method is applied to find a feedback controller to assure the stability of the closed-loop system. The simulation results indicate that the controller might be feasible for the continuous bioprocess controlling. |
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