Research On The Feedback Optimal Control In A Kind Of Microbial Fermentation

In this paper,we study the nonlinear(time-delayed)dynamic system of the fermentation process and linear optimal feedback controls of production 1,3-propanediol by microbial contin-uous fermentation.The production of 1,3-propanediol by microbial fermentation has advantages of simple production process and no toxic by-product compared with traditional chemical syn-thesis.However,due to its obvious disadvantages on yield compared with traditional methods,the research on its increase yield is of high value.Under this background,scholars have done a lot of research on the production of target products by means of optimal control theory and op-timization algorithm.Due to this kind of problem of this study has the characteristics of highly nonlinear and continuous state inequality constraints,it is difficult to use the method of classic Riccati equation to get the optimal feedback control law,the author will focus on optimal control problem of the production of 1,3-ropanediol in microbial continuous fermentation.Considering the influence of time delay factor and based on feedback control law design methods this prob-lem is discussed for the first time,the research for yield of target product has a certain theoretical basis for application and reference value.The main results of this dissertation can be summarized as follows:·1.We choose the dilution rate D and the concentration of glycerol in the input feed Cs0 as the control variables.According to the mechanism analysis of microbial fermentation,the main factors influencing the final concentration of 1,3-propanediol are the concentration of biomass and the concentration of glycerol.Based on the theory of the linear feedback con-trol law,we establish the linear feedback controller for the concentration of biomass and the concentration of glycerol to maximize the yield of 1,3-PD.First of all,by introducing linear feedback strategy,we transform the optimal control problem into a semi-infinite op-timization problem.Using the exact penalty method to deal with the constraint conditions and the gradient based optimization algorithm to get the optimal solution of the original optimization problem.Numerical results show that the linear feedback control strategy can realize the closed-loop control.·2.A nonlinear time-delayed dynamical system is investigated to describe continuous cul-ture of glycerol bioconversion to 1,3-propanediol(1,3-PD)by Klebsiella pneumoniae.The aim of this chapter is to maximize the concentration of 1,3-PD at the terminal time by controlling the dilution rate and the feeding glycerol concentration.Thus,taking the con-centration of 1,3-PD at terminal time as the objective function and the dilution rate,the feeding glycerol concentration as control variables,we propose an optimal control m odel of the time-delay system governed by continuous state inequality constraints.Based on the control vector parameterization approach,we use a sensitivity-based adaptive refine-ment method to find the optimal control variables,in which self-adaptation refers to the control of the number of time interval segmentation and the length of each time interval in the parameterized method.Moreover,in order to avoid falling into local optimum,we combined improved particle swarm with sensitivity-based adaptive refinement optimiza-tion algorithm to solve the problem.The numerical results illustrate the validity of the optimization algorithm.·3.We put forward a kind of multistage feedback control strategy in the continous cul-ture via microbial fermentation.The feedback control strategy has been widely used in industry,however,as far as we know,this is the first time it has been used in the pro-duction process of microbial fermentation for the production of 1,3-propanediol by the disproportionation of Klebsiella.Different from the chapter 3,we assume that the feed-back controller is linearly dependent on the concentration of biomass and the concentration of glycerol and the coefficients in the controller are continuous functions of t but not con-stant.By using the control parameterization method of coefficient function,the continuous function is discretized to simplify the original problem and the multistage feedback con-trol law is obtained.Then the optimal control problem is transformed into the optimal parameter selection problem.Our strategy makes the number and length of time intervals adaptive.The corresponding gradient is derived.Finally,the numerical calculation shows that the strategy is flexible and effective.·4.In order to further increase the concentration of the terminal point 1,3-propanediol,we take dilution rate D and the concentration of glycerol in the input feed Cs0 as control variables to study this optimal control problem with multistage linear feedback strategy.In the choice of linear feedback controller coefficients,we choose continuous functions.Because of the long time of the process of fermentation,we choose the coeffcients as the functions related to time t.By the control parameterization method,these two continu-ous functions are transformed into piecewise constant value functions.We also adopt the strategy of adjusting the number of segments adaptively.