Time Delay Optimal Control And Its Application In A Batch Fermentation Process

1,3-Propanediol can be used in the production of lubricants,pharmaceuticals,cosmetics,and other manufacturing industries,and is a very important organic chemical raw material.Microbial fermentation of glycerol to produce 1,3-Propanediol has the advantages of environmental protection and simple operation.Optimal control of the fermentation process can maximize product yield and substrate utilization.However,time-delay widely exist in the practical fermentation process,which poses a challenge for optimal control of fermentation processes.In this paper,the theory and algorithm of a class of optimal control with time delay are systematically studied.The main research contents are as follows:1.The single-objective optimal control of a nonlinear time-delay system for microbial batch fermentation is studied.In order to reasonably control biomass and initial concentration of glycerol,obtain a higher concentration of 1,3-propanediol at the terminal moment,and make the glycerol consumption rate less than a certain value,a time-delay optimal control model with constraints is proposed.Firstly,an equivalent optimal control problem is obtained through time-scaling transformation,and the penalty function method is used to deal with the constraints.Then,a hybrid algorithm combining simulated annealing with genetic algorithm is constructed to solve the optimal control problem.The numerical results show that the yield efficiency of 1,3-propanediol at the terminal time is 21.12% increases compared with existing result.2.The bi-objective optimal control problem of microbial batch fermentation process is studied.In order to maximize the production yield of 1,3-propanediol and the utilization rate of glycerol per unit time simultaneously,a bi-objective optimal control model is proposed involving on a nonlinear time-delay system for microbial batch fermentation.For the biobjective optimal control problem,it is transformed into an equivalent bi-objective optimal control problem with fixed terminals using a time scaling transformation.Furthermore,the normalized normal constraint method,convex weighted sum method,and normal boundary interpolation method are applied to transform the equivalent bi-objective optimal control problem into a corresponding single objective optimal control problem.By applying hybrid combining simulated annealing with genetic algorithm to solve a series of single objective optimal control problems,and a bi-objective optimal control strategy is obtained.Numerical results validate the effectiveness of the proposed solution method.