| 1,3-Propanediol(1,3-PD)is a new kind of chemical raw material.The production of1,3-PD by fed-batch fermentation is a green industrial production method.In recent years,optimal switching control has been widely used in production,communication network and automatic control and so on.It has been a hot topic in the optimization and control field.In this thesis,a class of nonlinear switching systems are established for the production of1,3-PD from glycerol in microbial fed-batch fermentation process.Considering the effect of changing the glycerol feeding rate on the optimal control strategy in the actual fermentation process,a class of optimal switching control problems with the cost of smooth feeding rate change and satisfying the path constraints are presented.The content of this thesis mainly includes the following two parts:The optimal switching control problem with control change cost for the production of 1,3-PD from Klebsiella pneumoniae by microbial fed-batch production is studied.A nonlinear switching control system is proposed to describe the fed-batch fermentation process.By taking the smooth feeding rate of glycerol and the switching moments between batch process and feed process as the control variables and taking 1,3-PD yield at the terminal time and the cost of smooth feeding rate change as the performance index,an optimal switching control problem subject to the continuous state inequality constraint is presented.By applying a new control parameterization scheme,the optimal switching control problem is converted to a series of parameter optimization problems.Furthermore,the optimization problem of variable switching time is transformed into the equivalent problem of fixed switching time by the time-scaling transformation method.Then,the equivalent problem is approximated by a series of nonlinear programming problems by using the constrained transcription technique.At the same time,the analytical expression of the total variation of the smooth feeding rate is derived.On this basis,a parallel particle swarm optimization algorithm with gradient information of the constraints is developed to find the optimal control strategy.Finaliy,numerical results show that sacrificing a small amount of 1,3-PD can significantly reduce the cost of glycerol feeding rate change.Considering the mechanism of microbial metabolism,that is,the generation of new biomass is delayed by the time of nutrient metabolism,a robust delayed optimal switching control problem with control change cost is studied in the fed-batch fermentation process.According to the actual fermentation process,this thesis proposes a nonlinear time-delay optimal switching system with path constraints to describe the fed-batch production process.The objective is to design an optimal control scheme for the process such that(i)the process produces a sufficiently high concentration of 1,3-PD at the terminal moment;(ii)the cost of smooth feeding rate change is minimized at the terminal moment of the process;and(iii)1,3-PD is robust to the change of time-delay.Based on this,an optimal switching control problem with 1,3-PD yield,cost of feeding rate variation and the sensitivity of 1,3-PD yield with respect to time-delay in the cost function is proposed.The control variables of this problem are the feeding rate of glycerol and the switching instants between batch process and feed process.By introducing an auxiliary switched time-delay system,the sensitivity expression of 1,3-PD production with respect to time-delay is obtained.By applying control parameterization method,time-scaling transformation method and constraint transformation technique,the approximate optimization problems of the optimal switching control problem are obtained.On this basis,an improved parallel particle swarm optimization algorithm is applied to solve the approximate optimization problems.Finally,numerical simulation results show that the obtained optimal control strategy has good robustness under time-delay uncertainty. |
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