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Abstract: The main control goal in fed-batch fermentation is to get a high concentration of production. In this paper, a new nonlinear dynamical system, in which the feed rate of glycerol is the control function and the switching instants between the batch and feed processes are the variables, is proposed to formulate the fed-batch fermentation process of glycerol bioconversion to 1,3-propanediol (1,3-PD). To maximize the concentration of 1,3-PD at the terminal time, an optimal control model involving the nonlinear system and subject to the continuous state constraints and the control constraint is presented. To seek the optimal solution of the constrained optimal control problem, the control parametrization enhancing transform together with the constraint transcription technique is first used to convert the constrained optimal control problem into a sequence of mathematical programming problems. An improved Particle Swarm Optimization is subsequently constructed to solve the resultant mathematical programming problem. Numerical results show that, by employing the obtained optimal strategy, 1,3-PD concentration at the terminal time can be increased considerably. [Copyright &y& Elsevier]

In this article, we propose a controlled nonlinear dynamical system with variable switching instants, in which the feeding rate of glycerol is regarded as the control function and the moments between the batch and feeding processes as switching instants, to formulate the fed-batch fermentation of glycerol bioconversion to 1,3-propanediol (1,3-PD). Some important properties of the proposed system and its solution are then discussed. Taking the concentration of 1,3-PD at the terminal time as the cost functional, we establish an optimal control model involving the controlled nonlinear dynamical system and subject to continuous state inequality constraints. The existence of the optimal control is also proved. A computational approach is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that, by employing the optimal control strategy, the concentration of 1,3-PD at the terminal time can be increased considerably. [ABSTRACT FROM PUBLISHER]

Considering the hybrid nature in fed-batch culture of glycerol biconversion to 1,3-propanediol (1,3-PD) by Klebsiella pneumoniae, we propose a state-based switching dynamical system to describe the fermentation process. To maximize the concentration of 1,3-PD at the terminal time, an optimal switching control model subject to our proposed switching system and constraints of continuous state inequality and control function is presented. Because the number of the switchings is not known a priori, we reformulate the above optimal control problem as a two-level optimization problem. An optimization algorithm is developed to seek the optimal solution on the basis of a heuristic approach and control parametrization technique. Numerical results show that, by employing the obtained optimal control strategy, 1,3-PD concentration at the terminal time can be increased considerably. [ABSTRACT FROM AUTHOR]

Abstract: This paper considers modelling and optimization of a microbial fed-batch fermentation process. A switched system with variable switching instants is proposed to describe the fermentation process of glycerol bioconversion to 1,3-propanediol (1,3-PD). Taking the concentration of 1,3-PD at the terminal time as the cost function and the switching instants as optimization variables, an optimization model involving switched system and subject to continuous state inequality constraints is then presented. By introducing a time-scaling transform, the optimization model is transcribed into an equivalent one with parameters and fixed switching instants. A computational approach to seek the optimal solution is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that, by employing the optimal switching instants, the concentration of 1,3-PD can be increased considerably compared with previous results. [Copyright &y& Elsevier]

Abstract: The mathematical model and optimal control of microbial fed-batch fermentation is considered in this paper. Since it is decisive for increasing the productivity of 1,3-propanediol (1,3-PD) to optimize the feeding rate of glycerol and the switching instants between the batch and feeding processes in the fermentation process, we propose a new nonlinear dynamical system to formulate the process. In the system, the switching instants are variable and the feed rate of glycerol is regarded as the control function. Some important properties of the proposed system and its solution are then discussed. To maximize the concentration of 1,3-PD at the terminal time, an optimal control model involving the proposed system and subject to continuous state inequality constraints is established. The existence of the optimal control of the model is also proved. Finally, a computational approach is constructed on the basis of constraint transcription and smoothing approximation techniques. Numerical results show that the concentration of 1,3-PD at the terminal time can be increased considerably. [ABSTRACT FROM AUTHOR]