Feeding Control Of Fermentation Process Based On Control Vector Parameterization Approach

Fermentation,as a small batch,high-profit,multi-variety fine chemical product production process,involves pharmaceuticals,chemicals,food,and other fields that are closely related to people's lives.Reducing the cost and energy consumption of the fermentation process can bring very considerable economic benefits.Therefore,the optimal control of the fermentation process has been used by industry and academia as an important means of system energy saving,consumption reduction and potential enhancement.The fermentation process often has complex characteristics,strong non-linearity and dynamic changes,and conventional static optimization control techniques are often not applicable.Control Vector Parameterization(CVP)method is the mainstream numerical solution in dynamic optimization and is suitable for fermentation processes with known process mechanism models The CVP method uses a piecewise approximation strategy to discretize the controlled variable in the time domain.The discretized piecewise parameter function is used to approximate the original control trajectory.Infinite-dimensional dynamic optimization problems are transformed into finite-dimensional static optimization problems.The CVP method is widely used because of its high accuracy and easy implementation.In the CVP method,the number of discrete segments is generally determined in advance and does not change during the optimization process.The greater the number of divided segments,the higher the general solution accuracy,but the dimension of the finite-dimensional static optimization problem will increase Increased the complexity of the solution process,resulting in slower algorithm convergence.In this paper,for the problem of industrial fermentation feed control,considering the contradiction between the solution accuracy and convergence speed of the CVP algorithm,the algorithm is improved,further taking feed consumption and target product output as conflicting goals,try to use game ideas to solve multi-objective problems in fermentation.The main innovations of this article are as follows:(1)The existing uniform control vector parameterization(UCVP)method often needs to divide more segments in order to approximate the control trajectory,and the UCVP method cannot optimize important time nodes such as important switching points of the common 'Bang-Bang' control problem in chemical processes.This paper proposes a non-uniform control vector parameterization(NCVP)method,which is used in a typical fermentation feed optimization problem,the results show that the total output of the target product can be improved.(2)CVP algorithm is a gradient optimization algorithm that depends too much on the initial given trajectory.This paper proposes a hybrid strategy of PSO and CVP algorithm to achieve effective solution to dynamic optimization problems.The PSO-CVP hybrid strategy is used in the feeding control of the fermentation process,and its solution accuracy is better than that of pure PSO,and the convergence speed is faster than that of pure CVP.(3)Aiming at the conflicting goals of feed consumption and target product during the fermentation process,the game theory is introduced into the fermentation process,and the Nash equilibrium solution was obtained using the CVP algorithm.The method is applied to the feed rate control of batch fed fermentation process,comparing with the traditional linear weighted multi-objective optimization method,this method is more efficient and can overcomes the disadvantages of linear weighted method,which indicates the feasibility for multi-objective optimization problem of fermentation process.