Abstract
When implementing the tasks of controlling technological processes, finding the optimal control actions, and creating control algorithms that implement the optimal modes of technological processes, it is necessary to present the criterion of optimality in the form of a goal function, the extremum of which best meets the purpose of this object and expressed as - Relevant technical and economic indicators. The criterion of optimality should be an integral indicator that reflects the main aspects of production. Profit is most often taken as such a criterion for typical microbiological industries - as the most generalized indicator, reflecting almost all aspects of the enterprise. Possible criteria of optimality are analyzed in the form of technical and economic indicators of the process of cultivation of microorganisms, the extremum of which best meets the objectives of production and reflects the main aspects of the functioning of the control object. The analysis of possible modes of microalgae cultivation has been carried out. Two optimization algorithms are substantiated. The first one is based on random search method with an absolute bias, an algorithm for optimizing the process of cultivating microorganisms with continuous regeneration of the flow in one cultivator. The second is an algorithm for determining the optimal residence time of chlorella particles in multistage cultivators, focused on the method of dynamic programming implemented in Wellman's recurrence relation. The developed algorithm for operational forecasting and automatic control of the chlorella cultivation process allows, under given production conditions and the composition of nutrients, to increase the productivity of technological equipment and improve the quality of the target product, as well as to prevent in advance various unforeseen and emergency production situations.
Highlights
An attempt to optimize the process according to the appropriate criteria at each moment of time leads to a forced drop in the culture's growth rate
When optimizing, it is necessary to choose such a mode and the desired trajectory of the growth rate, which would provide the optimal value of the objective function and at the same time satisfy the restrictions imposed on the operating mode of cultivators described by the system of equations (1) [5,6,7]
The optimal control problem consists of choosing U∈ V so that at some moment t, the model described by the system of equation (1) reaches the surface S and at the same time, the control (U1, ...,Un) and phase coordinates (x1, ..., xn, u1,..., un, t) would satisfy the constraints: FF1(xx1, ... , xxnn, uu1, ... , uunn, tt) ≤ 0, ii = 1,2, ... , kk
Summary
As the analysis of the modeling results has shown, the content of nutrients is constantly decreasing, and the growth rate decreases, at the initial stage, the value of these indicators increases intensively [1,2,3,4]. When optimizing, it is necessary to choose such a mode and the desired trajectory of the growth rate (depending on the mode of the microbiological process of the chemostat or pipe-stat), which would provide the optimal value of the objective function and at the same time satisfy the restrictions imposed on the operating mode of cultivators described by the system of equations (1) [5,6,7]. Μμii xxii ddddppiiii dddd (SSppii−1,jj SSppii,jj ).
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