The method of a three-dimensional integral functional in a study of multiparameter objects of control and management

На основі теорії реологічних переходів виконані дослідження технологічних процесів. Показано, що такі процеси можна описати інтегральними імпульсними дельта-функціями Дірака. Приведені аналітичні рівняння, за якими можна розраховувати екстремалі технологічного процесу. Це дозволяє забезпечити максимальну ефективність технологічного процесу при мінімумі енергетичних та матеріальних затрат.
На основе теории реологических переходов выполнены исследования технологических процессов. Показано, что такие процессы можно описать интегральными импульсными дельта-функциями Дирака. Приведены аналитические уравнения, по которым можно рассчитывать экстремали технологического процесса. Это позволяет обеспечить максимальную эффективность технологического процесса при минимуме энергетических и материальных затрат.
Technological processes of the chemical, oil processing, food processing, and other industries are based on transferring the impulses of mass, energy, and movement from their source to a rheological transition zone responsible for substance conversion. The processes are researched on the basis of the theory of rheological transitions and the zero gradient method. We have proved that such technological processes can be described by means of the Dirac integral impulse delta-functions(δ functions), which allows solving nonlinear equations of energy and mass transfer in an analytical form. We have revealed that such technological processes are characterized by three interrelated coordinates: incoming heat or material flows, time during which substances stay in the processing facility, and output coordinates that determine productivity and quality of the manufactured products. The multiparameter processes are characterized by initial coordinates, among which there exist extreme dependencies. The extremes used to be typically determined by equations of two-dimentional criteria that could not secure an optimal technological process on the basis of input and output coordinates and the time during which substances stay in the processing facility. We have proved that optimal correlation between the parameters can be achieved on the basis of a three-dimensional integral functional the extremes of which are the functions of the Lagrange, Pontryagin and Euler criteria. We have suggested analytical equations for calculating extremes of the technological process, which facilitates maximum efficiency of the process at minimum energy and material expenses.