Matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics in Simulink

Abstract

The dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics are based on the systems of algebraic and differential equations that describe a change in the basic technological parameters. The main difficulty in using such models in MathWorks Simulink™ computer simulation systems is the representation of ordinary differential equations (ODE) and partial differential equations (PDE) that describe the dynamics of a process as a MathWorks Simulink™ block set. The study was aimed at developing an approach to the synthesis of matrix dynamic models of elements of technological systems with perfect mixing and plug-flow hydrodynamics that allows for transition from PDE to an ODE system on the basis of matrix representation of discretization of coordinate derivatives. A sugar syrup cooler was chosen as an object of modeling. The mathematical model of the cooler is formalized by a set of perfect reactors. The simulation results showed that the mathematical model adequately describes the main regularities of the process, the deviation of the calculated data from the regulations did not exceed 10%. The proposed approach significantly simplifies the study and modernization of the current and the development of new technological equipment, as well as the synthesis of algorithms for controlling the processes therein.

Mathematical modeling of non-steady heat exchange process in cryogenic coil-wound heat exchangers

“…On this assumption, the waste gas flow can be described by the ideal mixing model, and the length of the section will be determined by the coiling h (m). 4 4…”

“…For solution of the system of equations (2), (3), (6), a model has been developed in MathWorks Simulink TM computer simulation system, based on the methods described in [4], and consisting in discretization of the spatial variable by the finite difference method, with replacement of the spatial derivative by the matrix equations. The use of "Repeating Sequence Interpolated" blocks in this model allowed specifying, in the form of arrays, the profiles of change of the temperatures of the air and waste has flows at the main heat exchanger inlet, as well as the dependences of the change of the waste gas flow through the heat exchanger and the pressure of the forward and return flows, simulating the real change of the said parameters.…”

Simulink models of technological systems with perfect mixing and plug-flow hydrodynamics

“…Один из подходов основан на дискретизации только пространственной переменной методом конечных разностей, при этом производные по времени остаются непрерывными и ДУЧП представляется в виде задачи Коши для системы ОДУ [10]. Реализация каждого уравнения системы ОДУ приводит к довольно громоздким структурным моделям в Simulink, и актуальным является компактное представление таких систем в матричном виде [11][12][13]. В этом случае необходимо заменить разложение производных по пространственной координате матричными уравнениями [12].…”