Комп’ютерне моделювання динаміки одновимірних нелінійних об’єктів з розподіленими параметрами - Федорчук, Володимир Анатолійович; Канарчук, Юрій Валерійович (Kamianets-Podilskyi National Ivan Ohiienko University, 2018)
The problem of computer simulation of one-dimensional non-linear objects with distributed parameters is considered. The method of straight lines for approximation transformation of the base model is used. Model is presented in the form of a differential equation in partial derivatives. As a result, a system of second-order ordinary differential equations is obtained. For computer implementation in the Simulink/Matlab environment, differential equations are represented as algebraic dependencies of the Laplace space. By equivalent algebraic transformations in the Laplace space, the mathematical model is reduced to a form that is convenient for building the Simulink model. The resulting structural model consists of subsystems that implement ordinary differential equations of second order, and the subsystems are connected using both direct and inverse relations. This gave the model the property of reversibility, that is, any subsystem can be both an object of external influence and a source of data on the change of parameters in time for the corresponding section of the modelled object. Another positive feature of the model is that at the level of subsystems that reproduce the dynamics of spatial areas of a distributed object, you can set different physical parameters. Then such a model can be used in the case when a non-uniform object is modelled in which physical parameters differ in different areas (for example, a long shaft with areas of different diameters or made of different materials). Since the physical parameters of the simulated object are present in an explicit form in the subsystems of the structural computer model, this makes it possible to specify non-linear dependencies between them. The paper describes the results of the computational experiments performed for the cases of linear and nonlinear objects with distributed parameters. The experiments confirmed the effectiveness of the proposed approach to the construction and computer implementation of models of nonlinear objects with distributed parameters.