Software Complex for Research of Stability of Discrete Dynamic Systems with Delay
Abstract
The article presents a software package written in C # (the Microsoft Windows) operating system that enables automation of studying stability of three-degree-of-freedom system stability with delay. Such systems are often found in practice (or systems of higher dimensionality can be brought to them by suitable simplification of the model) and therefore the considered model together with the results of analysis can be used to study other practically significant dynamical systems.
As an example of using a software package to study the stability of a three-degree-of-freedom system, in which the delay effect is manifested, we consider the problem of self-excitation of the oscillations of the system of electrode holders (EH) of an arc steel furnace. The equivalent mechanical model is three EHs modeled by solids that perform small torsional vibrations. Self-excitation of vibrations arises due to the mutual influence of electrodynamic forces acting between the electrodes and the elastic forces of the structure.
The idealized mathematical model of the oscillations of three EHs is a system of ordinary differential equations of the 6th order with delay. Using the software package, D – partition curves were constructed and stability regions were obtained for various values of the model parameters. The results of the study are presented in the form of figures and tables.
Since the mathematical apparatus is still quite simple for a three-degree-of-freedom system, the material presented in the article can be used in the educational process when preparing specialists in applied mathematics.
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