Open AccessQuasi-harmonic self-oscillations in discrete time: analysis and synthesis of dynamic systems
Author(s) -
В. В. Зайцев,
Alexander V. Karlov
Publication year - 2022
Publication title -
fizika volnovyh processov i radiotehničeskie sistemy
Language(s) - English
Resource type - Journals
eISSN - 2782-294X
pISSN - 1810-3189
DOI - 10.18469/1810-3189.2021.24.4.19-24
Subject(s) - van der pol oscillator , amplitude , realization (probability) , discrete time and continuous time , differential equation , harmonic oscillator , mathematical analysis , mathematics , control theory (sociology) , physics , computer science , nonlinear system , quantum mechanics , statistics , control (management) , artificial intelligence
For sampling of time in a differential equation of movement of Thomson type oscillator (generator) it is offered to use a combination of the numerical method of finite differences and an asymptotic method of the slowl-changing amplitudes. The difference approximations of temporal derivatives are selected so that, first, to save conservatism and natural frequency of the linear circuit of self-oscillatory system in the discrete time. Secondly, coincidence of the difference shortened equation for the complex amplitude of self-oscillations in the discrete time with Eulers approximation of the shortened equation for amplitude of self-oscillations in analog system prototype is required. It is shown that realization of such approach allows to create discrete mapping of the van der Pol oscillator and a number of mappings of Thomson type oscillators. The adequacy of discrete models to analog prototypes is confirmed with also numerical experiment.