Open AccessThe State-space Model of Micro-chaos
Author(s) -
Gábor Csernák,
Gábor Stépàn
Publication year - 2021
Publication title -
international journal of mathematical models and methods in applied sciences
Language(s) - English
Resource type - Journals
ISSN - 1998-0140
DOI - 10.46300/9101.2021.15.25
Subject(s) - chaotic , phase space , control of chaos , control theory (sociology) , chaos (operating system) , synchronization of chaos , state space , computer science , domain (mathematical analysis) , settling time , space (punctuation) , statistical physics , mathematics , control (management) , physics , mathematical analysis , control engineering , engineering , step response , artificial intelligence , statistics , computer security , thermodynamics , operating system
Micro-chaos is the phenomenon when the sampling, the delay and the round-off lead to small amplitude chaotic oscillations in a digitally controlled system. It has been proved mathematically during the last few years in a couple of simple cases that the evolving vibrations are indeed chaotic. In this study, we partially generalize these results to the case when an originally unstable state of a system is stabilized by digital feedback control. It is pointed out that this type of systems are sensitive to initial conditions and there exists a finite attracting domain in their phase-space. We also show that the oscillations, related to micro-chaos may have a considerable influence on the accuracy and settling time of the control system. The application of numerical techniques is unavoidable in the case of chaotic systems. Several possibilities are highlighted in the paper for the numerical determination of important characteristics of microchaotic oscillations.