Estimation the Domain of Attraction for a System of Two Coupled Oscillators with Weak Damping
Ładowanie...
Data
2021
Tytuł czasopisma
ISSN czasopisma
Tytuł tomu
Wydawca
Wydawnictwo Politechniki Łódzkiej
Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.
Lodz University of Technology Press
Lodz University of Technology. Faculty of Mechanical Engineering. Department of Automation, Biomechanics and Mechatronics.
Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki.
Lodz University of Technology Press
Lodz University of Technology. Faculty of Mechanical Engineering. Department of Automation, Biomechanics and Mechatronics.
Abstrakt
When solving a wide class of problems of nonlinear dynamics, the stability property
of a given system regime is a prerequisite for design. An important role is played by the
concept of the domain of attraction (DoA) of the equilibrium point (or limit cycle). However,
as a rule, this domain is difficult to find and describe in explicit form. Therefore, the search
for DoA estimate has been a fundamental problem in the control theory since the middle of
the last century. Currently, methods based on Lyapunov functions predominate in the literature.
We have studied the problem of obtaining the estimates of the DoA for equilibrium of
the mechanical systems. The method for using Lyapunov function of special kind for a system
with polynomial right-hand side to find the estimates for DoA is proposed. This procedure is
illustrated by the example of a mechanical system which consists of two coupled nonlinear
oscillators with weak damping.
Opis
Słowa kluczowe
domain of attraction, nonlinear oscillator, weak damping, domena przyciągania, oscylator nieliniowy, słabe tłumienie
Cytowanie
Puzyrov V., Awrejcewicz J., Losyeva N., Savchenko N., Nikolaieva O., Estimation the Domain of Attraction for a System of Two Coupled Oscillators with Weak Damping.
W: DSTA-2021 Conference Books – Abstracts (16th International Conference : Dynamical Systems Theory and Applications DSTA 2021 ABSTRACTS), Awrejcewicz J. (red.), Kaźmierczak M. (red.), Olejnik P. (red.), Mrozowski J. (red.), Wydawnictwo Politechniki Łódzkiej ; Politechnika Łódzka. Wydział Mechaniczny. Katedra Automatyki, Biomechaniki i Mechatroniki, Łódź 2021, s. 704-705, ISBN 978-83-66741-20-1.