Synchronization of oscillators not sharing a common ground

Download

index.pdf

Date

2023-5-01

Author

Tuna, Sezai Emre

Metadata

Show full item record

This work is licensed under a Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 International License.

Item Usage Stats

131
views

52
downloads

Networks of coupled LC oscillators that do not share a common ground node are studied. Both resistive coupling and inductive coupling are considered. For networks under resistive coupling, it is shown that the oscillator-coupler interconnection has to be bilayer if the oscillator voltages are to asymptotically synchronize. Also, for bilayer architecture (when both resistive and inductive couplers are present) a method is proposed to compute a complex-valued effective Laplacian matrix that represents the overall coupling. It is proved that the oscillators display synchronous behavior if and only if the effective Laplacian has a single eigenvalue on the imaginary axis.

Subject Keywords

Bilayer coupling, Effective Laplacian matrix, Harmonic oscillator, Nonstar network, Synchronization

URI

https://hdl.handle.net/11511/102752

Journal

Automatica

DOI

https://doi.org/10.1016/j.automatica.2023.110960

Collections

Department of Electrical and Electronics Engineering, Article

Suggestions

OpenMETU
Core

Synchronization of harmonic oscillators under restorative coupling with applications in electrical networks Tuna, Sezai Emre (2017-01-01) The role of restorative coupling on synchronization of coupled identical harmonic oscillators is studied. Necessary and sufficient conditions, under which the individual systems' solutions converge to a common trajectory, are presented. Through simple physical examples, the meaning and limitations of the theorems are expounded. Also, to demonstrate their versatility, the results are extended to cover LTI passive electrical networks. One of the extensions generalizes the well-known link between the asymptoti...
Synchronization of linearly and nonlinearly coupled harmonic oscillators Penbegül, Ali Yetkin; Tuna, Sezai Emre; Department of Electrical and Electronics Engineering (2011) In this thesis, the synchronization in the arrays of identical and non-identical coupled harmonic oscillators is studied. Both linear and nonlinear coupling is considered. The study consists of two main parts. The first part concentrates on theoretical analysis and the second part contains the simulation results. The first part begins with introducing the harmonic oscillators and the basics of synchronization. Then some theoretical aspects of synchronization of linearly and nonlinearly coupled harmonic osci...
Synchronization analysis of coupled Lienard-type oscillators by averaging Tuna, Sezai Emre (2012-08-01) Sufficient conditions for the synchronization of coupled Lienard-type oscillators are investigated via averaging technique. The coupling considered here is fixed, nonsymmetric, and nonlinear. Under the assumption that the interconnection topology defines a connected graph, it is shown that the solutions of oscillators converge arbitrarily close to each other, starting from initial conditions arbitrarily far apart, provided that the frequency of oscillations is large enough and the initial phases of oscillat...
Adaptive Harmonic Balance Methods, A Comparison Sert, Onur; Ciğeroğlu, Ender (2016-01-28) Harmonic balance method (HBM) is one of the most popular and powerful methods, which is used to obtain response of nonlinear vibratory systems in frequency domain. The main idea of the method is to express the response of the system in Fourier series and converting the nonlinear differential equations of motion into a set of nonlinear algebraic equations. System response can be obtained by solving this nonlinear equation set in terms of the unknown Fourier coefficients. The accuracy of the solution is great...
Structural Analysis of Synchronization in Networks of Linear Oscillators Tuna, Sezai Emre (2022-07-01) In undirected networks of identical linear oscillators coupled through dissipative and restorative connectors (e.g., pendulums undergoing small vibrations connected via dampers and springs), the relation between asymptotic synchronization and coupling structure is studied. Conditions on the interconnection under which synchronization can be achieved for some selection of coupling strengths are established. How to strengthen those conditions so that synchronization is guaranteed for all admissible parameter ...

Citation Formats

S. E. Tuna, “Synchronization of oscillators not sharing a common ground,” Automatica, vol. 151, pp. 0–0, 2023, Accessed: 00, 2023. [Online]. Available: https://hdl.handle.net/11511/102752.