Synchronization of small oscillations

Synchronization is studied in an array of identical oscillators undergoing small vibrations. The overall coupling is described by a pair of matrix-weighted Laplacian matrices; one representing the dissipative, the other the restorative connectors. A construction is proposed to combine these two real matrices in a single complex matrix. It is shown that whether the oscillators synchronize in the steady state or not depend on the number of eigenvalues of this complex matrix on the imaginary axis. Certain refinements of this condition for the special cases, where the restorative coupling is either weak or absent, are also presented.


Synchronization of linear oscillators coupled through a dynamic network with interior nodes
Tuna, Sezai Emre (Elsevier BV, 2020-07-01)
Synchronization is studied in an array of identical linear oscillators of arbitrary order, coupled through a dynamic network comprising dissipative connectors (e.g., dampers) and restorative connectors (e.g., springs). The coupling network is allowed to contain interior nodes, i.e., those that are not directly connected to an oscillator. It is shown that the oscillators asymptotically synchronize if and only if the Schur complement (with respect to the boundary nodes) of the complex-valued Laplacian matrix ...
Synchronization under matrix-weighted Laplacian
Tuna, Sezai Emre (Elsevier BV, 2016-11-01)
Synchronization in a group of linear time-invariant systems is studied where the coupling between each pair of systems is characterized by a different output matrix. Simple methods are proposed to generate a (separate) linear coupling gain for each pair of systems, which ensures that all the solutions converge to a common trajectory.
Synchronization of linear systems via relative actuation
Tuna, Sezai Emre (Elsevier BV, 2019-12-01)
Synchronization in networks of discrete-time linear time-invariant systems is considered under relative actuation. Neither input nor output matrices are assumed to be commensurable. A distributed algorithm that ensures synchronization via dynamic relative output feedback is presented.
Low order PWM inverter harmonics contributions to the inverter-fed induction machine fault diagnosis
Akin, Bilal; Orguner, Umut; Toliyat, Hamid A.; Rayner, Mark (Institute of Electrical and Electronics Engineers (IEEE), 2008-02-01)
In this paper, the effects of inverter harmonies on motor current fault signatures are studied in detail. It is theoretically and experimentally shown that the fault signatures caused by the inverter harmonies are similar and comparable to those generated by the fundamental harmonic on the line current. Theoretically-derived extended relations including bearing fault, eccentricity, and broken rotor bar relations are found to match experimental results. Furthermore, it is observed and reported that the asymm...
Circumferential Traveling Wave Slot Array on Cylindrical Substrate Integrated Waveguide (CSIW)
Bayraktar, Omer; Aydın Çivi, Hatice Özlem (Institute of Electrical and Electronics Engineers (IEEE), 2014-07-01)
Traveling wave slot array on cylindrical substrate integrated waveguide (CSIW) is designed, fabricated and measured at K-band. CSIW is formed by wrapping the substrate integrated waveguide (SIW) around the cylinder in the circumferential direction. 16 element longitudinal slot array on the broad wall of single CSIW is designed by the Elliot's design procedure. The spacings between the slot elements are determined to reduce the half power beam width (HPBW) and to obtain good matching at 25 GHz. A 4 x 16 slot...
Citation Formats
S. E. Tuna, “Synchronization of small oscillations,” AUTOMATICA, pp. 154–161, 2019, Accessed: 00, 2020. [Online]. Available: