TY - JOUR

T1 - Self-synchronization of unbalanced rotors and the swing equation

AU - Smirnova, Vera B.

AU - Proskurnikov, Anton V.

PY - 2021

Y1 - 2021

N2 - We consider a problem of self-synchronization in a system of vibro-exciters (rotors) installed on a common oscillating platform. This problem was studied by I.I. Blekhman and later by L. Sperling. Extending their approach, we derive the equations for a system of n rotors and show that, separating the slow and fast motions, the “slow” dynamics of this systems reduces to a special case of a so-called swing equation that is well studied in theory of power networks. On the other hand, the system may be considered as “pendulum-like” system with multidimensional periodic nonlinearities. Using the theory of such systems developed in our previous works, we derive an analytic criteria for synchronization of two rotors. Unlike synchronization criteria available in mechanical literature, our criterion ensures global convergence of every trajectory to the synchronous manifold.

AB - We consider a problem of self-synchronization in a system of vibro-exciters (rotors) installed on a common oscillating platform. This problem was studied by I.I. Blekhman and later by L. Sperling. Extending their approach, we derive the equations for a system of n rotors and show that, separating the slow and fast motions, the “slow” dynamics of this systems reduces to a special case of a so-called swing equation that is well studied in theory of power networks. On the other hand, the system may be considered as “pendulum-like” system with multidimensional periodic nonlinearities. Using the theory of such systems developed in our previous works, we derive an analytic criteria for synchronization of two rotors. Unlike synchronization criteria available in mechanical literature, our criterion ensures global convergence of every trajectory to the synchronous manifold.

KW - Synchronization, stability of nonlinear systems, vibrational mechanics

UR - https://www.sciencedirect.com/science/article/pii/S2405896321020449#!

U2 - https://doi.org/10.1016/j.ifacol.2021.11.028

DO - https://doi.org/10.1016/j.ifacol.2021.11.028

M3 - Conference article

VL - 54

SP - 71

EP - 76

JO - IFAC-PapersOnLine

JF - IFAC-PapersOnLine

SN - 2405-8963

IS - 17

T2 - 6th IFAC Conference on Analysis and Control of Chaotic Systems CHAOS 2021

Y2 - 27 September 2021 through 29 September 2021

ER -