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.

Self-synchronization of unbalanced rotors and the swing equation / Smirnova, Vera B.; Proskurnikov, Anton V.. - ELETTRONICO. - 54:(2021), pp. 71-76. ((Intervento presentato al convegno 6th IFAC Conference on Analysis and Control of Chaotic Systems CHAOS 2021 tenutosi a Catania, Italy nel 27-29 September, 2021 [10.1016/j.ifacol.2021.11.028].

Self-synchronization of unbalanced rotors and the swing equation

Proskurnikov, Anton V.
2021

Abstract

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.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11583/2939342