# Controlled synchronization of three co-rotating exciters based on a circular distribution in a vibratory system

## TL;DR

This paper studies how to synchronize three rotating machines in a vibrating system to achieve controlled motion patterns useful in industrial applications.

## Contribution

A fuzzy PID control method based on master-slave strategy is proposed to achieve controlled synchronization in vibratory systems.

## Key findings

- Self-synchronization cannot produce the required elliptical motion in vibrating systems.
- Fuzzy PID control enables stable and effective controlled synchronization.
- Lyapunov stability criterion confirms the robustness of the control method.

## Abstract

In this article, an engineering problem of three co-rotating exciters with the circular distribution in a vibrating system is investigated. The dynamical model constructed by the motion differential equations is established. By introducing the small parameter averaged method in the dynamic equation, the synchronization and stability conditions of the electromechanical coupling dynamical model is derived. To illustrate the necessity of the controlling method, the self-synchronization of the vibrating system is firstly analyzed with the theory, numerical simulations and experiments. With the self-synchronization results, it is indicated that the ellipse trajectory which is needed in the industry can’t be realizefd by the self-synchronization motion of the vibrating system. And then, a fuzzy PID controlling method based on the master–slave controlling strategy is introduced in the vibrating system to realize the controlled synchronization. The Lyapunov stability criterion is given to certify the stability of the controlling system. Through some simulations and experiments, the effectiveness of controlled synchronization is illustrated in the discussion. Finally, the present work illuminates the feasibility and practicality for designing some new types of vibrating screens in the industry.