Theoretical and experimental investigation on controlled synchronization of four co-rotating coupled exciters driven by induction motors in a vibrating system

Abstract

This paper aims at theoretically and experimentally investigating the controlled synchronization of four co-rotating coupled exciters in a vibrating system driven by induction motors. Using the Lagrange's equations, the motion equations of the vibrating system are derived. Combining the dynamic model of an induction motor with the dynamic model of a vibrating system, an electromechanical coupling model is developed. By virtue of the average method of modified small parameters and the Routh–Hurwitz principle, the self-synchronization criterion for four exciters and the stability criterion of synchronous states are obtained. Based on the numerical results, the stable inphase motion of four exciters fails to be implemented by means of self-synchronization, and as a result, the desired motion type of the vibrating system cannot be realized. Hence, the controlled synchronization is introduced into the vibrating system. Owing to the coupling characteristics of the vibrating system, the control challenge can be turned into a synchronization control problem between four exciters driven by induction motors. To perform the synchronized motion of zero phase differences between four exciters, sliding mode control algorithm and field-oriented control method on four induction motors are applied to develop the controlled synchronization scheme by adopting the master–slave control strategy. The stability of the closed loop system is proved by Lyapunov theorem. Experiments on a corresponding controlled synchronization bedstand are performed to examine the effectiveness of the developed controllers, including a comparison with self-synchronization method. Additionally, experimental results show the robustness of the proposed control scheme against the influence of parameter perturbations and external disturbances. The controlled synchronization method provides a novel approach to the development of vibrating machines.