The research of a linear transmission vibrating system of three motors with a circular distribution by the composite synchronization method

In this article, the problem of composite synchronization of three induction motors with the circular distributions is studied. Composite synchronization consists of self-synchronization and controlled synchronization. Firstly, the mechanical and electrical coupling dynamics model of the vibration system is established, the response of the system is obtained, the differential equation is analyzed by means of small parameter average method, synchronicity conditions and stability criteria for vibrating systems to achieve vibrationally synchronized motion are obtained. Then, the master–slave control strategy and fuzzy PID (proportional–integral–derivative) control method are introduced to realize the part of controlled synchronization in the vibration system. The stability of the control method is verified by Lyapunov criterion. The applicability of this control method and its feasibility for practical applications are proved by numerical simulation and experiment. The study in this paper illustrates the feasibility of designing some new vibratory transporters for industrial transportation.