Multifrequency controlled synchronization of four inductor motors by the fixed frequency ratio method in a vibration system

In this article, multifrequency controlled synchronization of four inductor motors by the fixed frequency ratio method in a vibration system is investigated. The electromechanical coupling dynamical model of the vibrating system is established. The synchronous condition of the vibrating system is obtained with the small parameter method. Through the theoretical derivation and numerical simulation, multifrequency self-synchronization of four induction motors in the vibration system can’t be realized. To achieve the purpose of multifrequency synchronization motion, the method of multifrequency controlled synchronization is proposed, and a fuzzy PID controlling method is introduced. The stability of the controlling system is certified by the Lyapunov criterion. An arbitrariness of the proposed controlling method which is applied to the vibration system is presented. To certify the accuracy of the theory and simulation, a vibrating test bench is constructed. Some experiments are operated to validate the effectiveness and the proposed controlled synchronization method.