Synchronization analysis and control of three eccentric rotors in a vibrating system using adaptive sliding mode control algorithm

In this paper, self- and controlled synchronizations of three eccentric rotors (ERs) in line driven by induction motors rotating in the same direction in a vibrating system are investigated. The vibrating system is a typical underactuated mechanical-electromagnetic coupling system. The analysis and control of the vibrating system convert to the synchronization motion problem of three ERs. Firstly, the self-synchronization motion of three ERs is analyzed according to self-synchronization theory. The criterions of synchronization and stability of self-synchronous state are obtained by using a modified average perturbation method. The significant synchronization motion of three ERs with zero phase differences cannot be implemented according to self-synchronization theory through analysis and simulations. To implement the synchronization motion of three ERs with zero phase differences, an adaptive sliding mode control (ASMC) algorithm based on a modified master-slave control strategy is employed to design the controllers. The stability of the controllers is verified by using Lyapunov theorem. The performances of the controlled synchronization system are presented by simulations to demonstrate the effectiveness of controllers. Finally, the effects of reference speed and non-zero phase differences on the controlled system are discussed to show the strong robustness of the proposed controllers. Additionally, the dynamic responses of the vibrating system in different synchronous states are analyzed.