Synchronization analysis of two eccentric rotors with double-frequency excitation considering sliding mode control

•Sliding mode control strategy is employed to control synchronization of vibration system excited with double-frequency.•The controlled synchronization theory and the self-synchronous mechanism of the vibration system are analyzed.•The proposed control method can successfully implement zero-phase difference motion of the double-frequency system.•Tracking controllers of velocity and phase have strong robustness to restrain the variation of geometrical parameters. In petroleum exploitation industry, self-synchronous vibrating screen excited with dual-frequency cannot obtained an ideal synchronization motion state due to its own inherent coupling characteristics, which is unsuitable to separate cuttings from drilling fluid. Thus, for solving the above-mentioned problem, a controlled system of two eccentric rotors (ERs) actuated with double-frequency is proposed by considering sliding mode control (SMC) method. Firstly, motion differential equation in each direction is established according to physical model of the vibration system. Then, self-synchronous mechanism between high-frequency rotor and low-frequency rotor is gradually analyzed by small parameters method and Poincare–Lyapunov theory, and it is revealed that the self-synchronous vibration system cannot implement a stable phase difference on account of the existence of velocity error and phase error. Subsequently, combining the SMC algorithm with master-slave control (MSC) structure, tracking controllers of velocity error and phase error are systematically designed to control the synchronization state of the dual-frequency system. Finally, Runge–Kutta method is assigned to validate the reliability of theory and the stability of system. Comparing controlled synchronization with self-synchronization, the results demonstrate that the phase difference between the rotors can be accurately stabilized at zero by the proposed control strategy. Meanwhile, the designed control system has strong robustness to restrain the dynamic behavior of vibration system under parameter variations. This study will be helpful for the improvement of separation technology.