This article investigates the stability issue of unknown nonlinear functions based on a controlled synchronous vibration system with three inductor motors. The vibration system of three inductor motors belongs to an underactuated system which needs the complex control law. The traditional RBF-neural network adaptive sliding model control (NNASMC) method requires clear functions to achieve better control results. For the dynamic system with time-varying and uncertain loads, there exist unknown nonlinear functions which will cause instability in the system. This paper proposes a modified RBF-NNASMC method. It can guarantee the stability of the controlling system through designing the control law by approximating the unknown nonlinear function. In this article, the differential equations of the dynamical system are derived. The synchronous conditions and stable criteria of the vibrating system are obtained based on the small parameters averaging method. Meanwhile, the stabilization of the controller is certified by the Lyapunov criterion, and the effectiveness and robustness of the controller are also illuminated through simulations. Compared the proposed method with the traditional methods, the novelty presents a smaller overshoot and less oscillation. Finally, this study indicates that the proposed control method has better rapidity and stability in the vibrating system and has well screening effects for the vibrating screens.
Jia et al. (Sat,) studied this question.