Numerical and Experimental Analysis of Multifrequency Composite Synchronization of Four Motors in a Vibrating System With the Modified Fuzzy Adaptive Sliding Model Controlling Method

Abstract

This article addresses the multifrequency composite synchronization of four motors within a vibrating system. Multifrequency synchronization is commonly utilized in engineering due to its effectiveness in screening mixed materials of varying shapes and stickiness. The frequency ratio parameter n influences both the efficiency of the screening process and the overall screening results. Although multifrequency self-synchronization motion can be realized, it can only be realized for integer frequency doubling (n = 2 and n = 3), which limits the diversity of material screening types. By introducing the multifrequency controlled synchronization method, the multifrequency synchronization with noninteger frequencies (n = 1.1–1.9) can be realized, which requires much cost on electrical equipment. To solve this problem, the multifrequency composite synchronization method in this article is proposed. The electromechanical coupling dynamics model of the vibration system is constructed by the Lagrange energy equation. Then, the synchronous condition and stability criteria are derived via the multiscale method by combining the speeds with phase differences. A novel fuzzy adaptive sliding model controlling method associated with a master–slave controlling strategy is introduced to realize multifrequency composite synchronization. The results show that speed errors in different frequencies are only 1000% and 3000%, respectively, and the swing response of the vibration system is small. It presents that the vibration system can not only realize the material screening stably and effectively but also reduce the cost of electrical equipment. The proposed method provides a new reference for multifrequency screening equipment.