biostudies-literatureJia L2021 Scientific research support for high-level talent from Shenyang Ligong University2022 Liaoning Education department General Project2467https://www.ebi.ac.uk/biostudies/studies/S-EPMC9922278biostudies-literatureUnknown13(1)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 proposeScientific reportsMultifrequency controlled synchronization of four inductor motors by the fixed frequency ratio method in a vibration system.PMC9922278LJKMZ202206021010147001001Liu ZWang CJia LfalseMultifrequency 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 propose2023-01-01T00:00:00Z2023 Feb2025-05-29T21:23:53.897Z2025-05-29T21:23:53.897ZS-EPMC99222783677438410.1038/s41598-023-29603-y