Global Sliding Model Synchronous Control Based on RBFN of Three Homodromy Exciters in Nonlinear Vibration System

To analyze the speed and phase synchronization control problems of three homodromy exciters in nonlinear vibration system of machinery-material (NVS-MM), the nonlinear vibration system dynamics model under the excitation of three exciters considering the nonlinear support and the influence of the material is derived. Aiming at the synchronous control problem of NVS-MM, a controller based on radial basis function network global sliding mode control (RBFN-GSMC) algorithm and adjacent cross-coupling control (ACCC) strategy is established. Using RBFN to adaptively approximate the total uncertainty of NVS-MM including nonlinear support and material nonlinear force can effectively reduce the estimation error. Using the RBFN method instead of the symbol function can suppress the chattering of the system and stabilized the response of the system. Stability of the controller proposed for NVS-MM is proved by Lyapunov theory. Performance of the proposed RBFN-GSMC algorithm is further analyzed and verified by numerical simulation. Results show that compared with other control methods, the effectiveness of the proposed ACCC strategy combined with RBFN-GSMC algorithm is verified. ACCC strategy considers the coupling between two adjacent exciters, which can improve phase and speed synchronization control accuracy of three homodromy exciters in the NVS-MM. Finally, by studying the influence of parameter disturbances in the NVS-MM on the performance of controller, it is proved that the proposed controller is robust to external loads or parameter disturbances.