Control Synchronization of Two Nonidentical Homodromy Exciters in Nonlinear Coupled Vibration System

In order to analyze synchronization control problems of two non-identical homodromy eccentric rotors (ERs) in a nonlinearly coupled system of vibrating machinery-part (NCS-VMP), a new electromechanical coupling nonlinear dynamic model considering nonlinear acting force of the part and nonlinear support is established, NCS- VMP's complex control is converted into rotating speed and phase synchronous control of two homodromy non- identical exciters. By considering the dynamic interactions among the vibration body, the part and the ERs, the nonlinear dynamical equation of the NCS-VMP are established. An accurate synchronization control of speed and phase method are proposed for two homodromy ERs in NCS-VMP. The precise speed and phase synchronization control is mainly reflected as: The cross-coupling control strategy is used which considering the coupling effect between two co-rotating exciters. The radial basis function network adaptive global sliding mode algorithm (RBFN- AGSMA) is used to adaptively approximate the total uncertainty of system including the nonlinear support and the nonlinear force of the parts, which can effectively reduce the estimation error. The radial basis function network method can suppress the jitter of the system and make the influence of the system more stable after replacing the sign function. The stability of RBFN-AGSMA controller is proved by Lyapunov theory. The controller's property is verified through numerical methods and taking the sliding mode control (SMC) algorithm into comparison. Results indicate that the designed control method can reduce chattering clearly compared with the SMC algorithm, and it is capable to improve the control accuracy of two non-identical homodromy exciters. By studying the effects of parameter change in the NCS-VMP on the system, the strong robustness of RBF network global sliding mode controller to parameter perturbations is proved. It is proposed that RBFN-AGSMA controller can control two nonidentical homodromy ERs in NCS-VMP to achieve accurate vibration trajectory in the working direction.