Research On Active Vibration Control Of Cantilever Plate With Distributed Piezoelectric Actuators

Aviation vehicles are subject to flutter in flight due to the effect of air flow,resulting in fatigue damage to the wing structure of the aircraft and undesirable noises.In severe cases,it may cause vicious accidents.Therefore,vibration control has a great significance for improving the flight safety.MFC actuators are widely used in vibration control due to their light weight and flexibility.In the vibration control of wing,it is difficult to obtain a good control effect using only a single MFC actuator.In this dissertation,the wing is simplified into a cantilever plate and distributed piezoelectric actuators are employed for vibration control.The accuracy of modeling and the efficiency of control algorithms are the key factors affecting the effect of vibration control.Therefore,this dissertation mainly studies the modeling and vibration control algorithms of the distributed piezoelectric cantilever plate system.The distributed piezoelectric cantilever plate system is a multi-input multi-output system.The MFC actuators used in this dissertation are composite material.Hence,a homogenization model is used to analyze the macroscopic properties of the MFC actuator.The finite element method is used for dynamic modeling of the system.For the problem that there is deviation between finite element model and the actual piezoelectric cantilever plate,a modal parameter identification method based on state observer is designed to improve the modeling accuracy through the free vibration experiment.In addition,the MFC actuators have hysteresis nonlinearity.A modified PI hysteresis model is used for the hysteresis nonlinearity modeling.According to the static deformation analysis of the system,this hysteresis nonlinear model is integrated into the entire dynamic model of the system.Based on the dynamic modeling of the system,a multi-input and multi-output active vibration control algorithm is proposed according to the system’s mechanical energy conversion relationship.Meanwhile,the hysteresis nonlinearities of MFC actuators are compensated in the control algorithm based on the inverse model of the modified PI model.In order to improve the controllability and observability of the control system,the MFC actuators’and laser sensors’displacements are optimized by choosing the H₂ norm of the system transfer function as the objective function.To study the applicability of the homogenization model to the modeling of MFC piezoelectric cantilever plate system,the static deformation of the MFC piezoelectric cantilever plate system was analyzed in ANSYS.The ANSYS simulation results show that the model is applicable to MFC cantilever plate system modeling.The relative error of the plate’s deflection between the homogenization model and non-homogenization model is less than 5.77%.The influence of the e32 effect on the deflection of the plate in the homogenization model is not a major factor.Ignoring the e32 effect of homogenization model,the plate’s deflection changed no more than 1.36%.In order to verify the control effect of the proposed vibration suppression control algorithm,a piezoelectric cantilever plate vibration suppression control experiment is designed.The experimental results show that the control algorithm proposed has great vibration suppression control effect for the distributed piezoelectric cantilever plate system.The time that the amplitude decays from 0.25mm to0.01mm using the proposed vibration suppression control algorithm is reduced from15.96s to1.33s compared to the uncontrolled response.The experimental results also prove the accuracy of the proposed modeling method.