Study On Hysteresis Nonlinear Modeling And Control Of Piezoelectric Ultra Precision Positioning Table

In recent years,with the development of ultra-precision machining,inspection and micro-assembly technology,the influence of micro-vibration on accuracy of machining precision has become extremely prominent.The traditional passive vibration isolation technology has poor suppression effect on low frequency vibration and cannot meet the requirement of vibration isolation in complex excitation environment.Active vibration isolation is widely used in vibration isolation of ultra-precision machining and testing equipment because it can effectively suppress vibration and compensate for the poor effect of passive vibration isolation on low-frequency vibration.In this paper,the key technical problems in active vibration isolation are studied,and the main contents include:1)The working principle and control algorithm of the adaptive active vibration isolation system are introduced.The theory and formula of adaptive filtering is deeply deduced.Based on the principle of adaptive filtering,the least mean square(LMS)algorithm for adaptive active vibration isolation controller is introduced.Based on the improved filtered-X least mean square(FXLMS)algorithm,the advantages and disadvantages of the FXLMS algorithm are analyzed,which lays a theoretical foundation for subsequent research.2)The influence of the secondary path on the adaptive active vibration isolation control algorithm is analyzed,the traditional secondary path online modeling methods are introduced,and the advantages and disadvantages of various modeling algorithms are analyzed.On this basis,based on fractional signal processing,a two-step variable step strategy for online secondary path identification is proposed,under the principle of minimizing the number of adaptive filters and not increasing the complexity of the algorithm,compared with the existing algorithms,the convergence speed of the secondary path identification of this algorithm is faster,the fluctuation of the system after convergence is smaller,and the identification accuracy of the secondary channel and the stability of the system are significantly improved.3)In this part,the improved Backlash-Like segment identification model is adopted to describe the static nonlinear characteristics of the piezoelectric actuator.The dynamic hysteresis model of piezoelectric micro-actuator is established by combining ARX model.At the same time,an improved particle swarm optimization(PSO)algorithm with cross-mutation strategy is proposed to identify the model parameters,so as to solve the problem that the traditional particle swarm optimization(PSO)algorithm is prone to fall into local optimization when identifying model parameters.Secondly,the inverse model of the piezoelectric actuator is established,and the hysteresis of the piezoelectric actuator is compensated by the inverse model feedforward control.The experimental platform of the piezoelectric actuator is built to verify the accuracy of the model describing the hysteresis nonlinearity of the piezoelectric actuator and the control effect of the inverse feedforward compensation on the linearization control of the piezoelectric actuator.4)In Matlab/Simulink tool,level-2m file-type S function is used to write the adaptive control module of FXLMS algorithm.Based on the adaptive control module,an adaptive active vibration isolation simulation system based on feed-forward and inverse compensation of the piezoelectric actuator is established,and the single frequency,mixing frequency,low frequency and high frequency signals are taken as vibration excitation signals to carry out the simulation research of micro-displacement active vibration isolation based on hysteresis nonlinear compensation of the actuator.