Control Method And Experimental Studyof Piezoelectric Based On Hammerstein Model

Piezoelectric actuator can realize high precision motion control and positioning,so it has been widely used in the field of photoelectric,micro-electromechanical and other precise positioning.However,the dynamic hysteresis nonlinearity in the piezoelectric actuator hinders its performance in control and positioning,which not only reduces the control accuracy of the system,but also causes the possibility of system disorder.The dynamic hysteresis nonlinearity is mainly manifested as rate-dependent dynamic hysteresis nonlinearity.Therefore,this paper takes the piezoelectric actuator as the research object and mainly studies the following aspects:1.In view of the piezoelectric actuator rate related to the hysteresis nonlinearity and Hammerstein rate related to the dynamic hysteresis model and the model by the static hysteresis nonlinearity and dynamic linear part concatenated,respectively with static MPI model and autoregressive exogenous model(ARX),and the least square algorithm with constraints is used to identify the static MPI model parameters,a linear dynamic part of the model parameters are identified by the least squares algorithm.Finally,the model test is carried out on the measured data of input and output of the piezoelectric actuator under different single frequency and composite frequency input signals,and the modeling experiment results prove that the proposed Hammerstein rate correlation dynamic model can accurately describe the piezoelectric actuator system.2.Based on the established piezoelectric actuator Hammerstein rate-dependent dynamic hysteresis model,two dynamic tracking control schemes are proposed :(1)PID feedback composite tracking control scheme.Based on feedforward hysteresis compensation.The MPI inverse model is constructed and used as feedforward hysteresis compensator for hysteresis nonlinear compensation.Considering the influence of modeling error and noise,the PID controller is used as the feedback controller to realize the precise tracking control of the system.(2)Internal mold tracking control scheme.TheHammerstein inverse model of piezoelectric actuator is constructed,and the internal mode controller is designed according to the basic principle of internal mode control.Finally,the effectiveness of the proposed control scheme is verified on the piezoelectric experimental platform based on d SPACE.3.A sliding mode control strategy based on Hammerstein rate-dependent dynamic model is proposed.The hysteresis nonlinear system is approximately linearized by compensating hysteresis nonlinearity with MPI inverse model.According to the state space equation of the dynamic linear system,the sliding mode control rate is designed to realize the sliding mode control of the piezoelectric nonlinear system.The experimental results show that the relative error of tracking control is less than 9% based on sliding mode control.4.An adaptive inverse control method based on Hammerstein rate-dependent dynamic hysteresis model is proposed.The constructed rate-dependent dynamic inverse model was used as a feedback controller.Considering the influence of modeling errors and disturbances,the Least Mean Square(LMS)was used to adjust and optimize the parameters of MPI inverse model online.The simulation results show that the proposed scheme can reduce the influence of modeling error caused by off-line modeling on the piezoelectric control system and effectively improve the control accuracy.