Modeling And Control Of Asymmetric Hysteresis In Piezoelectric Actuators

Piezoelectric actuators have a wide range of applications in many fields such as micromechanical systems,micro and nano manufacturing and precision measurement,ultra-precision positioning and vibration control,due to their fast response,high resolution,low energy consumption and high reliability.Due to the inherent hysteresis nonlinearity in piezoelectric actuators,which exhibit non-smoothness,multi-value mapping and memory,this hysteresis characteristic will affect the stability of the system and reduce the control accuracy.Therefore,there is a need to establish mathematical models that can accurately describe the piezoelectric hysteresis characteristics and to design effective control methods.In this paper,a normalized asymmetric Bouc-Wen model is proposed with a piezoelectric actuator as the research object,which can better reflect the actual hysteresis nonlinear characteristics.On this basis,an improved particle swarm optimization(PSO)algorithm is used to identify the parameters of the improved model,and different control methods are used for simulation and experimental verification of the piezoelectric actuator.The details of the study are as follows:1.A normalized asymmetric Bouc-Wen model is proposed and an improved PSO parameter identification method is used.In the normalized Bouc-Wen model,an asymmetric factor is introduced to solve the problem that the traditional Bouc-Wen model can only describe the symmetric hysteresis and improve the applicability of the model.The iterative search capability and recognition accuracy of the algorithm are improved.2.The improved nonlinear function-based active disturbance rejection control(ADRC)is proposed.An improved nonlinear function is proposed to solve the problem of jitter in the system caused by the existence of non-smooth inflection points of the traditional nonlinear function,and then an improved extended state observer(ESO)is designed,the convergence of the observer is improved,and the improved PSO algorithm is used to optimize the controller parameters.The experimental results show that the dynamic performance of the improved ADRC controller proposed in this paper is greatly improved,which can significantly enhance the tracking control effect of the piezoelectric actuator.3.The command filtered backstepping control based on reduced-order extended state observer(RESO)is proposed.Hysteresis and disturbances are estimated using RESO based on the Bouc-Wen model,and then a barrier Lyapunov function(BLF)is used to keep the tracking error within a constraint threshold to ensure trajectory tracking accuracy.The direct control of the hysteresis model is achieved by commanding a filtered backstepping controller,which simplifies the controller design and reduces the computational effort.Finally,an error compensation mechanism is introduced to suppress the effect of filter errors.The experimental results prove that the improved control method is improved in terms of control accuracy and speed,and the control structure is simple.