Research On Identification And Control For Hysteresis Nonlinear System Of Piezoelectric Ceramic Actuator

Micro-actuators with piezoelectric ceramics as displacement detecting sensors have the advantages of small size,low energy consumption,high positioning accuracy etc,But the inherent hysteresis nonlinearity in materials makes it difficult to fully demonstrate the efficacy in ultra-precision positioning systems.Compared with the macro actuator,the piezoceramic actuator has a shorter stroke and a complicated control scheme.This makes it an urgent problemfor academia and industry to reasonably model the hysteresis nonlinearity of piezoelectric ceramic actuators and design more concise and practical control schemes.Intelligent algorithm,as a new research strategy,is playing an important role in the modeling and control of hysteretic nonlinearity with its high efficiency,robustness and adaptability.In this paper,based on Intelligent algorithm,system identification and controller design for hysteretic nonlinearity are studied.Research contents are as follows:(1)A two-stage modeling method based on Hammerstein model is proposed for a class of piezoelectric actuators with hysteretic nonlinearity.First,a Preisach hysteresis operator is introduced to transform the hysteretic multivalued mapping into one-to-one mapping.and then introduce the isometric mapping method,so that the multi-dimensional hysteresis data can be mapped to the low-dimensional space.the processed low-frequency data is input into the improved extreme learning machine training to obtain a static hysteresis model,which is a one-stage identification;The second-stage identification,that is,the identification of the dynamic part.It input the high frequency hysteretic data after the same processing into the extreme learning machine model with known parameters,and the intermediate variables of the Hammestein model are obtained.Then the parameters of the dynamic linear part are identified by the Autoregressive Exogenous(ARX)model.The experimental results demonstrate the feasibility of the identification scheme.(2)Aiming at the hysteretic nonlinear modeling of piezoelectric actuator in precision positioning system,a modeling method based on Backlash description function operator is proposed.A class of novel Backlash operators is introduced to describe hysteresis nonlinear contours.On the basis of transforming the multi-valued mapping of hysteresis characteristicsinto a one-to-one mapping by the extended input space method,the static hysteresis model is established by using the support vector regression machine optimized by gravitational search algorithm.In order to reflect the dynamic characteristics of hysteresis,the rate dependence of hysteresis loops is characterized by ARX model,so the Hammerstein cascade model is established.The measured data are collected from the precise positioning system,and the displacement of the piezoelectric actuator at a given voltage is obtained by capacitive sensor.The model is tested.Experiments show that the model has good performance,and the identification process is simple and easy to implement in engineering.(3)For the control problem of piezoelectric ceramic actuators with hysteresis nonlinearity,an inversion preset performance control method is proposed for a class of hysteretic nonlinear systems with input saturation nonlinearity.Backlash-Like differential equation model,which can separate the disturbance term,is used to represent the hysteretic nonlinearity of the system.The neural network algorithm is used to approximate the disturbance term decoupled by the hysteretic model.The equivalent error model of the system is established by the improved presupposition performance function and error transformation method,and the inversion presupposition performance controller is designed.The input saturation problem is solved by designing an auxiliary anti-saturation compensator separately.Based on Lyapunov stability theory,stability analysis is carried out,The feasibility of the control method is verified by simulation.