Research On Hysteresis Modeling And Control Of Piezoelectric Actuators

With the rapid development of science and technology,industrial development has put forward higher requirements for the accuracy of high-precision positioning systems.Piezoelectric actuators are widely assembled in micro and no-scale systems due to their high positioning accuracy,good stability,and sensitive response,which can meet the requirements of ultra-high precision.However,the unavoidable disadvantage of piezoelectric actuators is the presence of hysteresis,which exhibits non-smooth,memorable multi-value mapping,and rate dependence.Therefore,when excited by a voltage with a wide frequency range,it is usually Frequency.It usually severely limits system performance,such as causing inaccuracies or bad oscillations,or even instability.Once the system lacks compensation for hysteresis,it may exhibit bad characteristics.To eliminate the harmful effects of hysteresis,it is necessary to establish a model describing the hysteresis so that a corresponding controller can be designed based on the obtained hysteresis model to eliminate the harmful effects of the hysteresis.The main research of this article includes the following:(1)A dynamic hysteresis model based on Elman neural network is proposed.First,an improved dynamic hysteretic operator(IDHO)is proposed as the one-dimensional input of the Elman neural network.Since Elman neural network cannot directly handle the multi-valued mapping problem,this paper adopts the construction idea based on spatial expansion to convert the lagging multi-valued mapping a one-to-one mapping on the newly expanded input space.Then,the Elman neural network combined with IDHO was used to approximate the rate-dependent hysteresis behavior.The combination of Elman neural network and IDHO can reflect the dynamic characteristics and extract the characteristics of rate-dependent hysteresis.(2)A Hammerstein-like model based on weighted dynamic hysteresis operator is proposed First,an improved dynamic hysteretic operator(IDHO)is proposed.The offset,dead-band width,and dead-band slope are added to the operator,and the height and width of the hysteresis loop are adjusted to reflect the asymmetry and rate dependence of the hysteresis.Then use the improved hysteresis operator weighted superposition to represent the static nonlinear part.The parameters and weights of the hysteresis operator can be adjusted online to adapt to changes in external conditions.The input autoregressive model is used to represent the dynamic linear part Hammerstein-like model with hysteresis.Finally,the parameters in the model were identified by least squares method,matrix expansion,and matrix singular value decomposition,and it was proved that the identified parameters were unbiased estimates,which verified the feasibility of Hammerstein-like model.(3)A hysteresis inverse compensation controller based on Elman neural network is designed.Firstly,the inverse hysteresis operator of IDHO was obtained using the analytical method as the one-dimensional input of the Elman neural network,and the two-input-single-output Elman neural network inverse model was designed by spatial expansion.The Elman neural network inverse model is trained through a large amount of measured data.Finally,the trained series is connected in front of the piezoelectric driver to realize inverse compensation control.Simulation shows that the inverse compensation controller designed by Elman neural network inverse model can achieve better compensation effect.