Research On Dynamic Modeling And Control Of Piezoelectric Actuators

Piezoelectric actuators are widely used in micro and nano positioning systems for their high positioning accuracy,fast response and high output force.However,the input rate-dependent hysteresis characteristics of piezoelectric actuators can seriously affect system performances.Therefore,it is necessary for piezoelectric actuators to model the input-rate dependent and design their corresponding controller in the ultra-precision systems.Operation principle and related characteristics of piezoelectric ceramics are introduced,and the modeling and control methods of the piezoelectric actuators are summarized.For the Bouc-Wen model has a very simple form and fewer parameters,it is more convenient for designing controller,so two improved rate-dependent Bouc-Wen models are proposed in this paper to describe the asymmetry and rate-dependence of hysteresis.Then,based on the two rate-dependent Bouc-Wen models,the corresponding controllers are designed respectively.The details of the study are listed as follows.First,an asymmetric Bouc-Wen model by applying an asymmetric input function to the traditional Bouc-Wen model is proposed to solve the symmetry problem of the hysteresis loop.Differential evolution algorithm is applied to identify the model parameters.In addition,the experimental results show the validation of the proposed asymmetric Bouc-Wen model.Next,the static asymmetric Bouc-Wen model cannot depict the hysteresis characteristics of piezoelectric actuators with the input frequency changing.Based on the relationship between hysteresis loop,the frequency of the input signal and the parameters in the model,a rate-dependent Bouc-Wen model with the information of input frequency is proposed.Moreover,the validation of the rate-dependent Bouc-Wen model is experimentally proved.Then,based on the established rate-dependent Bouc-Wen model,its pseudo-inverse model is obtained directly by identification,and its corresponding inverse compensator of the piezoelectric actuators is designed.Moreover,model free control(MFC)is introduced to improve the system performances.Therefore,a model free control strategy with the pseudo-inverse compensator of the piezoelectric actuators is designed.For comparison,this paper also uses the traditional model free control strategy and the PID control strategy with the pseudo-inverse compensator.And the experimental results show the better feasibility of the proposed method.Finally,the proposed rate-dependent Bouc-Wen model above cannot solve the inverse model directly,so a new invertible rate-dependent Bouc-Wen model is proposed.For its fewer parameters,it is more convenient for the novel model to solve the inverse model of the corresponding hysteresis,and it is easier to implement in practice.And the experiments verify that the two models are both describe the input-rate depended hysteresis,but the second model avoids the tedious inverse process.Then,based on this model,a model free control strategy based on the inverse model of the rate-dependent hysteresis is designed,too.The experimental results show that validation of the control strategy.