Research On Mathematical Modeling Of The Giant Magnetostrictive Actuator

The Giant Magnetostrictive Actuator(GMA),which is one of intelligent drivers made of one kind of smart materials,magnetostrictive material,is widely used in the fields of precision machining,sensors,hydraulic pressure and vibration control due to its superior performances such as high frequency response,fast response,large strain and so on.However,as kind of smart materials,the GMA itself also has hysteresis nonlinearity properties.The hysteresis nonlinearity is caused by the inherent physical properties of the material,and its microscopic interpretation is incompletely clear.Therefore,it is difficult to eliminate or reduce the impact of hysteresis nonlinearity on the system through structural optimization in product design.In order to achieve precise control of the GMA,an accurate mathematical model is needed to describe the dynamic characteristics of it.Considering the above,this paper focuses on the mathematical modeling of the GMA.Firstly,the working principle of the GMA will be introduced,and then the PrandtlIshlinskii(PI)model is selected for the mathematical modeling procedure.Next,the influence of each parameter of the asymmetric PI model on the model output will be analyzed in detail.Secondly,the experimental platform will be established to collect data of one type of GMA actuator(MFROTY 77,ETREMA Corporation).Then,the mathematical model will be derived based on the asymmetric PI model according to the experimental data based on the Sequential Quadratic Programming(SQP)optimal algorithm.Comparing the modeling simulation and experimental results,it has been found that the only asymmetric PI model cannot accurately describe the current-frequency correlation of the hysteresis nonlinearity.Considering the above,the Hammerstein structure is chosen to build mathematical model for the hysteresis nonlinearity of the GMA.In the Hammerstein structure of the GMA,the static nonlinear section is represented by the asymmetric PI model,and the dynamic section is represented by the Auto-Regressive with eXogenous(ARX)model.The transfer function of the ARX model is identified by the identification process based on the Akaike information criterion(AIC).Then,the asymmetric PI model established in the previous section is connected in series with the ARX model to obtain the Hammerstein model of the GMA.Then,the results of two different modeling methods are compared.It has been shown that the modeling accuracy of the established Hammerstein model is higher than that of the asymmetric PI model when the frequency of excitation current signal is increased.Finally,the Hammerstein modeling simulation and experimental data under sinusoidal and triangular wave signals are compared.And the results show that the Hammerstein model established can effectively match the hysteresis nonlinear curve of GMA in the range 50 Hz to 400 Hz under sinusoidal signal and the error is about 5%-8%.The modeling effect under triangular wave signal is good at the frequency of 50 Hz and 100 Hz,and the error is about 5% to 10%.It is shown that the established Hammerstein mathematical model can effectively describe the current-amplitude correlation and current-frequency correlation characteristics exhibited by the GMA.