Modeling Of Giant Magnetostrictive Actuator

The Giant Magnetostrictive Actuator(GMA),a kind of smart-material based actuator,has the advantages of fast response,high efficiency and high reliability comparing with the traditional hydraulic,pneumatic and motor actuators.However,the application of GMA is limited by the hysteretic nonlinearity,which is common condition for the smart-material based actuator.The detailed and throughout analysis of the hysteretic nonlinearity shown in the application of smart materials has not been effectively solved in the academic field,which is an internationally recognized problem in the field of mathematics and control areas.Scientists have tried many methods to describe the hysteretic nonlinearity of smart materials.At present,the most popular method is the operator-based hysteresis model,which is constructed by superposing weighted elementary operators.The operator itself has no physical meaning.It should be noted that the model should consider the application problems comprehensively,as well.A large number of operator-based hysteresis models have complex structures,hard to get the inverse analytically,and then it is difficult to apply the existing nonlinear control theory to the application of smart-material based actuators.Based on the above reasons,this paper utilizes the Prandtl-Ishlinskii model(PI model),in which the inversed PI model can be achieved in some degree,to describe the dynamic properties of one type of GMA.The main contents in this study are following:1.Set up the experimental platform: the experimental platform consists of a host computer/the dSPACE software system,a dSPACE-DS1104 control board,the 7224 AE Techron power amplifier,a giant magnetostrictive actuator(Model: MFR OTY77,100-LL)from Etrema Products Inc,a capacitive position sensor manufactured by Lion Precision,etc.2.The experimental scheme is designed and the hysteresis behavior of giant magnetostrictive actuator are analyzed.Aiming at the wiping out property and minor loop consistency property of Prandtl-Ishlinskii model,as well as accommodation phenomena of some hysteresis,the experiments are carried out to verify whether the hysteresis curve and hysteresis loop of giant magnetostrictive actuator conform to such properties.3.The experimental scheme,to obtain the hysteresis loop with the initial curve,has been established.The model parameters of the classical Prandtl-Ishlinskii model and the asymmetric Prandtl-Ishlinskii model are identified according to the data of the hysteresis loop with the initial curve under the sinusoidal signal.4.In the classical Prandtl-Ishlinskii model,the weight of play operator under different threshold distribution is optimized through the Sequential Quadratic Programming(SQP)algorithm and Genetic Algorithm(GA),respectively.Finally,the model parameters are optimized by SQP algorithm under the setting threshold distribution between 0-2 with interval 0.4.5.In order to describe the asymmetric characteristic of the hysteresis loop,the improved model is established based on the classical Prandtl-Ishlinskii model and the shift model,and then the asymmetric Prandtl-Ishlinskii model is obtained.The Lipschitz continuity of the asymmetric Prandtl-Ishlinskii model is obtained through proving the Lipschitz continuity of the shift operator.In the asymmetric Prandtl-Ishlinskii model part,the threshold distribution of play operator is the same as the classical Prandtl-Ishlinskii model part.The distribution of different characteristic parameters of shift operator is discussed.The optimum weight of play operator and shift operator is obtained through SQP algorithm.6.Both the classical and the asymmetric Prandtl-Ishlinskii model are rate independent models.In order to describe the rate dependent phenomenona,the Hammerstein model structure is established.The asymmetric Prandtl-Ishlinskii model is used as the static nonlinear part of Hammerstein model.The dynamic linear part of Hammerstein model are determined according to FitPercent and Akaike's Final Prediction Error(FPE)of the data under chirp signal,and mean square error of the data under a designed amplitude decreasing sinusoidal input signal.The influences of different frequencies and amplitudes are considered comprehensively.Although the final Hammerstein model may not be as effective as the asymmetric Prandtl-Ishlinskii model in describing the sinusoidal signal with the frequency below 200 Hz,especially when the frequency is very low,the effect on the sinusoidal signal with the frequency above 200 Hz is obviously better than the asymmetric Prandtl-Ishlinskii model.The Hammerstein model can also describe the data under square wave input well.Totally,the established static nonlinear part of Hammerstein model proposed in this paper uses 6 play operators and 2 shift operators with 8 operators and 16 parameters,and the dynamic linear part contains 7 parameters.Comparing with the models presented in the available literatures,the proposed model has less model parameters with good accuracy.