中文摘要：

针对一直动型磁致伸缩致动器（GMA）的非线性迟滞建立了数学模型，对限制三角形进行均匀离散网格划分，给出了非负约束最小二乘参数辨识模型，在一阶回转实验数据（FOD）的基础上，得到了GMA迟滞输出预测模型，并采用LabVIEW虚拟仪器平台进行了迟滞预测实验．为减小涡流对实验结果的影响采用了低频信号（1Hz）．实验结果表明，用非负约束最小二乘参数辨识算法得到的数值模型对GMA迟滞位移输出有较高的预测精度，预测误差小于6％．进一步的误差分析表明，经典Preisach模型同余性要求与GMM变化率依赖型迟滞之间的差异是预测误差产生的主要原因，必须通过模型的改进，放松其对系统同余性的要求才能够进一步提高经典Preisach模型的迟滞预测精度．

英文摘要：

A Preisach-based numerical model for describing the nonlinear hysteresis of a reciprocating type giant magnetostrictive actuator （GMA） was established. The Preisach plane was discretized into L levels uniformly, and a constrained least-squares algorithm was employed to identify a discrete approximation to the Preisach measure. Then the model was implemented with first order reversal experiment data （FOD）. Experiment was carried out on labVIEW virtual instrument development platform to verify the identification of the measure, in which GMA was applied at a low frequency （1Hz） to cancel out the eddy effect. The results revealed that the algorithm was effective, and the error between the real displacements of GMA and the theoretical data calculated by the model was less 6%. Further analysis shows that the congruency restriction of Preisach theory to hysteresis is the main reason for producing the prediction error, so the only way to reduce the error is to modify the theory to relax the restriction.