Piecewise modified Prandtl-Ishlinskii model for precise nano-positioning
Piecewise modified Prandtl-Ishlinskii model for precise nano-positioning
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DOI：
10.1080/10739149.2023.2291404
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发表时间：
2023-12-06
影响因子：
1.6
通讯作者：
Fan，Xian-guang
中科院分区：
文献类型：
--
作者：
Zhi，Yu-liang;Chen，Jian-sheng;Fan，Xian-guang
压电陶瓷具有体积小、灵敏度高、可控性强等优点，是一种不可缺少的微纳驱动器，在微纳加工、医药、化学、材料等领域有着广泛的应用。然而，其非线性和非对称迟滞特性直接影响其定位精度。具有线性对称算子的经典和广义Prandtl-Ishlinskii模型通常用于处理这些问题，但它们在非对称系统中仍然面临困难。为此，本文提出了一种分段修正的Prandtl-Ishlinskii （PMPI）模型来补偿非线性和非对称迟滞。在PMPI模型中引入了新的非线性算子和分段非线性包络函数。采用独立的左右分量来描述迟滞增加和减少的阶段，阈值和权向量与之相对应。对权向量进行了扩展，构造了新的对角矩阵，避免了过多的参数和计算量。仿真和实验表明，该模型具有良好的补偿性能和有效性，具有拟合效果好、精度高、参数少、计算量少等优点，能够很好地应用于精密纳米定位系统中，非线性和非对称误差较小。
Piezoelectric ceramic, an indispensable micro-nano actuator, has advantages of small size, high sensitivity and strong controllability, which is widely applied in various fields like micro-nano processing, medicine, chemistry and materials. However, its nonlinear and asymmetric hysteresis features directly affect its positioning accuracy. The classical and generalized Prandtl-Ishlinskii models with linear symmetry operators are commonly used to deal with these issues, but they still face difficulties in asymmetric systems. Therefore, a piecewise modified Prandtl-Ishlinskii (PMPI) model is proposed to compensate nonlinear and asymmetric hysteresis in this paper. The new nonlinear operator and piecewise nonlinear envelope function are introduced into the PMPI model. Independent right and left parts are adopted to describe hysteresis increasing and decreasing stages, while the threshold and weight vectors correspond to them. Weight vectors are extended and a new diagonal matrix is constructed for avoiding excessive parameters and computation. Simulations and experiments are shown that the PMPI model has good compensation performance and effectiveness, which has better fitting, higher accuracy, fewer parameters and computation, and can be well applied to the precise nano-positioning systems with less nonlinear and asymmetric errors.