Abstract Piezoelectric bending actuators are widely used in micro positioning tasks. Due to material nonlinearities such as hysteresis and creep, the position-force control of these actuators is necessary. However, position sensors for micro scale applications are expensive and require a complex configuration. Sensorless approaches are alternative methods in which by resorting to the linear charge-position characteristic, the actuator position can be estimated. But, in piezoelectric actuators with small impedances, due to charge leakage caused by piezoelectric internal resistance, the charge-position characteristic is not linear. Due to nonlinear behavior of piezoelectric internal resistance, its compensation would be more complicated. This paper targets at a modified procedure in which with the help of nonlinear functions for the internal resistance, the linear charge-position characteristic can be obtained. To this purpose, a modified active Prandtl-Ishlinskii (PI) operator is proposed which estimates and compensates the charge leakage. As a result, the ideal linear mapping can be achieved and actuator position can be appropriately estimated. The results are finally validated by experiments and compared with previous methods.

中文翻译：

---

一种改进的压电弯曲致动器无传感器位置估计方法

摘要 压电弯曲致动器广泛应用于微定位任务。由于滞后和蠕变等材料非线性，这些执行器的位置力控制是必要的。然而，用于微型应用的位置传感器价格昂贵且需要复杂的配置。无传感器方法是替代方法，其中通过采用线性电荷位置特性，可以估计执行器位置。但是，在阻抗较小的压电促动器中，由于压电内阻引起的电荷泄漏，电荷-位置特性不是线性的。由于压电内阻的非线性行为，其补偿会更加复杂。本文针对一种改进的程序，其中借助内阻的非线性函数，可以获得线性电荷位置特性。为此，提出了一种改进的主动 Prandtl-Ishlinskii (PI) 算子，用于估计和补偿电荷泄漏。结果，可以实现理想的线性映射，并且可以适当地估计执行器位置。结果最终通过实验验证并与以前的方法进行了比较。