Badel A, Qiu J, Nakano T
Institute of Fluid Science, Tohoku University, Aoba-ku, Sendai-Shi, Japan.
IEEE Trans Ultrason Ferroelectr Freq Control. 2008 May;55(5):1086-94. doi: 10.1109/TUFFC.2008.761.
Piezoelectric actuators (PEAs) are commonly used as micropositioning devices due to their high resolution, high stiffness, and fast frequency response. Because piezoceramic materials are ferroelectric, they fundamentally exhibit hysteresis behavior in their response to an applied electric field. The positioning precision can be significantly reduced due to nonlinear hysteresis effects when PEAs are used in relatively long range applications. This paper describes a new, precise, and simple asymmetric hysteresis operator dedicated to PEAs. The complex hysteretic transfer characteristic has been considered in a purely phenomenological way, without taking into account the underlying physics. This operator is based on two curves. The first curve corresponds to the main ascending branch and is modeled by the function f1. The second curve corresponds to the main reversal branch and is modeled by the function g2. The functions f(1) and g(2) are two very simple hyperbola functions with only three parameters. Particular ascending and reversal branches are deduced from appropriate translations of f(1) and g(2). The efficiency and precision of the proposed approach is demonstrated, in practice, by a real-time inverse feed-forward controller for piezoelectric actuators. Advantages and drawbacks of the proposed approach compared with classical hysteresis operators are discussed.
压电致动器（PEA）由于其高分辨率、高刚度和快速频率响应，通常被用作微定位装置。由于压电陶瓷材料是铁电材料，它们在对施加电场的响应中从根本上表现出滞后行为。当压电致动器用于相对长距离应用时，由于非线性滞后效应，定位精度会显著降低。本文描述了一种专门用于压电致动器的新型、精确且简单的不对称滞后算子。复杂的滞后传递特性已以纯粹现象学的方式被考虑，而没有考虑其潜在的物理原理。该算子基于两条曲线。第一条曲线对应于主要上升分支，由函数f1建模。第二条曲线对应于主要反转分支，由函数g2建模。函数f(1)和g(2)是两个非常简单的双曲线函数，仅具有三个参数。特定的上升和反转分支是通过对f(1)和g(2)进行适当平移推导出来的。在实践中，通过用于压电致动器的实时逆前馈控制器证明了所提出方法的效率和精度。讨论了所提出方法与经典滞后算子相比的优缺点。
