Non-linear material modelling and control of piezoelectric actuators and sensors

压电材料（PEM）具有耦合的机电特性，即机械应力产生电极化，电场产生机械应变。由于这个原因，PEM在精密执行器（执行运动的设备）和传感器（检测运动的设备）的设计中取得了巨大的成功。然而，PEM表现出机械蠕变（恒定载荷下随时间变化的变形）和电迟滞（电场极化的历史依赖性）之间的耦合。这些非线性效应不能被标准模型正确捕获，并且在执行器的情况下，它们会导致长时间间隔内位置的不确定性，而在传感器的情况下，它们严重限制了传感器线性行为的范围。我们发现了普遍采用的通过在线性本构律上添加项来获得非线性本构律的方法中的一个缺陷。在这个项目中，我们提出了一个更激进的方法。我们不是通过添加额外的项来扩展经典的线性方程，而是直接研究非线性状态并在必要时进行线性化。从早期弹塑性模型中获得灵感，我们获得了理想刚性铁电材料的初步概念验证模型，该模型能够正确地表示迟滞（极化/电场）行为。该项目的目标是建立具有耦合弹塑性和铁电性的全非线性模型，并为围绕PEM构建的超精密设备提供基于非线性模型的控制算法。潜在的结果是该模型和控制算法在先进材料和制造（AMM）应用中的应用，其中致动器和传感器对于精确和受控的运动至关重要。AMM推动了纳米技术、清洁技术、生物医学材料和数字产业等关键领域的发展。这些都是阿尔伯塔省和加拿大被认为具有高增长潜力的地区。

Piezoelectric materials (PEM) have a coupled electro-mechanical behaviour, by which a mechanical stress produces an electric polarisation, and an electric field produces a mechanical strain. For this reason, PEM have had immense success in the design of precision actuators (devices that perform movement) and sensors (devices that detect movement). However, PEM exhibit a coupling between mechanical creep (time-dependent deformation at a constant load) and electrical hysteresis (history-dependence of the polarisation on the electric field). These non-linear effects are not properly captured by the standard models, and in the case of actuators, they cause uncertainty in position over long time intervals, whereas in the case of sensors, they severely limit the range in which the sensor behaves linearly.We discovered a flaw in the widely adopted practice of obtaining non-linear constitutive laws by adding terms to the linear ones. In this project, we propose a more radical approach. Rather than extending the classical linear equations by adding extra terms, we directly study the non-linear regime and linearise where necessary. Taking inspiration from the early models of elastoplasticity, we obtained a preliminary proof-of-concept model of an idealised rigid ferroelectric material, which was able to correctly represent the hysteretic (polarisation / electric field) behaviour. The goal of this project is to establish the fully non-linear model, with coupled elastoplasticity and ferroelectricity, and to deliver a non-linear model-based control algorithm for ultraprecise devices built around PEM.The potential outcome is the application of this model and control algorithm in advanced materials and manufacturing (AMM) applications, where actuators and sensors are critical to precise and controlled movement. AMM drives key sectors such as nanotechnology, clean technology, biomedical materials, and digital industries. These are all areas deemed as having high growth potential in Alberta and Canada.