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

压电材料(PEM)具有机电耦合行为，机械应力产生电极化，电场产生机械应变。因此，PEM在设计精密执行器(执行运动的设备)和传感器(检测移动的设备)方面取得了巨大的成功。然而，PEM表现出机械蠕变(恒定载荷下随时间变化的变形)和电滞回(极化对电场的历史依赖)之间的耦合。这些非线性效应没有被标准模型很好地捕捉到，对于执行器，它们会导致长时间间隔位置的不确定性，而对于传感器，它们严重限制了传感器线性行为的范围。我们发现了广泛采用的通过在线性本构关系中添加项来获得非线性本构关系的做法的缺陷。在这个项目中，我们提出了一种更激进的方法。我们不是通过增加附加项来扩展经典的线性方程，而是直接研究非线性区域，并在必要时线性化。受早期弹塑性模型的启发，我们得到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滞后(极化/电场)行为。该项目的目标是建立具有弹塑性和铁电性耦合的完全非线性模型，并为围绕质子交换膜制造的超精密器件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，在AMM应用中，执行器和传感器对于精确和可控的运动至关重要。AMM带动纳米技术、清洁技术、生物医药材料和数字产业等关键行业。这些都是艾伯塔省和加拿大被认为具有高增长潜力的领域。

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.