近场声悬浮物体的建模与闭环控制
Modelling and closed loop control of near-field acoustically levitated objects
摘要：
本文介绍了一种新的方法建模的治理，近场声悬浮物体的慢动力学。该模型是足够简单和简洁，使设计一个闭环控制器，能够准确的垂直定位的一个携带的对象。近场声悬浮现象利用了被困在快速振荡表面和自由悬浮的平面物体之间的气体的可压缩性、非线性和粘性，以将其时间平均压力提升到环境压力以上。通过这些装置，重达几公斤的负载的垂直位置可以在几十到几百微米之间变化。本文提出的简化模型是一个二阶常微分方程，其中的气体层的高度依赖的刚度和阻尼项推导明确。该简化模型取代了传统的模型，该模型由悬浮物体的运动运动方程组成，该运动方程与非线性偏微分方程耦合，解释了截留气体的行为。由于这里开发的模型的相对简单的形式，它构成了基于模型的控制算法，管理近场声悬浮物体的缓慢动态的一个方便的基础。实际上，基于前者，高度相关，增益调度PID控制器的开发和验证的数值和实验，都提供了令人满意的结果。
英文摘要：
The present paper introduces a novel approach for modelling the governing, slow dynamics of near-field acoustically levitated objects. This model is sufficiently simple and concise to enable designing a closed-loop controller, capable of accurate vertical positioning of a carried object. The near-field acoustic levitation phenomenon exploits the compressibility, the nonlinearity and the viscosity of the gas trapped between a rapidly oscillating surface and a freely suspended planar object, to elevate its time averaged pressure above the ambient pressure. By these means, the vertical position of loads weighing up to several kilograms can be varied between dozens and hundreds of micrometers. The simplified model developed in this paper is a second order ordinary differential equation where the height-dependent stiffness and damping terms of the gas layer are derived explicitly. This simplified model replaces a traditional model consisting of the equation of motion of the levitated object, coupled to a nonlinear partial differential equation, accounting for the behavior of the entrapped gas. Due to the relatively simple form of the model developed here, it constitutes a convenient foundation for model based control algorithms, governing the slow dynamics of near-field acoustically levitated objects. Indeed, based on the former, a height dependent, gain scheduled PID controller is developed and verified numerically and experimentally, both providing satisfying results.
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