Exact Controllability and Observation of Structural Acoustics and Thermoelastic Systems

结构声学和热弹性系统的精确可控性和观察

• 批准号: 0208121
• 负责人: George Avalos
• 金额: $ 11.79万
• 依托单位: University of Nebraska-Lincoln
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2002
• 资助国家: 美国
• 起止时间: 2002-07-01 至 2006-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0208121&HistoricalAwards=false
• 关键词: Exact; Controllability; Observation; Structural; Acoustics

0208121AvalosThis project is concerned with studying exact boundary controllability properties of those systems of coupled partial differential equations (PDE's) which govern structural acoustic flow within a chamber. Exact and null boundary controllability problems for two-dimensional systems of thermoelasticity will also be studied. In part, the work will entail a study of the dual problem; namely, the attainment of related observability inequalities for solutions of homogeneous adjoint equations. In line with the intended engineering applications, the focus will be on situations which allow control of the structural acoustic dynamics on as small a (boundary) control region as possible. Moreover, this project is aimed at finding conditions on the geometry and prescribed controls so that, with control implemented on the flexible portion of the acoustic chamber only, one will have exact controllability of the acoustic flow, for arbitrary initial data of finite energy. It is anticipated that key ingredients in the work will include the following: (i) sharp trace regularity for the wave equation in the absence of the so-called Lopatinski condition (intrinsic to the wave equation under Neumann boundary conditions); (ii) microlocal analytical estimates which will allow the absorption of tangential wave traces by time derivatives on the boundary; and (iii) recent results involving Carleman's estimates for the wave equation with controlled Neumann part of the boundary. In addition, the project will focus on problems of linear and (globally) nonlinear exact controllability for thermoelastic systems. In particular, thermoelastic PDE's will be considered which have their associated (non-Lipschitz) nonlinearities in place; e.g., the von Karman bracket and the quasilinearities which appear in the modeling of extensible plates. This work will attempt to use, in an essential way, the now-known analyticity of linearized thermoelastic models and our recent stability work for uncontrolled (but fully nonlinear) thermoelastic systems. Examples of coupled partial differential equations (PDE's), such as those to be investigated, have long existed in the literature. However, recent innovations in smart material technology, and the potential applications of these innovations within the context of control engineering design, have greatly increased the interest in these PDE models. The project is aimed at obtaining information about certain qualitative properties of these equations, which in turn can be used to design effective control laws for the structures/interactions that these equations govern. For example, structural acoustic PDE's are used to model the interaction of an aircraft cabin's interior acoustic field with the surrounding walls of the cabin. For the benefit of the passengers, it is desirable to negate or control pressure disturbances that act directly on the interior acoustic field. These disturbances typically emanate from outside the cabin environment; e.g., vibrations due to aircraft engine and propeller noise, or effects due to weather turbulence. In practice, engineers attempt to control this external noise by placing piezoelectric actuators/sensors on a portion of the cabin wall, these devices to act in such a way so as to remove, or at least lessen, the harmful acoustic pressure effects. However, the efficacy of this technology is profoundly sensitive to the shape of the cabin, as well as to the particular region of the cabin walls where the actuators are placed. The goals of this project include: (i) the precise mathematical characterization of those cabin geometries for which active control design by piezoelectric actuation is indeed possible; and (ii) when such control design is practicable, the construction of a reliable method to prescribe the amount and region of control actuation which will be necessary to maintain a calm acoustic field within the cabin.

0208121AvalosThis项目与研究那些耦合部分微分方程（PDE）系统的确切边界可控性能有关，该偶联偏微分方程（PDE）管理腔室内结构声流。还将研究热弹性二维系统的精确和无效的边界可控性问题。在某种程度上，这项工作将需要研究双重问题。也就是说，达到均质伴随方程解决方案解决方案的相关可观察性不平等。与预期的工程应用相一致，重点将放在允许在尽可能小的A（边界）控制区域控制结构声学动力学的情况下。此外，该项目旨在查找几何和规定控件的条件，以便仅在声学室的柔性部分实现控制，一个人将具有声流的确切可控性，以供有限能量的任意初始数据。预计工作中的关键成分将包括以下内容：（i）在没有所谓的lopatinski条件的情况下，波动方程的尖锐痕量规律性（在诺伊曼边界条件下固有的波动方程）； （ii）微局部分析估计值将允许通过边界上的时间衍生物吸收切向波的痕迹； （iii）最近的结果，涉及卡尔曼对边界的受控部分的波动方程的估计。此外，该项目将集中于热弹性系统的线性和（全球）非线性确切可控性的问题。特别是，将考虑使用热弹性PDE，这些PDE具有相关的（非lipschitz）非线性。例如，冯·卡曼支架和出现在可扩展板的建模中的准线性。这项工作将尝试以必不可少的方式使用线性化热弹性模型的分析性，以及我们最近的稳定性工作，用于不受控制的（但完全非线性的）热弹性系统。文献中长期存在的耦合部分微分方程（PDE）的示例（例如要研究的）示例。但是，智能材料技术的最新创新以及这些创新在控制工程设计背景下的潜在应用大大提高了对这些PDE模型的兴趣。该项目旨在获取有关这些方程的某些定性属性的信息，而这些方程式可以用于设计有效的控制定律，以针对这些方程式管理的结构/相互作用。例如，结构声PDE用于对飞机机舱内部声场与机舱周围壁的相互作用进行建模。为了使乘客的利益，希望否定或控制直接在内部声场上作用的压力干扰。这些干扰通常是从机舱环境外散发出来的。例如，由于飞机发动机和螺旋桨噪声引起的振动或由于天气湍流而引起的效果。在实践中，工程师试图通过将压电执行器/传感器放置在机舱墙的一部分来控制这种外部噪声，这些设备以某种方式采取行动，以消除或至少降低有害的声压力效应。但是，这项技术的功效对机舱的形状以及放置执行器的机舱壁的特定区域非常敏感。该项目的目标包括：（i）那些机舱几何形状的精确数学表征确实可以通过压电驱动的主动控制设计； （ii）当这种控制设计是可行的时，建造一种可靠的方法来规定控制驱动的数量和区域，这对于维持机舱内平静的声学领域是必不可少的。