PDE Boundary Control for Active Flutter Prevention Using Finite Dimensional Input-Output Maps

颤振是飞机机翼中一种研究得很好的现象，在高飞行速度下通常会影响机翼。传统上，飞机设计师试图完全避免颤振；如果在高级设计阶段或飞行测试中遇到颤振，则使用设计修复和/或低效的操作修改来处理。多年来，随着机翼变得更轻，从而变得更加灵活，主动减轻颤振的重要性已经增加。波音747-8I上安装的舷外副翼模式抑制(OAM)系统是最近主动颤振抑制的一个例子，该系统也已在商业上部署。虽然OAM的细节尚不清楚，但“模式抑制”一词表明，它的设计属于传统机翼控制方法的范围，传统的机翼控制方法使用动力学的有限维近似来设计稳定控制器。虽然这种方法允许设计者利用常微分方程组(ODE)描述的系统的大量控制技术，但它有三个主要缺陷：常微分方程组的近似往往具有大的阶数，常微分方程组的状态很少具有物理意义，以及控制设计过程容易受到溢出不稳定的影响，这可能是由于不正确的模式近似造成的。偏微分方程(PDE)描述的系统的控制技术避免了有限维近似，在最近的过去一直在稳步发展，并有望消除上述两个缺点。PI先前的工作导致了两种新的自适应控制技术，它们属于这一不断发展的技术家族。其中一种由PI开发的技术使用有限维输入输出(FDIO)映射，这些映射对于给定的PDE的特定输入输出对自然地产生。使用FDIO映射，可以将控制设计问题精确地转化为常微分方程组的问题。虽然类似于在有限维系统中设计静态输出反馈控制器的危险方法，PI发现偏微分方程的结构提供了一种即使在静态输出反馈下也可以扩展系统稳定包络的方法。PI的工作也为潜在的稳定机制提供了部分解释。本项目的目的是开发和演示一种针对柔性机翼的低阶自适应控制设计技术，该技术有效地利用了动力学的基本偏微分方程结构，并巧妙地重新表述了控制问题。控制器将基于PI的先前工作[1，6]。我们将主要将该技术扩展到更现实的2-DOF机翼模型和自适应律，以帮助控制器处理建模和参数不确定性。这是确保控制技术的实际适用性的关键，也需要大量的理论发展。我们将通过风洞试验来验证控制技术。该项目的结果将是一个具有分析性能和稳定性保证的低阶自适应控制器。此外，控制设计将通过在设计过程中尽可能避免常模近似来最小化反馈律所需的传感器集。这项研究的好处包括学术界和航空业，特别是那些参与开发和部署气动弹性解决方案的人。提案中的其他地方描述了拟议研究的更广泛影响。

Flutter is a well-studied phenomenon in aircraft wings, and typically affects wings at high flight speeds. Traditionally, aircraft designers sought to avoid flutter altogether; if it was encountered at all during advanced design stages or flight testing, it was dealt with using design fixes and/or inefficient operational modifications. The importance of active flutter mitigation has increased as the wings have become lighter and consequently more flexible over the years. A recent example of active flutter mitigation, which is also commercially deployed, is the outboard aileron modal suppression (OAMS) system incorporated on the Boeing 747-8I. While the details of OAMS are unknown, the phrase "modal suppression" suggests that its design falls within the ambit of traditional wing control methods which use a finite dimensional approximation of the dynamics to design a stabilizing controller. Although this approach allows a designer to tap into the vast family of control techniques for systems described by ordinary differential equations (ODEs), it has three major drawbacks: the ODE approximations tend to have large orders, the states of the ODE are seldom physically meaningful, and the control design process is susceptible to spillover instabilities which can result from an improper modal approximation.Control techniques for systems described by partial differential equation (PDEs), and which avoid finite dimensional approximations, have been evolving steadily in the recent past and promise to do away with both aforementioned drawbacks. The prior work done by the PI led to two new adaptive control techniques that fall within this evolving family of techniques.One of the techniques developed by the PI uses finite dimensional input-output (FDIO) maps that arise naturally for specific input-output pairs for a given PDE. Using FDIO maps, it is possible to convert the control design problem exactly to one for ODEs. Although akin to the risky approach of designing a static output feedback controller in finite dimensional systems, the PI discovered that the structure of the PDE provides a means for expanding the stable envelope of the system even under static output feedback. The PI's work also provided a partial explanation for the underlying stabilization mechanism. The aim of the present project is to develop and demonstrate a low-order adaptive control design technique for flexible wings which exploits the underlying PDE structure of the dynamics effectively, together with a clever reformulation of the control problem. The controller would be based on the PI's prior work [1, 6]. We will provide a major extension of the technique to more realistic, 2-dof wing models and adaptive laws to help the controller deal with modeling and parametric uncertainties. This is key to ensuring practical applicability of the control technique, and requires non-trivial theoretical development as well. We will validate the control technique using wind tunnel testing. The outcome of this project would be a low-order adaptive controller accompanied by analytical performance and stability guarantees. Additionally, the control design would minimize the set of sensors required for the feedback laws, by avoiding ODE approximations as far as possible during the design process.Beneficiaries of this research include the academic community and the aircraft industry, notably those that are involved in developing and deploying aeroelastic solutions. The broader impact of the proposed research has been described elsewhere in the proposal.