EAGER: Advancing Adaptive Vibrational Control

这个早期概念探索性研究（EAGER）项目将推进振动控制的实用理论，这是稳定复杂系统的有力方法。稳定是抑制不需要的变化并迫使系统适应特定的期望动态行为的过程。通常，稳定需要反馈，其中测量值转换为输入信号，导致不必要的行为消失。人们已经付出了相当大的努力来了解振动控制在不需要任何测量的情况下稳定的能力，不仅因为它在科学上很有趣，而且因为它在工程上的优势。近年来，振动稳定的新应用已经被发现，包括减少翼型阻力和稳定聚变反应堆中的等离子体。该项目的目标是开发自适应振动稳定的新方法，其中稳定信号将在运行过程中根据需要进行调整。该项目将允许在以前无法管理的情况下使用振动控制，例如当输入信号不能以非常高的速度驱动时，或者当系统属性发生变化或不确定时，或者当输入信号不能以极高的精度控制时。本项目将研究处理简单、缓慢、复合测量的方法，以找到稳定的振动控制输入。这种自适应的创新应用保证了保持振动控制的所有优点，而控制器的复杂性只增加了一点点。与数学和计算研究并行，提供对潜在动力学的洞察，开发的方法将应用于核聚变反应堆中磁约束氢等离子体的模型。研究结果有可能通过改善新型能源发电设备的性能、效率和可靠性来造福社会。振动控制是唯一已知的控制方法，可以稳定不可控或不可观察的动态，包括在高维，空间分布系统有限的传感和驱动。本项目将探索自适应控制算法如何使用慢速、低维系统输出来调整振动控制输入信号。这种混合方案有可能稳定复杂和具有挑战性的过程，在不需要传统振动控制相关的高频输入的情况下获得稳健的结果。在与一位聚变反应堆专家的合作下，研究结果将被应用于抑制被称为边缘局域模式的不稳定行为的快速爆发，这种模式会干扰聚变等离子体的持续稳定运行。该奖项反映了美国国家科学基金会的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This EArly-concept Grant for Exploratory Research (EAGER) project will advance the practical theory of vibrational control, a powerful method for stabilizing complex systems. Stabilization is the process of suppressing unwanted changes and forcing the system to settle into specific desired dynamic behavior. Conventionally, stabilization requires feedback, in which measurements are converted to input signals that cause the unwanted behaviors to die out. Considerable effort has been devoted to understanding the ability of vibrational control to stabilize without the need for any measurements, not only because it is scientifically interesting, but also because of its advantages in engineering. In recent years, new applications of vibrational stabilization have been discovered, including reduction of drag over airfoils and stabilization of plasma in fusion reactors. The goal of this project is to develop new methods for adaptive vibrational stabilization, where the stabilizing signal will be adjusted as needed during operation. This project will enable the use of vibrational control in previously unmanageable situations, such as when the input signal cannot be driven at very high speeds, or when the system properties are changing or uncertain, or when the input signal cannot be controlled with extreme precision. This project will investigate ways of processing simple, slow, composite measurements in order to find a stabilizing vibrational control input. This innovative use of adaptation promises to maintain all the benefits of vibrational control, with only a small increase in controller complexity. In parallel with mathematical and computational studies that provide insight into the underlying dynamics, developed methods will be applied to models of magnetically confined hydrogen plasmas in nuclear fusion reactors. The results have the potential to benefit society by improving the performance, efficiency, and reliability of novel energy generation devices.Vibrational control is the only known control method that can stabilize uncontrollable or unobservable dynamics, including in high-dimensional, spatially distributed systems with limited sensing and actuation. This project will explore how adaptive control algorithms may use slow, low-dimensional system outputs to tune the vibrational control input signal. This hybrid scheme has the potential to stabilize complex and challenging processes, achieving a robust result without the need for the high frequency inputs traditionally associated with vibrational control. In collaboration with an expert in fusion reactors, the result will be applied to suppress rapid bursts of unstable behavior called edge-localized modes, which can interfere with sustained stable operation of fusion plasmas.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.