EAGER: Advancing Adaptive Vibrational Control

这一早期概念探索性研究资助(EARGER)项目将推进振动控制的实用理论，这是稳定复杂系统的一种强大方法。稳定是抑制不必要的变化并迫使系统适应特定的所需动态行为的过程。传统上，稳定需要反馈，在反馈中，测量被转换为导致不想要的行为消失的输入信号。人们一直致力于了解振动控制在不需要任何测量的情况下稳定下来的能力，这不仅是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，振动稳定化被发现了新的应用，包括减少翼型阻力和聚变反应堆中等离子体的稳定。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控制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，或当系统特性变化或不确定时，或当输入信号无法以极高精度控制时。该项目将研究处理简单、缓慢、复合测量的方法，以便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好处，而控制器的复杂性只有很小的增加。在对潜在动力学提供洞察的数学和计算研究的同时，所开发的方法将被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提高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能够稳定不可控或不可观测动态的控制方法，包括在高维、空间分布的有限感知和执行系统中。本项目将探索自适应控制算法如何使用缓慢、低维的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，在不需要传统上与振动控制相关的高频输入的情况下实现稳健的结果。与聚变反应堆专家合作，这一结果将用于抑制被称为边缘局域模式的不稳定行为的快速爆发，这种不稳定行为可能会干扰聚变等离子体的持续稳定运行。这一奖项反映了NSF的法定使命，并通过使用基金会的智力优势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.