EAGER: Advancing Adaptive Vibrational Control

Regents Of The University Of Michigan - Ann Arbor, Ann Arbor MI

Investigators

Abstract

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.