Exploiting Noise for Response Control: From Simple Nonlinear Systems to Slender Structures

随机波动称为噪声，在许多系统中自然发生，在许多生物和化学系统中，噪声被用来在系统响应中产生巨大的变化。然而，利用噪声有益地影响工程系统的响应只得到了有限的关注。随着工程系统的运行环境变得极端，无论是在小尺度上还是在大尺度上，非线性、不确定性和噪声的影响变得越来越重要。对这些通常被忽视的元素的研究和可能的利用，可能会在系统设计和控制方面取得突破性进展，并有助于扩展工程和科学的前沿。通过该奖项的支持，将继续进行基础研究，以开发使用组合确定性和噪声输入的知识库，以实现非线性系统中所需的响应变化。一个显著的影响预计将是我们对基于噪声的非线性系统控制方案的理解的进步，以及这些方案的应用领域从简单系统扩展到复杂系统。通过实验证明这些方案的可行性，人们有望构建用于实际应用的方案，其中使用细长的旋转结构，如钻井和采矿作业，以及减法制造作业，如铣削作业。这项工作将迎来新一代研究人员，他们接受过培训，能够使用适合于有噪声的非线性系统的工具。一个研究小组将在马里兰大学进行的关于非线性振荡器受噪声影响的响应的先前工作和对旋转系统旋转运动的调查的基础上，追求共同的目标，即了解如何通过对噪声进行部分控制来改变机械和结构系统的响应。该小组将进行原创性实验，以探索为Hénon映射和Duffing振子开发的部分控制方案对双稳态Duffing振荡器的实验原型的适用性。根据实验结果，将对改进的Jeffcott转子系统进行分析和数值研究，以构建适当的部分控制算法，并将这些发现扩展到细长旋转结构的动力学控制。这些发现有望为组合使用噪声和确定性输入来控制表现出逃逸动力学的非线性机械系统打开大门，并引导旋转系统的响应远离旋转运动等可能对系统有害的状态。

Random fluctuations, which are called noise, occur naturally in many systems, and in many biological and chemical systems, noise is utilized to engender a large change in the system response. However, the use of noise to beneficially influence the response of an engineering system has received only limited attention. As the operating environments of engineering systems become extreme, both at the small scales as well as the large scales, the influence of nonlinearities, uncertainties, and noise gain increased importance. The study, and possible exploitation, of these usually ignored elements may allow for breakthrough advances in design and control of systems and help extend the frontiers of engineering and science. Through support of this award, fundamental studies will be pursued to develop a knowledge base for the use of combined deterministic and noise inputs to realize desired response changes in nonlinear systems. A salient impact is expected to be the advancement of our understanding of noise based schemes for control of nonlinear systems and extension of the application realm of these schemes from simple systems to complex systems. By experimentally demonstrating the feasibility of these schemes, it is expected that one can construct schemes for practical applications where slender, rotating structures are used, such as drilling and mining operations and subtractive manufacturing operations such as milling operations. This work will usher in a new generation of researchers trained to use tools suited for nonlinear systems with noise.Building on prior efforts on noise-influenced responses of nonlinear oscillators and investigations into whirling motions of rotary systems carried out at the University of Maryland, a research team will pursue the common goal of understanding how mechanical and structural system responses may be altered by exercising partial control with noise. The group will conduct original experiments to explore the applicability of partial control schemes developed for Hénon maps and Duffing oscillators to an experimental prototype of a bi-stable Duffing oscillator. Informed by the experimental findings, analytical and numerical studies will be initiated with modified Jeffcott rotor systems to construct appropriate partial control algorithms and these findings will be extended to control the dynamics of slender, rotating structures. The findings are expected to open the doors to the combined use of noise and deterministic inputs for control of nonlinear mechanical systems that exhibit escape dynamics and steer responses of rotary systems away from states such as whirling motions, which can be detrimental to a system.