发表机构
The University of Arizona; Georgia Southern University（亚利桑那大学; 佐治亚南方大学）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
针对串联多回路热虹吸系统，提出分散自适应控制方法，通过比例反馈稳定混沌流动，并给出增益下界及未知参数下的自适应增益设计，数值模拟验证有效性。
AI 中文摘要
一个串联的高维双向耦合$N$回路热虹吸系统由$3N$个Lorenz型微分方程建模。每个回路中的流体流动由热源（瑞利数）以及相邻回路之间的动量交换和热交换驱动。当瑞利数较大时，流动变得混沌。采用通过比例局部状态反馈的分散控制器设计来稳定每个回路中的混沌流动。稳定性分析的结果表明，存在控制器增益的下界，保证系统的全局稳定性。在未知参数的情况下，我们用反馈增益的附加动态方程来增广原始系统，以自适应地确定稳定系统的可行增益。该分析还揭示了热耦合在控制系统稳定性中的作用，这使我们能够将结果扩展到负$z$状态耦合系数以及一类非线性$z$状态耦合函数。数值模拟进一步证明了所提出的控制器设计的有效性。
英文摘要
A high dimensional bi-directionally coupled $N$-loop thermosyphon system in a tandem is modeled by $3N$ Lorenz type of differential equations. The fluid flow in each loop is driven by the heat source (Rayleigh numbers) as well as the moment and heat exchanges between the adjacent loops. The flow becomes chaotic when the Rayleigh numbers are large. A decentralized controller design via proportional local state feedback is employed to stabilize the chaotic flows in each loop. As a result of the stability analysis, we show that there exist lower bounds on the controller gains that guarantee global stability of the system. Under the scenario of unknown parameters, we augment the original system with additional dynamic equations of the feedback gains to adaptively determine the feasible gains that stabilize the system. The analysis also sheds insight on the role of thermal coupling in the stability of the control system, which allows us to extend the results to negative $z$-state coupling coefficient as well as a class of nonlinear $z$-state coupling functions. Numerical simulations further demonstrate the effectiveness of the proposed controller design
