A New Perspective in Designing Delayed Feedback Control for Thermo-Acoustic Instabilities (TAI)
A New Perspective in Designing Delayed Feedback Control for Thermo-Acoustic Instabilities (TAI)
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热声不稳定性 (TAI) 延迟反馈控制设计的新视角
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
A. S. Kammer
中科院分区：
文献类型：
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作者：
N. Olgaç;Umut Zalluhoglu;A. S. Kammer
本文提出了一种独特的数学工具来评估Rijke管中的热声不稳定性（TAI），并提出了其反馈控制的分析设计策略。TAI的一个被广泛接受的特点是它的时滞动力学，这源于再生声耦合项。线性系统理论也发展了类似的问题，特别是在最近几年。这份文件在这两个研究领域之间架起了一座桥梁。我们首先回顾了TAI现象的解析模型，它呈现了一组延迟微分方程。然后，我们应用了一种新的数学工具，称为特征根的聚类处理（CTCR）范式。CTCR为这类系统提供了非保守和详尽的稳定性预测。这种能力适用于非控制和反馈控制的Rijke管结构。从两个角度来看，这些发现是独一无二的：(i)稳定性声明是在系统的参数空间中做出的，例如几何尺寸（与同行研究中最好的点评估大不相同），以及（ii）这些声明的稳定运行参数集是详尽的（即，对于给定的系统，没有其他参数选择可以提供稳定性）。在设计热声稳定的燃烧器以及确定其工作条件时，这些能力变得至关重要。作为本文的突出贡献，对于那些引起不稳定的操作条件，我们提供了一种方法来综合可以恢复稳定的反馈控制律，再次利用CTCR范式。提供了这些新奇事物的示例案例研究和分析论证。
This article suggests the deployment of a unique mathematical tool for assessing the thermo-acoustic instability (TAI) in a Rijke tube and proposes an analytical design strategy for its feedback control. A widely accepted characteristic of TAI is its time-delayed dynamics, which originate from the regenerative acoustic coupling terms. Linear systems theory has also evolved on similar classes of problems especially in recent years. This document offers a bridge between the two veins of research. We first review the analytical model of the TAI phenomenon, which renders a set of delayed differential equations. Then, we apply a new mathematical tool called the cluster treatment of characteristic roots (CTCR) paradigm on this dynamics. CTCR provides non-conservative and exhaustive stability predictions for this class of systems. This capability is employed for both uncontrolled and feedback-controlled Rijke tube structures. The findings are unique from two angles: (i) stability declarations are made in the parametric space of the system, such as geometric dimensions (much differently from the peer studies that are at best point-wise evaluations), and (ii) these declared sets of stable operating parameters are exhaustive (i.e., for a given system no other parametric selection can provide stability). These capabilities become crucial when designing thermoacoustically stable combustors as well as determining their operating conditions. As a highlight contribution in this article, for those operating conditions that induce instability, we offer a methodology to synthesize a feedback control law that can recover stability, again utilizing the CTCR paradigm. Example case studies and analytical justifications of these novelties are provided.