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Stability analysis and decentralized control of coupled oscillators with feedback delays.

机译：具有反馈延迟的耦合振荡器的稳定性分析和分散控制。

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摘要

Most dynamic systems do not react instantaneously to actuation signals. The temporal evolution of some others is based on retarded communications or depends on information from the past. In such cases, the mathematical models used to describe these systems must include information about the past dynamics of the states. These models are often referred to as delay or retarded systems. Delays could channel energy in and out of a system at incorrect time intervals producing instabilities and rendering controllers' performance ineffective.;The purpose of this research is two folds. The first investigates the effect of inherent system delays on the stability of coupled oscillators subjected to decentralized control and the second studies the prospectus of augmenting the delay into a larger delay period that could actually stabilize the coupled system and enhance its damping characteristics. Towards these ends, a system of two linearly-coupled oscillators with decentralized delayed-proportional feedback is considered. A comprehensive linear stability analysis is utilized to generate maps that divide the controllers' gain and delay domain into regions of stability for different coupling values. These maps are then used to draw definite conclusions about the effect of coupling on the stability of the closed-loop in the presence of delay.;Once the stability maps are generated, the Lambert-W function approach is utilized to find the stability exponents of the coupled system which, in turn, is used to generate damping contours within the pockets of stability. These contours are used to choose gain-delay combinations that could augment the inherent feedback delays into a larger delay period which can enhance the damping characteristics and reduce the system settling time significantly.;An experimental plant comprised of two mass-spring-damper trios coupled with a spring is installed to validate the theoretical results and the proposed control hypothesis. Different scenarios consisting of different gains and delays are considered and compared with theoretical findings demonstrating very good agreement. Furthermore, the proposed delayed-proportional feedback decentralized controller is tested and its ability to dampen external oscillations is verified through different experiments.;Such a research endeavor could prove very beneficial to many vital areas in our life. A good example is that of the coupled system of the natural and artificial cardiac pacemakers where the natural pacemaker represents a rhythmic oscillating system and the coupled artificial pacemaker provides a stabilizing signal through a feedback mechanism that senses the loss in rhythm. In this system, even the minute amount of delay in the sensing-actuating could prove very detrimental. The result of this research contributes to the solution of this and similar problems.
机译：大多数动态系统不会立即对驱动信号做出反应。其他一些的时间演变是基于沟通迟缓或依赖于过去的信息。在这种情况下，用于描述这些系统的数学模型必须包括有关状态的过去动态的信息。这些模型通常称为延迟或延迟系统。延迟可能会在不正确的时间间隔内将能量引入系统或从系统传出能量，从而产生不稳定并导致控制器的性能无效。;本研究的目的有两个方面。第一个研究固有系统延迟对经过分散控制的耦合振荡器的稳定性的影响，第二个研究将延迟增加到更大的延迟周期的招股说明书，该延迟实际上可以使耦合系统稳定并增强其阻尼特性。为此，考虑了具有分散的延迟比例反馈的两个线性耦合振荡器的系统。利用全面的线性稳定性分析来生成将控制器的增益和延迟域划分为针对不同耦合值的稳定性区域的映射。然后使用这些映射图得出关于存在延迟时耦合对闭环稳定性的影响的确定结论。;一旦生成了稳定性映射图，就使用Lambert-W函数方法来找到线性方程组的稳定性指数。耦合系统继而用于在稳定腔内产生阻尼轮廓。这些轮廓用于选择增益延迟组合，这些组合可以将固有的反馈延迟增加到较大的延迟周期，从而可以增强阻尼特性并显着减少系统建立时间。装有弹簧的装置可以验证理论结果和提出的控制假设。考虑了由不同的增益和延迟组成的不同方案，并将其与理论结果进行了比较，证明了非常好的一致性。此外，还对所提出的时滞比例反馈分散控制器进行了测试，并通过不同的实验验证了其抑制外部振荡的能力。这种研究成果可能对我们生活中的许多重要领域都非常有益。一个很好的例子是自然心脏起搏器和人工心脏起搏器的耦合系统，其中自然起搏器代表有节奏的振荡系统，而耦合的人工起搏器通过反馈机制来提供稳定信号，该反馈机制感测到节律的丧失。在该系统中，即使是感应致动中的微小延迟也会被证明是非常有害的。这项研究的结果有助于解决这一问题和类似问题。

著录项

  • 作者

    Keni, Saurabh.;

  • 作者单位

    Clemson University.;

  • 授予单位 Clemson University.;
  • 学科 Engineering Mechanical.
  • 学位 M.S.
  • 年度 2008
  • 页码 92 p.
  • 总页数 92
  • 原文格式 PDF
  • 正文语种 eng
  • 中图分类 机械、仪表工业;
  • 关键词

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