Nonlinear Dynamics and Control of Complex Patterns in Disturbed Chemical Systems

化学系统的特点是非常复杂 动力学例如，在商业化学反应器中， 可能面临未知动力学、多相流、困难质量 和热传输以及所有这些的复杂耦合 不规则领域的机制。 因此，反应 工程师们在过去研究过理想化的问题， 希望获得有用的经验法则。 因为 化学系统的动力学通常只由少数几个 “主人”的空间结构，低的建设 三维，非线性动力学模型，从纯粹的经验 估计是可能的。 PI计划开发空间和时间相关性 识别和构建规范的技术 主模的分布演化方程。 因为 这样的正则方程只包含几个系数， 一般的反应堆动态理论将采用 分叉理论涵盖和分类所有动态 分布参数化学反应器中的现象。 具体来说，反应堆的反应，如不断增长的热点， 蠕变反应区，传播的自旋不稳定性， 前线等将连接到特定类别的 理论中的分布式干扰。 生长和 这些不稳定性的传播将在数学上 在一般反应堆稳定性理论中描述。 初步 结果表明，该方法也可用于 成功控制反应堆动态和模式， 显式模型 该技术允许模型在线更新， 包括对模型阶数的调整，因此 克服了一些鲁棒性问题。 平行实验 将进行研究，以确认动态模式 理论预测，并验证所得到的控制 schemes.

Chemical systems are characterized by very complicated dynamics. For example, in a commercial chemical reactor, one may face unknown kinetics, multi-phase flow, difficult mass and thermal transport and a complex coupling of all these mechanisms in an irregular domain. Therefore, reaction engineers have studied idealized problems in the past, with the hope of obtaining useful rules of thumb. Because the dynamics of chemical systems are often dominated by only a few "master" spatial structures, the construction of low dimensional, nonlinear dynamic models from purely empirical estimations is possible. The PI plans to develop a spatial and temporal correlation technique for the identification and construction of canonical distributed evolution equations of the master modes. Because such canonical equations contain only a few coefficients, general reactor dynamic theory will be developed using bifurcation theory to encompass and classify all dynamic phenomena in distributed parameter chemical reactors. Specifically, reactor responses like growing hot-spots, creeping reaction zones, spinning instabilities of propagating fronts, etc. will be connected to specific classes of distributed disturbances in the theory. The growth and propagation of these instabilities will be mathematically delineated in a general reactor stability theory. Preliminary results suggest that the methodology can also be used to successfully control reactor dynamics and patterns without an explicit model. The technique permits model updating on-line, including adjustments on the order of the model, thus overcoming some robustness issues. Parallel experimental studies will be carried out to confirm the dynamic patterns predicted by the theory and to verify the resultant control schemes.//