Nonlinear Dynamics and Control of Complex Patterns in Disturbed Chemical Systems

化学系统具有非常复杂的动力学特征。例如，在商业化学反应器中，人们可能面临未知的动力学，多相流，困难的质量和热传递以及所有这些机制在不规则域中的复杂耦合。因此，反应工程师过去一直在研究理想化的问题，希望获得有用的经验法则。由于化学系统的动力学通常仅由少数“主”空间结构控制，因此从纯粹的经验估计中构建低维非线性动力学模型是可能的。PI计划开发一种时空相关技术，用于识别和构建主模态的规范分布演化方程。由于这些典型方程只包含几个系数，因此将采用分岔理论发展通用反应器动力学理论，以涵盖和分类分布参数化学反应器中的所有动态现象。具体来说，反应器的响应，如增长热点、爬行反应区、传播锋的旋转不稳定性等，将在理论中与特定类别的分布式干扰联系起来。这些不稳定性的增长和传播将在一般反应堆稳定性理论中用数学方法描述。初步结果表明，该方法也可用于成功地控制反应器动力学和模式，而无需显式模型。该技术允许在线更新模型，包括调整模型的顺序，从而克服了一些鲁棒性问题。将进行平行实验研究，以证实理论预测的动态模式和验证由此产生的控制方案。//

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.//