Geometric Methods for Nonlinear Multivariable Process Control

化学处理系统本质上是非线性的。 这些 系统包括诸如聚合反应器、高 纯度蒸馏塔等。目前的控制方案 在使用中通过获得近似线性模型来设计， 在工作稳定状态附近有效，并应用线性 控制技术 对于不围绕 稳态，例如间歇过程，近似 沿标称时变路径的线性化沿着导致 时变参数线性系统。 与 对高产品质量（高价值）的需求不断增加 例如，添加化学品），增加能源成本， 环境问题，以及降低实施成本 先进的控制系统（更复杂，成本更低 计算机），使用复杂的非线性控制系统， 变得可行。 这个研究项目的目标是开发一种新的方法 用于分析非线性过程的行为， 综合稳定鲁棒非线性控制方案 系统. 具体而言，PI的重点是： 1. 建立一个理论框架， 非线性系统的基本结构变得清晰， 很好理解。 在这个方向上，结果来自差分 几何系统理论将重新从工程 对其他理论问题的观点和解决方法， 追求。 2. 综合通用控制算法。 3. 开发软件工具， 上述算法变得简单明了。 4. 实验性地将结果算法应用于 聚合反应器，从而评估性能 控制方案。

Chemical processing systems are inherently non-linear. These systems include units such as polymerization reactors, high purity distillation columns, etc. Control schemes presently in use are designed by obtaining an approximate linear model, valid around an operating steady state, and applying linear control techniques. For processes that do not operate around a steady state, for example batch processes, approximate linearization along a nominal time-varying path results in a linear system with time-varying parameter are used. With increasing demand for high product quality (for high value added chemicals, for example), increasing energy costs and enviromental concerns, and, decreasing cost of implementing advanced control systems (with more sophisticated lower cost computers), the use of complex nonlinear control systems is becoming viable. The goal of this research project is to develop a new method for analyzing the behavior of nonlinear processes and to synthesize stable robust nonlinear control schemes for such systems. Specifically the PI's focus is to: 1. Develop a theoretical framework so that the properties and underlying structure of a nonlinear system become clear and well understood. In this direction, results from differential geometric systems theory will be revisited from an engineering viewpoint and solutions to other theoretical problems will be pursued. 2. Synthesize general control algorithms. 3. Develop software tools so that the implementation of the above algorithms becomes straightforward. 4. Experimentally apply the resultant algorithm to a polymerization reactor and thus evaluate the performance of the control schemes.