Geometric Methods for Nonlinear Multivariable Process Control

化学处理系统本质上是非线性的。这些系统包括聚合反应器、高纯度精馏塔等装置。目前使用的控制方案是通过获得近似线性模型来设计的，该模型在运行稳态周围有效，并应用线性控制技术。对于不围绕稳定状态运行的过程，例如批处理过程，沿着标称时变路径的近似线性化在具有时变参数的线性系统中使用。随着对高质量产品（例如高附加值化学品）的需求不断增加，能源成本和环境问题不断增加，以及实施先进控制系统（使用更复杂的低成本计算机）的成本不断降低，复杂非线性控制系统的应用正变得可行。本研究项目的目标是发展一种新的方法来分析非线性过程的行为，并为这类系统合成稳定的鲁棒非线性控制方案。具体来说，PI的重点是：1。建立一个理论框架，使非线性系统的性质和基本结构变得清晰和容易理解。在这个方向上，微分几何系统理论的结果将从工程的角度重新审视，并将寻求其他理论问题的解决方案。2. 综合一般控制算法。3. 开发软件工具，使上述算法的实现变得简单明了。4. 将所得算法应用于聚合反应器实验，从而评价控制方案的性能。

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.