Dynamic Analysis and Control of Nonlinear Processes via Nonlinear Transfer Functions

摘要- Palazoglu - 9400304 大多数化学过程本质上是非线性的，并且缺乏用于非线性系统的分析工具阻碍了建立全面的控制范例的努力，正如已经对线性系统所做的那样。 缺乏关于非线性过程行为的信息导致不必要地限制安全操作的区域;过度设计以试图软化非线性;或设计保守的控制系统以维持可接受的操作。 这样的工程解决方案可能产生次优的工厂操作，并且更经济有利的制度可能不必要地被认为是不安全或不可靠的。 PI正在开发一种用于非线性动力学表示的技术，非线性动力学方程的解的参数化，以及非线性反馈控制问题的解析解。 该方法是基于一个特定的操作，通过拉普拉斯变换产生非线性传递函数的非线性。 这使得非线性常微分方程的代数解在变换域和随后的实现在时域，非常类似于线性系统分析。 这样的程序产生的非线性常微分方程的解析解。 它还提供了操纵非线性传递函数来构造和分析非线性闭环控制系统的工具。 这种分析环境，支持符号计算，有可能改变以前的看法，非线性系统分析和铺平了道路，为非线性控制和教育的新方法。

Abstract - Palazoglu - 9400304 The majority of chemical processes are inherently nonlinear and the lack of analytical tools for nonlinear systems hampers efforts to establish a comprehensive control paradigm, as has been done with the linear systems. The lack of information regarding the behavior of nonlinear processes results in unnecessarily limiting the region of safe operation; to overdesign in an attempt to soften nonlinearities; or to design conservative control systems such that an acceptable operation is maintained. Such engineering solutions may yield suboptimal plant operations, and more economically favorable regimes may be unnecessarily deemed unsafe or unreliable. The PI is developing a technique for the representation of nonlinear dynamics, a parametrization of the solution of nonlinear dynamic equations, and an analytical solution for the nonlinear feedback control problem. The method is based on a particular operation for nonlinearities that yields nonlinear transfer functions via Laplace-like transformations. This permits the algebraic solution of nonlinear ODEs in the transform domain and subsequent realization in the time domain, quite analogous to linear systems analysis. Such a procedure yields an analytical solution for the nonlinear ODEs. It also provides tools for manipulating nonlinear transfer functions to construct and analyze nonlinear closed-loop control systems. This analytical environment, supported by symbolic computations, has potential in altering previous perceptions about nonlinear systems analysis and paves the way for a new approach for nonlinear control and education.