Control of Nonlinear Differential-Algebraic Equation Systems

摘要/ Abstract摘要：化学工程过程本质上是非线性和多变量的，通常由耦合微分方程和代数方程（DAEs）来建模。微分方程来源于动力守恒方程，代数方程来源于热力学平衡关系、经验本构方程、闭合条件、准稳态假设等。对于许多化学过程，代数方程本质上是隐式的和奇异的，不允许将过程模型直接简化为一个由纯微分方程组成的过程。本研究的目的是建立一个分析和控制非线性多变量DAE系统的综合框架。为此目的将采用状态空间方法框架，并将使用非线性分析和综合工具。将获得对控制问题性质的基本见解，并将开发一般控制方法。软件工具也将被开发并用于将这些方法应用于具有代表性的化学反应和分离过程。

Abstract - Daoutides - 9320402 Chemical engineering processes are inherently nonlinear and multivariable, and are typically modeled by coupled differential and algebraic equations (DAEs). The differential equations arise from dynamic conservation equations, while the algebraic equations arise from thermodynamic equilibrium relations, empirical constitutive equations, closure conditions, quasi-steady-state assumptions, etc. For many chemical processes, the algebraic equations are implicit and singular in nature and do not allow the direct reduction of the process model to one consisting of pure differential equations. The objective of this research is to develop a comprehensive framework for the analysis and control of nonlinear multivariable DAE systems. A state-space methodology framework will be adopted for this purpose and nonlinear analysis and synthesis tools will be used. Fundamental insight on the nature of the control problem will be obtained and general control methods will be developed. Software tools will also be developed and used for the application of the methods to representative chemical reaction and separation processes.