Nonlinear control of two-time-scale and distributed-parameter systems.

摘要

All chemical engineering processes are inherently nonlinear. In addition to nonlinear nature, many chemical engineering processes are characterized by multiple-time-scale behavior and spatial variations. The mathematical models of chemical engineering processes are typically obtained from the dynamic conservation equations and consist of systems of nonlinear Ordinary Differential Equations (ODEs) and nonlinear Partial Differential Equations (PDEs). However, no mathematical model can precisely predict the dynamic behavior of a real process; there is always uncertainty. Model uncertainty is typically due to disturbances and unknown process parameters.; In the last decade, significant progress has been made towards the development of nonlinear control methods for systems of nonlinear ODEs. Differential geometry has proven to be a natural framework for the analysis and control of such systems. Within this framework, basic control problems, including the modification of the input/output behavior, the elimination of measurable disturbances, and the attenuation of unmeasured disturbances and unknown parameters have been successfully addressed. Although geometric control methods may lead to satisfactory control quality in nonlinear processes without time-scale multiplicity, they usually lead to poor performance in processes where multiple-time-scale behavior is present. Furthermore, few results are available for the synthesis of nonlinear controllers for nonlinear PDE systems. The need to develop control methods for nonlinear two-time-scale ODE systems and nonlinear PDE systems has been well-recognized both by industry and academia.; Motivated by the above, this doctoral thesis presents a general framework for the synthesis of nonlinear controllers for nonlinear two-time-scale ODE systems and nonlinear PDE systems that systematically addresses the problems of modification of the input/output behavior, elimination of measurable disturbances, and attenuation of unmeasured disturbances and unknown parameters. The proposed control algorithms are applied to industrially important chemical processes.