Modeling and control of chemical process systems described by partial differential equations.

摘要

The focus of this research is the modeling and control of distributed chemical process systems described by sets of partial differential equations. The dissertation is divided into three sections: eigenvalue inclusion region analysis, distributed sliding mode control and the method of characteristics, and Lie group theory.;The use of the eigenvalue inclusion concept in analyzing model approximations and order reduction strategies is demonstrated. This analysis tool enables one to study, in a rigorous fashion, the effect of model discretization on the open and closed-loop properties of the process. Two examples of packed-bed reactors under isothermal and nonisothermal operating conditions are presented to illustrate the development of inclusion regions.;Sliding mode control theory is applied to three chemical process systems described by first order partial differential equations. The method of characteristics exactly transforms the distributed parameter system into a finite set of ordinary differential equations. Geometric methods are used to extend sliding mode ideas for application on a class of partial differential equations. Through simulations of a forced-flow steam heater, an adiabatic packed-bed reactor, and a double-pipe heat-exchanger, the method is shown to be effective in controlling typical chemical engineering systems.;Lie group theory is utilized to calculate the infinitesimal generators associated with a second order parabolic PDE which models an isothermal packed-bed reactor with axial dispersion. A conjecture is formulated which implements these vector fields in a sliding mode control law in a geometric construction similar to the method of characteristics. A simulation study validates the conjecture as an effective method for control design.