Parametric Optimization of Digitally Controlled Nonlinear Reactor Dynamics using Zubov-like Functional Equations

Abstract

The present work aims at the development of a systematic method to optimally choose the parameters of digitally controlled nonlinear reactor dynamics. In addition to traditional performance requirements for the controlled reactor dynamics such as stability, fast and smooth regulation, disturbance rejection, etc., optimality is requested with respect to a physically meaningful performance. The value of the performance index is analytically calculated via the solution of a Zubov-like functional equation and becomes explicitly parameterized by the digital controller parameters. A standard static optimization algorithm yields subsequently the optimal values of the above parameters. Within the proposed framework, stability region estimates are also provided through the solution of the above functional equation. Finally, a nonlinear chemical reactor example following Van de Vusse kinetics is used in order to illustrate the proposed parametric optimization method.