SINGULAR PERTURBATION MODELING OF NONLINEAR PROCESSES WITH NONEXPLICIT TIME-SCALE MULTIPLICITY

In this article, a modeling framework is proposed for two-time-scale c hemical processes modeled by nonlinear ordinary differential equations (ODEs) with large parameters of the form 1/epsilon, to Obtain a stand ard singularly perturbed representation where the slow and fast variab les are explicitly separated. Initially, a result is derived that prov ides necessary and sufficient conditions for the existence and the exp licit form of an E-independent coordinate change that transforms the t wo-time-scale process into a standard singularly perturbed form. Whene ver these conditions are not satisfied, it is established that an epsi lon-dependent coordinate change, singular at epsilon = 0, has to be em ployed to obtain a standard singularly perturbed representation of the original two-time-scale process, and the construction of such a trans formation is addressed. The application of the proposed framework in d eriving standard singularly perturbed representations and its signific ance in the synthesis of well-conditioned controllers is demonstrated through chemical reactor applications. (C) 1998 Elsevier Science Ltd. All rights reserved.