Singular Perturbation Modeling of Nonlinear Processes with Non Explicit Time-Scale Separation

Abstract This work addresses the problem of singular perturbation modeling of two-time-scale chemical processes described by nonlinear ODEs that involve large parameters of the form 1/e. Initially, a result derived in (Kumar et al., 1995) is reviewed that provides necessary and sufficient conditions for the existence and the explicit form of a coordinate change, which is independent of e and transforms the two-time-scale process to a standard singularly perturbed form where the separation of fast and slow modes is explicit. Whenever these conditions are not satisfied, it is established that the state-space region in which the system exhibits a two-time-scale property depends on the value of e and an e-dependent coordinate change, singular at e = 0, has to be employed to obtain a standard singularly perturbed form of the system. The significance of the proposed singular perturbation modeling framework in the design of well-conditioned controllers that account for the two-time-scale behavior, is demonstrated on a chemical reactor which exhibits a slightly non-minimum phase behavior.