Identification of low order manifolds: Validating the algorithm of Maas and Pope

The algorithm of Maas and Pope (1992) is presented as a method for identification of invariant reduced-order manifolds for stable systems which exhibit dynamics with a time-scale separation. While this method has been published previously in the literature, theoretical justification for the algorithm was not presented in the original work. Here, it will be shown rigorously that the algorithm correctly identifies the slow manifold. Before the theoretical results are presented, a brief background on the behavior of singularly perturbed systems is presented. The algorithm of Maas and Pope (1992) is then introduced. This method will be applied to two different examples, a distillation column and a two-phase chemical reactor. For each of these examples, the resulting reduced-order description will be compared to other standard methods of producing reduced-order models. In addition, some preliminary thoughts on how this method can be used to form reduced-order models are presented.