An Algorithm for Obtaining Proper Models of Distributed and Discrete Systems

Abstract

The development of automated modeling software requires strategies for synthesizing mathematical models of systems with distributed and discrete characteristics. A model order deduction algorithm (MODA) is developed to deduce a Proper System Model by selecting the proper complexity of submodels of components in a system subject to a frequency based metric. A Proper Model in this context means that (1) the system model has the minimum spectral radius out of all possible system models of equivalent or greater complexity, and (2) any increase in the model complexity will result in spectral radius beyond a specific frequency range of interest. Proper Models are also defined to have physically meaningful parameters. Proper Models are intended to be useful for design, where mapping the relationship between design parameters and dominant system dynamics is critical. While MODA is illustrated using the application of machine-tool drive systems, it is readily applicable to other modeling applications.