A Frequency-Based Interpretation of Energy-Based Model Reduction of Linear Systems

Various modeling techniques have been proposed in order to make modeling a more systematic procedure and to facilitate the development of modeling software that provide users, even experienced users, more ease when developing good models for control and design. The author has previously developed an energy-based modeling metric called “element activity” that was implemented in the model order reduction algorithm (MORA). While MORA was originally developed for the reduction of nonlinear models, the purpose of this paper is to gain insight into this methodology when applied to the reduction of linear models. Toward this end, the steady-state response to sinusoidal inputs is considered. Element activity is calculated analytically for any given excitation frequency, and a series of reduced models, which depend on the excitation frequency content, are generated. The results show through a quarter-car vehicle model that MORA generates a series of models whose spectral radius increases, as successively lower activity elements are included. It is demonstrated that low activity elements are related with high-frequency dynamics.