Model Reduction of Modal Representations

Abstract

Dynamic analysis is extensively used to study the behavior of continuous and lumped parameter linear systems. In addition to the physical space, analyses can also be performed in the modal space where useful frequency information of the system can be extracted. More specifically, modal analysis can be used for the analysis and controller design of dynamic systems, where reduction of model complexity without degrading the accuracy is often required for the efficient use of the model. The reduction of modal models has been extensively studied and many reduction techniques are available. The majority of these techniques use frequency as the metric to determine the reduced model. This paper describes a new method for calculating the modal power of lumped parameter systems with the use of the bond graph representation, which is developed through a power conserving modal decomposition. This method is then used to reduce the size of the model. This technique is based on the previously developed Model Order Reduction Algorithm (MORA), which uses an energy-based metric to generate a series of proper reduced models. An example is provided to demonstrate the calculation of the modal power and the elimination of unimportant modes or modal elements using MORA.