Bond Graph Based Modal Decomposition of Systems with Non-proportional Damping

Modal analysis of lumped parameter and continuous dynamic linear systems is extensively used to study their dynamic behavior and controller design. In both cases, a reduction of the model size that does not degrade accuracy is often necessary for the efficient use of these models during the design process. Previous work by the author addressed the development and reduction of modal representations using the bond graph formulation. That work introduced a methodology, based on the activity metric, which reduces the model complexity by eliminating entire or partial modes. This approach has many advantages, however, it is limited to systems with proportional damping. The goal of the current work is to propose a new methodology such that a similar modal decomposition can be developed for systems with non-proportional damping. In this case, modes are coupled through damping elements, which can lead to various levels of coupling. It is proposed that weak coupling can be quantified using the activity metric. Coupling elements with low activity can then be eliminated from the model in order to decouple the modes. An illustrative example is provided to demonstrate the proposed modal decomposition methodology for real systems and how the importance of coupling elements can be quantified.