Bond Graph Based Modal Representations and Model Reduction of Lumped Parameter Systems

Modal analysis is extensively used to study dynamic behavior of continuous and lumped parameter linear systems. More specifically, modal analysis can be used for the analysis and controller design of dynamic systems. In both cases, reduction of model size 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 Model Order Reduction Algorithm (MORA), which uses an energy-based metric to generate a series of proper reduced models. An illustrative example is provided to demonstrate the calculation of the modal power and the elimination of unimportant modes or modal elements using MORA.