Development of Proper Models of Hybrid Systems: a Bond Graph Formulation

To improve the ability of engineers to use dynamic models as part of the design process, a model deduction procedure for developing proper bond graph models of hybrid systems is presented. An accuracy criterion and a search pattern are presented, in a bond graph format, for a model order deduction algorithm (Extended MODA) previously published. The Extended MODA process consists of systematically incrementing the rank of each component model in the system, until a set of critical system eigenvalues has been defined. Then, the rank of component models is incremented until each critical system eigenvalue has converged to within a specified tolerance. The bond graph representation is shown to provide a natural framework for assembling component models that may be modal expansions, finite segments and or bounded representations of the components. In addition, through an example the bond graph formulation is shown to have great potential utility in providing the design engineer a “visual” perspective on the dominant components (and elements of those components) in a proposed system. The example also shows that the proper system model deduced depends on both the model approximations used for the components as well as the model deduction search algorithm. A bond graph based automated modeling system using Extended MODA appears to hold much promise for improving the tools available to design engineers.