To handle mixed continuous/discrete behavior, we have developed a hybrid modeling approach that incorporates local discontinuous changes by imposing finite state machines on a bond graph model of the system. A discontinuous change may trigger a sequence of instantaneous changes in the system, so traditional notions of observability and controllability have to be developed anew for hybrid models. A critical aspect in model verification is the issue of loops of instantaneous changes which prevent real-time from progressing and violate the physical principle of divergence of time. We have shown that a multiple energy phase space analysis technique can be applied to prove divergence of time for hybrid physical system models. This approach relies on the principle of invariance of state which states that, though signal values may change discontinuously across a number of discontinuous changes, stored energy cannot. At present, we are implementing this analysis technique to perform automated model verification before simulation.
To support behavior generation of hybrid models we have developed the Mythical Mode Algorithm (MMA) to correctly infer the new operational mode as well as correctly transfer the system state between modes. The effectiveness of this methodology is demonstrated by modeling complex rigid-body mechanical systems, such as the cam-rod mechanism in automobiles, where discontinuous changes in system configuration often cause inertial elements (masses) to become dependent. Other example systems we have worked on include a cylinder in a spark-ignition combustion engine, and the more academic thin rod colliding under a specific angle with a floor with Coulomb friction.
Bond graphs provide a generic representation across physical domains which makes this approach perfectly suited for conceptual design (e.g., replacing mechanical functions by devices from other physical domains to reduce cost and increase reliability and performance). Furthermore, given a bond graph, a system of dependency relations can be derived algorithmically for simulation. It provides a systematic framework for compositional modeling and the localized discrete events methodology provides a powerful mechanism for modeling large-scale, complex systems. The integration of controller and process into one model offers a complete spectrum of solutions to a design problem, and, therefore, design optimization does not apply to a system sub-part but covers all alternatives (e.g., active control). Finally, the qualitative nature of reachability and controllability analyses are of great use for design and analysis.