A Formal Hybrid Modeling Scheme for andling Discont inuit ies in hysical System Models

Physical systems are by nature continuous, but often exhibit nonhnearities that make behavior generation complex and hard to analyze. Complexity is often reduced by linearizing model constraints and by abstracting the time scale for behavior generation. In either case, the physical components are modeled to operate in multiple modes, with abrupt changes between modes. This paper discusses a hybrid modeling methodology and analysis algorithms that combine continuous energy flow modeling and localized discrete signal flow modeling to generate complex, multi-mode behavior in a consistent and correct manner. Energy phase space analysis is employed to demonstrate the correctness of the algorithm, and the reachability of a continuous mode.