Mode Transition Behavior in Hybrid Dynamic Systems

Physical system modeling benefits from the use of implicit equations because it is often an intuitive way to describe physical constraints and behaviors. To achieve efficient models, model abstraction may lead to idealized component behavior that switches between modes of operation (e.g., an electrical diode may be on or off) based on inequalities (e.g., voltage > 0). In an explicit representation, the combination of these local mode switches leads to a combinatorial explosion of the number of global modes. It is shown how an implicit formulation can be used to formulate these mode switches, thereby circumventing the combinatorial problem. This leads to the use of differential and algebraic equations (DAEs) for each of the modes. In case these DAEs are of high index, jumps in generalized state variables may occur. In combination with the inequalities that define mode switching, this leads to rich and complex mode transition behavior. An overview of this mode switching behavior and an ontology is presented.