Recorded Webinar: Hybrid Dynamic Systems in Automotive Control Design

Model-Based Design of automotive systems is reaching enterprise-wide implications. For example, the extensive use of models throughout the design process has put forward a prominent need to facilitate model reuse. This requires design tools that support model exchange between engineering teams.

Because of the widely differing execution semantics that different models may employ, execution engines are required to be versatile and powerful such that efficient algorithms, tailored to the needs of a specific model, can be invoked. For example, to obtain a high-fidelity plant model rather than having each team involved in the design process to redo the modeling effort, it is more efficient to export a SolidWorks CAD model into a SimMechanics multi-body model that captures the dynamics of the multi-body geometry. On the other hand, a controller model may initially be a discrete state based model that is then extended to include implementation effects such as input data validation. This implies that an execution engine for a supporting tool set such as Simulink® and Stateflow® has to efficiently handle both a data driven approach as well as an event driven approach.

This support for such hybrid systems is amplified and complicated because the high-level language support is essential to negotiate the complexity in both controller modeling and plant modeling. In case of the former, this includes language features such as hierarchy, parallelism, and event broadcast. In case of plant modeling, support for modeling of the power structure is essential and this leads to implicit equations that often are 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 systems of equations (DAE) for each of the modes. The discrete switching behavior between modes and the continuous-time behavior within each mode each have very different execution semantics. Complications and idiosyncrasies in the behavior of such hybrid dynamic systems are presented and an ontology of mode transition behavior is developed. In particular, in case the 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.