Quantifying the Gap Between Embedded Control Models and Time-Triggered Implementations

Mapping a set of feedback control components to executable code introduces errors due to a variety of factors such as discretization, computational delays, and scheduling policies. We argue that the gap between the model and the implementation can be rigorously quantified leading to predictability if the implementation is viewed as a sequence of control blocks executed in statically allocated time slots on a time-triggered platform. For linear systems controlled by linear controllers, we show how to calculate the exact error between the model-level semantics and the execution semantics of an implementation, allowing us to compare different implementations. The calculated error of different implementations is demonstrated using simulations on illustrative examples.