Time-Triggered Implementations of Dynamic Controllers

Bridging the gap between model-based design and platform-based implementation is one of the critical challenges for embedded software systems. In the context of embedded control systems that interact with an environment, a variety of errors due to quantization, delays, and scheduling policies may generate executable code that does not faithfully implement the model-based design. In this article, we show that the performance gap between the model-level semantics of linear dynamic controllers, for example, the proportional-integral-derivative (PID) controllers and their implementation-level semantics, can be rigorously quantified if the controller implementation is executed on a predictable time-triggered architecture. Our technical approach uses lifting techniques for periodic time-varying linear systems in order to compute the exact error between the model semantics and the execution semantics. Explicitly computing the impact of the implementation on overall system performance allows us to compare and partially order different implementations with various scheduling or timing characteristics.