Time-triggered implementations of dynamic controllers

Abstract

Bridging the gap between model-based design and platformbased 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 paper, we show that the performance gap between the model-level semantics of 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, timevarying 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. Disciplines Computer SciencesThis conference paper is available at ScholarlyCommons: http://repository.upenn.edu/cis_papers/500 ABSTRACTBridging the gap between model-based design and platformbased 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 paper, we show that the performance gap between the model-level semantics of 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.

Computing Schedules for Time-Triggered Control using Genetic Algorithms

“…This work builds upon previous research on time-triggered implementations of control systems (Yazarel et al (2005); Nghiem et al (2006)). Time-triggered architectures offer opportunities for a more predictable mapping of control models (Kopetz and Bauer (2003)).…”

“…The control blocks are assumed to be well-defined so that given the plant state at time t 0 and the plant outputs for time t ≥ t 0 , the plant state variables and controller state variables at time t ≥ t 0 are uniquely determined. The interconnection of the control blocks defines a set of differential and algebraic equations (see Nghiem et al (2006) for details). In this paper, we consider controller models which are linear…”

“…, B r ) to express the same controller model. In this paper, the structure considered is the same as in Nghiem et al (2006), in which a block B I integrates the controller state z i and m blocks B 1 , . .…”

“…In detail, Theorem 2 in Nghiem et al (2006) allows the exact computation of e M (ρ, τ, δ, x(0)). Theorem 4.…”

“…In a time-triggered implementation, instead of mapping control blocks to periodic tasks, the compiler can allocate well-defined time slots to control blocks. Given a mapping of all the control blocks to the time slots, one can precisely define the trajectories of the implementation and quantify the error with respect to the model-level semantics as indicated in (Yazarel et al (2005); Nghiem et al (2006)). …”