Dynamic Sampling for FOCUS Hybrid Components

Abstract

Abstract-The combination of embedded systems with physical components, termed Cyber-Physical Systems (CPSs), poses important challenges in the design, modelling, simulation and verification of systems, also why they combine discrete software elaborations with analogues time evolutions and different engineering disciplines. In this domain, the software part is increasing the dimension and has a more important role. An important formalism for describing continuous and discrete systems is the hybrid system formalism. We present our approach based on the FOCUS modelling theory to model hybrid systems, which have discrete transitions and continuous differential equations. The modular and logical structure of FOCUS components combined with hybrid systems improves the support for the modelling of CPSs. Anyway, a fully continuous simulation may be too complex and not represent the final hardware where the model will be deployed. Therefore, we propose two sampling techniques to transform the continuous time in discrete steps, in which the length of the sampling period it is dynamically changed.Index Terms-Hybrid systems, embedded systems, model-based development, sampling, hybrid systems simulation.

Interface Behavior Modeling for Automatic Verification of Industrial Automation Systems' Functional Conformance

“…reason, the Focus theory is recently extended within the MoDEMAS project to supporting continuous time elaboration and data types [34,35]. The behavior of hybrid components is defined by a modified version of the hybrid automaton, called I/O hybrid state machine and introduced in [34].…”

“…In general, a dynamic sampling is a more convenient solution with respect to the periodic one [46]. For Focus I/O hybrid state machines, two dynamic sampling algorithms to discretize their differential equations has been already developed [34]. The first approach is based on the slope of the differential function: The actual period is halved if there is an enough high difference between the slope of the actual value with respect to the slope of the precedent value; instead the period is doubled (until a maximal value) if the slope is below a predefined value after some suitable sampling steps.…”

“…The behavior of hybrid components is defined by a modified version of the hybrid automaton, called I/O hybrid state machine and introduced in [34]. Components which have discrete as well as continuous interfaces are referred to as hybrid components.…”

Interaction of model-driven engineering and signal-based online monitoring of production systems: Towards Requirement-aware evolution

“…the observable behavior of a component's interfaces. The latter can be understood as a mathematical stream function which maps input streams to output streams defined with (hybrid) state automata [26].…”