Abstract
Model-based design methodologies are commonly used in industry for the development of complex cyber-physical systems (CPSs). There are many different languages, tools, and formalisms for model-based design, each with its strengths and weaknesses. Instead of accepting some weaknesses of a particular tool, an alternative is to embrace heterogeneity, and to develop tool integration platforms and protocols to leverage the strengths from different environments. A fairly recent attempt in this direction is the functional mock-up interface (FMI) standard that includes support for co-simulation. Although this standard has reached acceptance in industry, it provides only limited support for simulating systems that mix continuous and discrete behavior, which are typical of CPS. This paper identifies the representation of time as a key problem, because the FMI representation does not support well the discrete events that typically occur at the cyber-physical boundary. We analyze alternatives for representing time in hybrid co-simulation and conclude that a superdense model of time using integers only solves many of these problems. We show how an execution engine can pick an adequate time resolution, and how disparities between time representations internal to co-simulated components and the resulting effects of time quantization can be managed. We propose a concrete extension to the FMI standard for supporting hybrid co-simulation that includes integer time, automatic choice of time resolution, and the use of absent signals. We explain how these extensions can be implemented modularly within the frameworks of existing simulation environments.
Highlights
Model-based design of cyber-physical systems (CPS) requires modeling techniques that embrace both the cyber and the physical parts of a system [24]
3.1.1 Advancing time In functional mock-up interface (FMI), simulation is driven by a master that keeps time and instructs functional mock-up units (FMUs) to advance their time in increments called “steps.” Once all participating FMUs have advanced their time by some delta, an iteration has finished
Cyber-physical systems pose interesting challenges, because they marry a world, the cyber side, where time is largely irrelevant and is replaced by sequences and precedence relations, with a physical world, where even the classical Newtonian idealization of time stumbles on discrete, instantaneous behaviors and notions of causality and simultaneity
Summary
Model-based design of cyber-physical systems (CPS) requires modeling techniques that embrace both the cyber and the physical parts of a system [24]. We describe instead a representation of time that eliminates the problems associated with floating-point representations, allows for multiplicity of time resolutions, and allows for cyber abstractions where events can occur discretely in time and in sequences without time advancing For the latter property, we adopt a form of superdense time [33,34] We propose a model of time that supports a multiplicity of time resolutions, differing even within the same simulation, supports discrete events with an exact notion of simultaneity, invulnerable to quantization errors, and is efficiently converted to and from legacy floating-point representations of time to accommodate legacy simulators within a co-simulation environment It supports abstractions of time such as sequences of events where time does not elapse, enabling better integration of cyber models with physical ones Our implementation of the proposed FMU wrappers, a simple method to achieve compatibility with FMI-HC, is explained in detail in “Appendix”
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