We discuss the challenges of building a simulation framework for hybrid systems, in particular the wellknown Zeno effect and correct composition of models idealised by abstracting irrelevant behavioural details (e.g. the bounce dynamics of a bouncing ball or the process of fuse melting in an electrical circuit). We argue that the cornerstone of addressing these challenges is the definition of a semantic framework with an appropriate underlying model of time.Using two simple examples, we illustrate the properties of such a model and explain why existing models are not sufficient. Finally, we propose a new Zeno-free semantic model that allows mixing discrete and continuous behaviour in a rigorous way and provides for the compositional behavioural abstraction.Although it is based on non-standard analysis, we explain how our semantic model can be used to develop hybrid system simulators.
Modelica provides intuitive constructs to create and group model definitions. However, models themselves do not compose. In other words, the connection of type-compatible and locally balanced submodels does not generally yield a valid (e.g., balanced, structurally non-singular) model. Starting from simple examples of such invalid models (resulting from commonly encountered situations when using Modelica), this paper explains how those problems could be avoided by introducing a safer notion of physical connector, similar in some aspects to the VHDL-AMS notion of terminal. An extension of the notion of connection is also presented, providing new opportunities to make efficient use of ideal models in Modelica.
Cyber-physical systems have developed into a very active research field, with a broad range of challenges and research directions going from requirements, to implementation and simulation, as well as validation and verification to guarantee essential properties. In this survey paper, we focus exclusively on the following fundamental issue: how to link physicality and computation, continuous time-space dynamics with discrete untimed ones?We consider that cyber-physical system design flow involves the following three main steps: 1) cyber-physical systems modeling; 2) discretization for executability; and 3) simulation and implementation. We review-and strive to provide insight into possible approaches for addressing-the key issues, for each of these three steps.
In this paper, we show that, provided the Modelica language specification is enriched with the notion of external connector, interesting applications follow, where Modelica can be used to describe synchronous event-activated blocks that communicate efficiently with the "outside world". Such blocks described in Modelica and compiled separately can still be connected together to form new blocks. Scicos (www.scicos.org), a freely available modeling environment, can make efficient use of those blocks, that in addition enable seamlessly integration of Modelica into a causal environment.
Modelica models involving discrete-time aspects may lead to surprising results due to the way events are currently handled in the language. Indeed, simultaneity is interpreted as synchronism (see [2] for details) and, as a consequence, two unrelated sources of events may interfere in unexpected ways. In this paper, we present minimal examples of models that exhibit unexpected or surprising results, then we explain the general causes of such behaviors and propose to introduce the notion of clock in the language to solve the issues. In contrast to [1] and [2], we focus here on models resulting from the composition of other models: we aim at showing that the current discrete-time theoretical model of Modelica is not robust with respect to model composition. For the final user, it means that it is generally not possible to build reliable models involving discrete-time aspects by simply connecting generic library models: manual adjustments are often required to obtain the expected behavior 1 .
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