Formal Modeling of Grafcets With Time Petri Nets

Abstract

Grafcet standard (IEC60848) is a formalism used in the world of manufacturing control, at the behavioral specification stage of a system. For specifying safe-critical systems, mathematical models associated with model-checking tools are necessary for the validation of the correctness. However, grafcets (meaning grafcet diagrams) are only semiformal models since certain aspects may be a source of different interpretations. The usual practice is to go through an intermediate formalism. In this brief, time Petri nets (TPNs) are chosen because they combine simplicity with wide-spreading and they also allow quantitative time analyses useful for the verification of real-time specifications. The main goal is to propose a principle of transforming a grafcet into TPN and to define the rules of this translation. The obstacle to overcome is to conciliate synchronous semantics of grafcet with asynchronous semantics of TPN.

SE-LTL Model-checking on Timed GRAFCETS via ε-TPN

“…Here is newly proposed the formal syntax of a classical chart, in accordance with the restrictions used to define the translation into a ε-TPN [7]. The semantics (with the required clarifications and the related restrictions) is neither formally defined here, nor recalled: it is the one already described in [7].…”

“…The work [7] has proposed a procedure of translating a grafcet into a TPN model, of which syntax is extended by ε infinitesimal delays as bounds on some transitions, allowing to simulate the synchronous semantics of GRAFCET.…”

“…However, GRAFCET and SFC semantics are only semi-formal, and so contain some ambiguities to clarify via a translation of the chart into another formalism, such as SMV textual language [5], timed automata [6] or time Petri nets (TPN) [7]: timed automata are used in [8] for SFC, and in [6] for GRAFCET. TPNs are structurally and historically closer to the GRAFCET than the other formalisms, and are adopted here.…”

“…For a TPN, delay bounds related to each transition determine the possible relative instant of the successive firings. The work in [7] has proposed a procedure of translating a grafcet into a TPN model called ε-TPN, of which syntax is extended by ε infinitesimal delays as bounds on some transitions, allowing to simulate the synchronous semantics of GRAFCET.…”

ε-TPN: definition of a Time Petri Net formalism simulating the behaviour of the timed grafcets

“…To allow a formal verification of GRAFCET (or SFC) models integrating quantitative time informations, many authors proposed to translate them into formal and well-reputed languages such as timed automata [11] or TPN [13,12]. The work in [12] is focused on defining some transformation rules which are used to translate the entities composing a timed and not necessarily sound grafcet chart (steps, transitions, literal variables, actions) into connected blocks to obtain the resulting TPN. The method exploits the similarity between TPN and GRAFCET to avoid exponential size of the translation, and implicitly relies on a clear choice about the GRAFCET semantics.…”