Grafcet

GRAFCET (Acronym of “Functional Graph of Order Stages/Transitions” and from “Graph of group AFCET” ) is a mode of representation and analysis of a automatism, adapted particularly well to the systems with sequential evolution, i.e. decomposable in stages.

The GRAFCET thus represents graphically the operation of an automatism by a unit:

of stages with which are associated actions
of transitions between stages with which are associated receptivities
connections directed between the stages and the transitions

Mode of representation

The mode of representation which is standardized (standard NF C03190 of the UTE) is the following:

a stage is represented by a square located by an identifying number. An active stage can be indicated by a point below the number. The associated actions are indicated in a literal way or symbolic system, in a rectangle connected to the right part. An initial stage is represented by a doubled square. (In blue, fig. opposite)
a directed connection is represented by a line, is traversed by from top to bottom defect or from left to right. In the contrary case, one uses arrows. The crossings are avoided. (In black, fig. opposite)
a transition between two stages is represented by a bar perpendicular to the directed connections which connect it at the stages the preceding one (S) and following (S). A transition indicates the upgrading capability between stages. With each transition a receptivity registered on the right with the bar of transition is associated. A receptivity is a logical condition which makes it possible to distinguish among all the combinations of information available that which is likely to make pass the system at the following stages (In red, fig. opposite).

Single sequence and multiple sequences

1. single Sequence : an automatism is described by a grafcet with single sequence when it can be represented by a whole of several stages forming a continuation whose unfolding is always carried out in the same order. (The grafcet above is an example) 2. simultaneous multiple Sequences: when the crossing of a transition results in activating several stages, the sequences resulting from these stages are known as simultaneous sequences . The simultaneous sequences always begin on a receptivity unique and always finish on a receptivity unique. Indeed, the various sequences “start” at the same time then evolve/move then independently from/to each other. It is thus only when all the final stages of these sequences are active simultaneously (what often occurs after reciprocal waiting) that the evolution can continue with the simultaneous crossing of the same transition. The beginning and the end of the simultaneous sequences are represented by two parallel features (in red, fig. opposite), which do not constitute specific entities of the grafcet, but which must be included/understood like the widening of the entry or the exit of the transition. Sometimes (One speaks about “divergence” and “convergence in AND” for this representation.) 3. exclusive multiple Sequences: when, starting from a stage, one can carry out a choice between several possible sequences conditioned by several exclusive receptivities, one deals with selection of sequences or shunting . For a better legibility, the various possible sequences are installed under a horizontal feature (in red fig. opposite) which represents the widening of the exit of the stage, and are found by a similar feature representing the entry of the again common stage. In a way similar to the double feature considering above, one speaks about “divergence” and “convergence in OR” for this representation.

Two particular cases of selection of sequences frequently meet in the majority of the sequential automatisms. They are the jump of stage and the resumption of sequence.

the jump of stages makes it possible to jump a certain number of stages if a logical condition is carried out (In fact, it is the general case, with an empty branch of action).
the resumption of sequence makes it possible to repeat the same sequence until the receptivity of end of sequence is true.

If receptivities are not exclusive (for example if c12 and c13 can be true at the same time), the continuation is unspecified; the grafcet is faulty.

Rules of evolution of the grafcet

Rules of syntax

Alternation stage-transition must be respected. Two stages should never be connected directly. Two transitions should never be connected directly.

Regulate evolution

initialization: an initial situation is characterized by the fact that a certain number of stages are active at the beginning of operation. These stages are located on the grafcet by a double square.
the crossing of a transition: a transition either is validated or not validated. It is validated when all the immediately preceding stages are active (see the following table). It cannot be crossed:
1. that when it is validated
2. and that the associated receptivity is true.
evolution of the active stages: the crossing of a transition involves the activation of all the immediately following stages and the desactivation of all the immediately preceding stages.
simultaneous Evolution: several simultaneously passable transitions are simultaneously crossed. For example, on the figure opposite, if the variable " c" is true, the grafcet goes évouler towards the simutanée desactivation of stages 5 and 10 and the simultaneous activation of stages 6 and 11.
simultaneous Activation and desactivation: so during operation, the same stage must be simultaneously decontaminated and activated, it remains ACTIVE

Nature of the actions

The criterion of classification of the most used actions is: duration of the action compared to the duration of the stage:

Action continues : the action continues as much as the stage with which it is associated is active. That results in the time series chart (chronogram 1) opposite.
conditional Action : the action is carried out if, in addition to the activity of the stage with which it is associated, a specified logical condition is true (see chronogram 2 opposite). These conditional actions are particularly important because they make it possible, in a stage, to carry out combinative local in sight, for example, That makes it possible to carry out the action only during one certain time, or after a certain time of activity of the stage (see 2 chronograms 3 and 4 opposite).
Action: to maintain the continuity of an action having to be prolonged during the activity of several stages, it is possible:

to repeat the action continues in all the stages concerned;

to memorize the action by functions put at 1 (SET) and put at zero (RESET).

the figure below presents these various equivalent methods of maintenance of an action on several stages:

Nature of the receptivities

It is always about the result of a single Boolean expression which can utilize

states of Boolean variables (direct state, face, end of temporization…)
Of the comparisons on numerical values.
Of the tests on the active states of stages (allowed but to avoid for a better legibility).
etc

Synchronization and coupling of sequences

simultaneous Activation of 2 stages: 5 and 8 are activated simultaneously:
Waiting of events: the stages 25 and 23 are stages of reciprocal waiting. When they are active at the same time and that T2=1 one passes at stage 26:
Prohibition of events: so certain actions of a sequence are prohibited when other actions of another simultaneous sequence take place, it is necessary to make depend crossing on the transitions from the 1st sequence from the active states from the stages from the 2nd sequence. Stage 3 cannot be activated if stages 6 or 7 are active.
Sequences repeated or under program: when the same sequence is used several times in a cycle, one can avoid repeating it by replacing it by a rectangle with double vertical features inside whose the stage of entry and the stage of exit are noted.

Macro-stages

A macro-stage is a means of representation of a single whole of transitions and stages in only one stage: the macro-stage. A macro-stage Mi can be completely replaced by its expansion which contains a stage of entry I.E.(internal excitation) and one of exit If . (see image opposite)

This means of representation can thus be regarded as a " zoom" who allows to simplify the reading of Grafcet of important size. An expansion can be used only once: its use is single and it should not be confused with a subroutine, following the example others computer programming languages.

If one wants to use the same expansion, it should be duplicated. That returns, in fact, to make an authority of the expansion by call, following the example calls of functions in the standard IEC 1131-3.

Standard IEC 1131-3

The standard IEC 1131-3 (1993) standardizes five languages of which the language SFC (Sequential Function Chart) which is very close to the GRAFCET. Several differences can nevertheless be noted:

the objective of the language :

SFC is a Computer programming language intended to be established on controller, like a industrial programmable Automate for example.
the GRAFCET is a language of representation which can be used to specify an awaited behavior or to describe the behavior of existing automated systems.

syntax :

Contrary to the GRAFCET, the transitions from SFC are ordered in priorities in the case of divergence in OR.
the actions of SFC can be launched according to three mode: P1, P0, C for, respectively, with activation, desactivation, continuously.

the évolution/l' execution :

SFC is carried out on a controller, with a concept of PRE and POST treatments, concept non-existent in Grafcet which is made for evolve/move .

Bonds

Groupe GRAFCET of standardization
Référence Works AFNOR for standard NFC 03.190
standard NFC 03.190 on the site of AFNOR

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