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GRAFCET: A Powerful Tool

for Specification of Logic Controllers

OS3URV 2012

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History

1975 Decision of the workgroup "Logical Systems" daAFCET (Association Franaise de Cyberntique Economiqueet Technique) on the creation of a committee to study astandard for the representation of logical systems andautomation

1977 GRAFCET definition (Graphe Fonctionnel deCommande Etape-Transition).

1979 Dissemination in schools and adopted as researcharea for the implementation of solutions of automation inthe industry.

1988 - GRAFCET becomes an international standarddenominated as "Sequential Function Chart, IEC 60848, IEC1131-3

GRAFCET is referred to as Sequential Function Charts (SFC).

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Industry needs:

Describe the sequence of states of a discrete-event system

which may contain a very large number of states

Take into account the concurrency (for both simplicity and

easy understanding), since some subsystems may be partially

independent.

Generally, given a state of the system, only a few inputs affect

the state, and only a few outputs may change. Then, describe

only the behavior corresponding to these input changes.

Have a clear understanding of the input-output behavior of a

logic controller, i.e., what is the control applied to the process

to be controlled (output of the PLC) as a function of a change

of the process or its environnment (input of the PLC).

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Motivation tank filling

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Motivation tank filling

A roman symbol represents a device (sensor or actuator)and an italic symbol the corresponding Boolean variable.

Tank 1 is empty when the level is less than b1, i.e., b1 = 0,and is full when the level is greater than h1, i.e., h1 = 1.

At the initial state, both tanks are empty.

If push button m is pressed, both tanks are filled byopening valves V1 (V1=1 means that valve V1 is open) andV2.

When a tank is full, e.g., tank 1, filling stops (by closing

valve VI) and its contents start to be used (by opening valveW1). When tank 1 is empty, valve W1 is closed. Filling mayonly start up again when both tanks are empty and if thebutton m is pressed.

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Example

Grafcet - The squares labeled 1 to 6 aresteps, i.e., components of states.

At initial time, the steps in the set {1, 4}are active. Then transition (1) whichfollows these steps can be fired as soon

as the Boolean variable m, associatedwith (1), has the value 1.

After this firing, steps 2 and 5 are active.When step 2 is active, the output V1 = 1(represented by V1 written in a rectangleassociated with step 2). When step 2 is

active, transition (2) can be fired ifh1 = 1.And so on

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GRAFCET graphical syntax

Grafcet has a graphicalsyntax

Steps - drawn as squares,

Transitions - represented asbars

The initial step isrepresented as a double

square Grafcet has support for

alternative and parallelbranches

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Steps

A step is represented by a square

A step may have two states:

active (this is represented by a token in thestep) as is the case of step 2

inactive as is the case of step 1

The steps which should be active when thesystem is started and represented by adouble square -initial steps (step 3).

Actions are associated with the steps, andthese are the outputs of the grafcet.

To each step one or several actions can beassociated. The actions are performedwhen the step is active.

1

2

3

Inactive

Active

Initial

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Transitions

The transition symbol is a bar, but thelatter must be preceded or/and followedby a double bar in some cases.

It is preceded by a double bar when two ormore arcs join this transition [transitions(2) and (4)]; this implies that it involves

waiting for multiple input steps to beactive before firing the transition.

A transition is followed by a double barwhen two or more arcs leave thistransition [transitions (3) and (4)]; thisimplies that it involves activating multiple

output steps when the transition is fired. A receptivity will be associated with

each transition ().

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Firing of Transitions

A transition is firable if both the following conditionsare met: All the steps preceding the transition are active (the

transition is said to be enabled)

The receptivity of the transition is true.

These operations (activation and

deactivation) are carried out

simultaneously.

Firing of (1) leads from the situation{ 1 } to the situation {2,3}.

Then firing of (2) leads to the

situation {2, 4}, and firing of (3) leads

back to the initial situation

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When a receptivity is true?

Lets consider three cases: the receptivity is a:

condition (i.e., a Boolean function),

an event,

or both a condition and an event.

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Actions and Outputs

There are two major categories of actions,

Level action is modeled by a binary variable

and has a finite duration. Action remains

set all the time while the step, to which the

action is associated, is active.Unconditional

Conditional

Impulse actions is responsible for changing

the value of a variable. An impulse action iscarried out as soon as the step changes

from being inactive to active.

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Actions and Outputs

Action B* is an impulse action.

The asteriskwas recommended at the origin of Grafcet toindicate the impulse character of an action.

It does not always, however, serve a purpose. For example,incrementing a counter C can be written as (C

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Stable/unstable situations

A situation can be stable or

unstable.

If the transition following a step is immediately fireable

when the step becomes active, the situation is said tobe unstable.

An impulse action is carried out even if the situation isunstable

A level action is performed only if the situation isstable.

Between two different external events it is assumedthat there is always enough time to reach a stablesituation.

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Unconditional/Conditional

Unconditional Conditional

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Concurrency and Synchronization

From the situation {1}, the situation{2, 3} is reached by firing transition(1) as soon as a

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Dynamic behavior

The dynamic behavior of Grafcet is defined by five rules

1. The initial situation of a Grafcet is determined by its initialsteps.

2. A transition is enabled if all of its previous steps are active.

A enabled transition is fireable if its associated receptivityis true. A fireable transition is immediately fired.

3. Firing of a transition results in deactivation of its previousstep and a simultaneous activation of its following steps.

4. Simultaneously fireable transitions are simultaneously

fired.5. If a step is to be simultaneously activated and deactivated

it remains active.

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Example tank filling

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Tank Filling Modified The controlled system is the same. The control

specifications are modified: The filling process is no longer allowed if the button m is

pressed (i.e., ifm = 1) but it is triggered by pressing push buttonm (i.e., bym).

A counter is added: the value C in the counter represents thenumber of cycles (emptying and filling of Tank 2).

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Example

A system consisting of a tank is shown. The tank has an inlet valve V1 and

an outlet valve V2. There are two level sensors L0 and L1, one temperature

sensor Tand one heater Q.

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Example

When the system is started, valve V1 should open and thefilling should start.

When the level in the tank reaches L0, the heating shouldstart. The tank is now heated and filled in parallel.

When the level in the tank reaches L1 the filling is stoppedand when the temperature reaches Tthe heating isstopped.

When both the right level and the right temperature arereached, the tank is emptied. This is done by opening the

outlet valve V2. When the system is empty, the sequence can be restarted.

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Formal Definition A Grafcet can be defined as a 5-tuple = {, , , , } where:

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Example

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Example: modeling a

control/automation system

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