Grafcet as a language whach as used for the specaficataon of control systems, allthough at as not very well suated for the verzficataon of the specaficataon. Thzs paper descrabes the translataon of grafcet specaficataons anto hybrad automata. Thas translataon as a part of a framework whzch enables not only the veraficataon of a grafcet but of a hybrad system consastang of a dascrete controller and Q contanzrous process. The approach taken as based on the constructaon of a satuataon gmph whach serves as the underlyzng structure an the translataon of a grafcet an ats equavalent hybrad automaton.
GrafcetConsidering software development for real-time processcontrol systems a model of the system must incorporate all subsystems. Grafcet [4] is used for the specification of the controller since it allows the incorporation of logical and sequential aspects. Furthermore it has a graphical representation which makes it fairly easy to use. Nevertheless Grafcet is not very well adapted for the verification of the specification. It is also preferred to analyse a closed system, i.e. both controller and process, since the behavior of each of the sub-systems is related to the other. Therefore we translate a given specification of a controller in a hybrid automaton. In combination with a hybrid automaton modelling the process, a closed model is obtained, which is used for verification.In figure 1 the context of the translation of grafcet into hybrid automata is shown. Advantages of our approach are: i) the framework enables the verification of the controller in relation with the process, ii) a user can specify a controller without being bothered by mathematical details of the underlying model suitable for verification, iii) the specification can be formally analyzed by means of existing tools and iv) the formal defined mapping of Grafcet on hybrid automata formalizes the interpretation of a grafcet.A Grafcet is a tuple G = (V, X , A , T , C , I , E ) , in which V is the set of state variables, X is the set of steps, A is the set of actions, i.e. action a, is associated with step x, and a function over V and X , T is the set of transitions, C is the set of conditions, i.e. condition cj is associated with transition t i and a boolean function over V and X , I , the set of initial steps and E is the set of edges from steps to transitions or vice verse.A step is active or inactive. Action ai, associated with step xi, is carried out when the step is activated. A transition is firable if and only if i) the steps preceeding the transition are active and ii) the condition associated with the transition is true. Firing a transition consists of activating the succeeding steps and simultaneously inactivating the preceeding steps. The firing takes place according to the following rules: i) all firable transitions are immediately fired, ii) simultaneously firable transitions are simultaneously fired and iii) when a step is at the same moment activated and inactivated it remains active.
Hybrid AutomataHybrid automata, proposed by Alur and Henz...