Analysis of controlled technological systems using high level petri nets

Abstract

Based on the formal correspondence between constraint type qualitative differential equations (QDEs) with order of magnitude quantity space and colored Petri nets (CPNs) a formal relation is identified between 1.(i) the reachability tree of the stochastic CPNs and the behaviour tree of the related constraint type QDEs generated by the EQSIM method (Hangos et al., 1992);2.(ii) the reachability tree of deterministic CPNs and solution of constraint type QDEs generated by interval arithmetic methods.The behavioural properties of controlled technological systems, their reachability, boundedness and liveness, are investigated. It is shown that the technological subnet is live and bounded. The analysis of these properties in general case is based on the reachability tree of the CPN (Jensen and Rozenberg, 1991) which is of high computational time complexity. In contrary the structural properties of the overall CPN is analysed by the invariant method, which has polynomial time complexity. It is shown that places and transitions in the technological subnet are place and transition invariants of the overall net if the technological system has a steady state.