In: Cybernetics and Systems, Vol. 31, No. 6, pages 689-711. 2000.
Abstract: Petri nets are useful tools for the modeling and analysis of manufacturing systems. This work deals with the firing sequences estimation for transition-timed Petri nets by measurement of the places marking. Firing durations are unknown, but not supposed to be null. In fact, the Petri net marking is measured, on-line, with a sampling period dt small enough so that each transition is fired, at the most, one time during dt. The estimation problem has exact and approximated solutions that are described in this paper. Sufficient conditions are given on the accuracy of the marking measurement, such that the estimation if the firing sequences is an exact one. If the estimation provides several solutions, the Petri net is completed in order to give one unique solution, Lastly, the firing sequence estimation is used to evaluate the transition firing occurrences and the firing frequencies. As a consequence of this, the proposed method provides the machine's occupation rate for manufacturing and assembly workshops modeled by timed Petri nets. Thus, systems performances are evaluated and can be improved with the help of these results. The firing sequences estimation is also interesting for fault diagnosis and timed Petri net identification.
Keywords: firing sequences, manufacturing systems, timed Petri nets.