Estimation of the firing frequencies in discrete and continuous Petri netsmodels

Production frequencies provide useful information for performance analysis, monitoring and control applications of manufacturing systems. However, suc h frequencies are not always measurable. In this case, they must be estimat ed from the observation of other variables. This paper deals with productio n frequencies estimation for systems modelled by discrete or continuous Pet ri nets. For this purpose, the content of the buffers is measured on-line w ith a sampling period, and the evolution equations of the model are reverse d. In the case of timed Petri nets, the production frequencies estimation i s obtained from the approximation of the firing sequences and in the case o f continuous Petri nets it results directly from the variations of the mark ing vector. The exact and approximated solutions of the estimation problem are described. Accuracy of the estimation is related to measurement error. Petri net structure and sampling period. Moreover, when the estimation prov ides several solutions, the Petri net model is extended such that a unique solution is obtained.