A new pattern based Petri net to model sintering production process

Abstract

In this paper, a new Petri net model based on pattern recognition method is presented for describing a certain stochastic hybrid systems. The application of this method concerns sintering production process. The main idea consists in describing the variation of patterns over time through the so-called ‘pattern class variable’ rather than state variable or output variable. A new petri net control model is constructed based on pattern class variable. The marks are defined as posterior probability of the cluster. By redefining the marks and transition on the basis of ordinary Petri nets, it can represent any combination of discrete-event and continuous element and has probability property. The simulation results are provided based on real plant data to illustrate the effectiveness of the proposed approach. This method might provide the satisfied results for the practical applications without having the exact mathematical models.

Stability and stabilization for a class of complex production processes via LMIs

“…In this paper, the pattern class variable is measured by an output‐class center. However, if it is measured by others, eg, the interval number and the output‐class posterior probability, other stabilization methods will be required. This is our future work.…”

“…Step 1 : At the sampling time k , the trajectory point dx ( k ) in the pattern‐moving “space” is measured by a point in a computable space, eg, a class center, an interval number, or the output‐class posterior probability, ie, where is a point of the computable space, D is a measurement mapping. In this paper, is an output‐class center in the Euclidean space.…”

“…Because of the incomputibility of patterns, eg, pattern 1 ± pattern 2 = pattern 3, the pattern class variable defined in the pattern‐moving “space” was mapped to computable space. Initial control (or predict) models were built by using the pattern class variable in the computable space, and the pattern class variable was measured by class center, the interval number, and the output‐class posterior probability . At last, the output of the model was mapped to the pattern‐moving “space” by a classification mapping, and a new trajectory point was obtained.…”

“…Thus, dynamic properties of the system were depicted in the pattern‐moving “space,” and control methods of the system were given. In recent years, many research results have been published on the proposed method of modeling and control …”

“…1,2 For the processes, a method of pattern-moving-based modeling and control was put forward. 3 Subsequently, many papers on the method [4][5][6][7][8][9][10][11][12][13][14] have appeared. However, the stability of a pattern-moving-based control system is rarely defined and analyzed.…”