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A novel continuous model to approximate time Petri nets: modelling and analysis

100%
Gu T., Dong R.
International Journal of Applied Mathematics and Computer Science
|
2005
|
tom 15
|
nr 1
141-150
EN
In order to approximate discrete-event systems in which there exist considerable states and events, David and Alla define a continuous Petri net (CPN). So far, CPNs have been a useful tool not only for approximating discrete-event systems but also for modelling continuous processes. Due to different ways of calculating instantaneous firing speeds of transitions, various continuous Petri net models, such as the CCPN (constant speed CPN), VCPN (variable speed CPN) and the ACPN (asymptotic CPN), have been proposed, where the continuous flow is specified uniquely by maximal firing speeds. However, in applications such as chemical processes there exist situations where the continuous flow must be above some minimal speed or in the range of minimal and maximal speeds. In this paper, from the point of view of approximating a time Petri net, the CPN is augmented with maximal and minimal firing speeds, and a novel continuous model, i.e., the Interval speed CPN (ICPN) is defined. The enabling and firing semantics of transitions of the ICPN are discussed, and the facilitating of continuous transitions is classified into three levels: 0-level, 1-level and 2-level. Some policies to resolve the conflicts and algorithms to undertake the behavioural analysis for the ICPN are developed. In addition, a chemical process example is presented. sm
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Timed Petri-net based formulation and an algorithm for the optimal scheduling of batch plants

81%
Gu T., Bahri P. A., Cai G.
International Journal of Applied Mathematics and Computer Science
|
2003
|
tom 13
|
nr 4
527-536
EN
The effective scheduling of operations in batch plants has a great potential for high economic returns, in which the formulation and an optimal solution algorithm are the main issues of study. Petri nets have proven to be a promising technique for solving many difficult problems associated with the modelling, formal analysis, design and coordination control of discrete-event systems. One of the major advantages of using a Petri-net model is that the same model can be used for the analysis of behavioural properties and performance evaluation, as well as for the systematic construction of discrete-event simulators and controllers. This paper aims at presenting a Petri-net based approach to the scheduling of operations in batch plants. Firstly, the short term of the 'scheduling of batch plants' is formulated by means of a timed Petri net which can accommodate various intermediate storage policies, such as unlimited intermediate storage (UIS), no intermediate storage (NIS), finite intermediate storage (FIS), and mixed intermediate storage (MIS). Secondly, a heuristic search algorithm for the optimal scheduling of batch plants is given, which is based on generating and checking the markings in the reachability tree of the Petri-net model. Finally, the novel formulation and algorithm are tested with several simulation case studies.
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