Differential Petri nets: representing continuous systems in a discrete-event world

Abstract

Differential Petri nets are a new extension of Petri nets. Through the introduction of the differential place, the differential transition, and suitable evolution rules, it is possible to model concurrently discrete-event processes and continuous-time dynamic processes, represented by systems of linear ordinary differential equations. This model can contribute to the performance analysis and design of industrial supervisory control systems and of hybrid control systems in general.Index Terms-Differential Petri nets, discrete-event dynamic systems, hybrid systems, Petri nets, supervisory control systems.

Modelling and Simulation for Production Logistics System in Industrial Enterprises Based on Hybrid Network

“…Meaning P 1 -P 5 Opening gauge for control valve of flux P 6 State of start or stop for loop heat pump PP P 7 State of start or stop for loop heat pump PP State Place Meaning P 8 Charging rate P 9 Temperature of feedstock P 10 Pressure in the tank P 11 Liquid level Switchover between different opening gauge of flux control valve T 9 -T 10 Switchover for loop heat pump PP T 11 Influence of opening gauge of control valve for flux T 12 Influence of state of loop heat pump for feedstock temperature T 13 Controlling the pressure in the tank T 14 -T 16 Influence of charging rate, feedstock temperature and pressure in the tank for liquid level…”

“…On this basis, hybrid Petri net has been proposed firstly by Bail et al [13], which consists of common Petri net and continuous Petri net and can describe integer variables, real variables and symbolic variables in the hybrid system. Hybrid Petri net has been further developed in the following, and different hybrid network programs have been proposed worldwide, such as batch Petri net [14,15], differential Petri net [16], programmable and timed Petri net [17] and first order hybrid net [18], etc. This paper has set up a new hybrid Petri network model on the basis of common hybrid Petri net and combining differential Petri net and controlled Petri net together and unified simulation and analysis under one model framework.…”

Modelling Systems by Hybrid Petri Nets: an Application to Supply Chains

“…HFNs are well suited for the modeling and control of industrial transformation processes, for which the dynamics behavior has a hybrid nature. Differential Petri Nets (DPNs) have been firstly presented in (Demongodin & Koussoulas, 1998). The main feature of this class of PNs is that it allows us to model continuous-time dynamic processes represented by a finite number of linear first-order differential state equations.…”

IdleStop and Go: a way to improve fuel economy

“…The computer scientists developed models, which are usually based on extensions of traditional finite-state machine [27] or Petri net formalisms [28]. System scientists, in contrast, have tended to employ equational models, in which system trajectories are governed by some set of differential equations.…”