Discrete Event Systems simulation using
Petri nets with Inputs
2017, 2021, José Gaspar
Introduction
Petri nets with
input/output are a
way of designing programs for Programmable Logic Controllers (PLCs). Direct
implementations in PLCs are not considered in this webpage. The focus of this
webpage is the simulation of complete systems based on Petri nets.
This page contains one runner (simulator) of Petri nets, to use in Matlab, and a demonstration. The demonstration is based on the well know philosophers dinner problem represented as a Petri net.
Running a Petri net with I/O requires a simulator of a system to interact with or, in other words, to supervise. In other words, are required I/O functions interfacing the Petri net with a system. See in figure1 the arrows "PN actuation" meaning the outputs required to drive the system, and see "PN inputs" meaning the signals observed in the system and used to drive the Petri net.
Figure1: Petri net supervising the system "HW to be controlled".
The simulation of a Petri net consists of two main steps namely (i) the verification that the pre-conditions are met and (ii) the state evolution after selecting just the possible-to-fire events. See in figure2 an implementation using Matlab.
Figure2: Running a Petri net.
Interacting with the system to be supervised by the Petri net involves defining inputs and outputs. In the simulator, the inputs and the outputs are handled by two functions having predefined names "PN_s2act.m" and "PN_tfire.m". A working example encompassing inputs is made available in the next section and described in a later section.
Download and Usage
Download the zip file lab2_sim_5philosophers_v4.zip and decompress it to a folder of your choice. Then run the main demo:
>> pdinner_tst
Note: In order to use a tool that reads a Petri net from file, download also the Petri Nets Toolbox by Zdenek Hanzalek and Martina Svadova and add it to the path.
Downloaded Example
Explained
The main demo loads a Petri net model shown in figure3 and built using the editor PMEDIT (editor available here but not required for this demo). The firing of the transitions is regulated by signals described in the next paragraphs.
Figure3: Petri net model representing the 5 philosophers dinner problem.
Firing transitions of the Petri net corresponds to having the philosophers issuing requests to eat. In the current simulation these requests are time signals described in a script. The script, more precisely a Matlab function, is run at each time stamp which, according to the time stamp, return an array of flags where is philosopher is indicated his desired to eat or not. See in figure4 part of the script and a graphics representation of the time signals.
Figure4: Requests to eat issued by the philosophers.
The Petri net answers positively when a philosopher can get both the fork and
the knife.
Given the input signals, the running of the Petri net shows which philosophers can be effectively eating at each time (see figure5). In case of a real system, where various subsystems are requiring access to shared resources, the Petri net would be indicating at each moment which subsystems are allowed to use the resources without conflicting with others.
Figure5: Served requests to eat.
Note that modern operating systems must work better than failing early like in this simulation. The most common solution is to change the Petri net to not receive directly requests but, instead, to have a resources manager, which always tries to have the largest possible number of clients served.
Maintenance
This program was created for the purpose of helping classes. There is no continuous maintenance other the requirements associated to the classes.
This program is distributed in the hope that it will be useful, but without any warranty; without even the implied warranty of merchantability or fitness for a particular purpose.
Acknowledgment
In case you find this software useful and do any publication in the sequel please refer to the course Industrial Automation.
Contact
|
Prof. José Gaspar Instituto de Sistemas e Robótica, Instituto Superior Técnico, Torre Norte Av. Rovisco Pais, 1 1049-001 Lisboa, PORTUGAL |
Office: Torre Norte do IST, 7.19 |