In this second part of the tutorial series, we continue the investigation of Petri net theory as it applies to laboratory automation systems. The focus of this tutorial is the application of theoretical results to the analysis of laboratory automation system models. The mathematical description of a Petri net is introduced. Several analytical methods are reviewed and applied to examples of laboratory automation systems. Analytical results include the identification of deadlock situations, computation of cycle times, optimization of design, and the automatic calculation of system-control schemes.
RussoM. F.SassoA.Modeling, analysis, simulation and control of laboratory automation systems using Petri nets: Part 1. modeling. J. Assoc. Lab. Autom.2005, 10(3), 172–181.
2.
PetriC. A.Kommunikation mit Automaten; Schriften des IIM Nr 2; Institut für Instrumentelle Mathematik; Bonn, Germany, 1962; Technical Report RADC-TR-65–77 (Engl. Trans.), Vol. 1, Suppl. 1, New York, 1966.
3.
MurataT.Petri nets: Properties, analysis and applications. Proceedings of the IEEE1989, 77(4), 541–580.
4.
ZhouM.Di CesareF.Petri Net Synthesis for Discrete Event Control of Manufacturing Systems.Boston: Kluwer Academic Publishers; 1993.
5.
Di CesareF.HarhalakisG.ProthJ. M.SilvaM.VernadatF. B.Practice of Petri Nets in Manufacturing.New York: Chapman and Hall; 1993.
6.
VanijjirattikhanR.KaberD.ChowM.StollN.Timed Petri net modeling and simulation of a high-throughput biological screening process. Proceedings of the 3rd Annual IEEE Conference on Automation Science and Engineering, Scottsdale, AZ, USA, Sept 22–25, 2007, IEEE New York, NY, pp. 442–447.
Platform Independent Petri net Editor 2. Department of Computing, Imperial College London, http://pipe2.sourceforge.net/ (accessed Nov 2007).
9.
UzamM.Synthesis of feedback control elements for discrete event systems using Petri net models and theory of regions. Int. J. Adv. Manuf. Technol.2004, 24, 48–69.
10.
GiuaA.Petri net techniques for supervisory control of discrete event systems. In Proc. First Int. Work on Manufacturing and Petri Nets, Osaka, Japan, June 1996, pp. 1–30.
11.
MartinezJ.SilvaM.A simple and fast algorithm to obtain all invariants of a generalised Petri net In Application and Theory of Petri Nets, Informatik Fachberichte, 52; GiraultC.ReisigW., Eds.; Springer: 1982; pp 301–310.
12.
IordacheM. V.AntsaklisP. J.Software tools for the supervisory control of Petri Nets based on place invariants. Technical Report ISIS-2002–003, Department of Electrical Engineering, University of Notre Dame, April, 2002.
13.
Petri Net Toolbox for MATLAB. Department of Automatic Control and Industrial Informatics of the Technical University “Gh. Asachi” of Iasi, Romania http://www.ac.tuiasi.ro/pntool/ (accessed Nov 2007).
14.
FloudasC. A.Nonlinear and Mixed-Integer Optimization: Fundamentals and Applications.Oxford University Press: New York, NY; 1995.
YamalidouK.MoodyJ.LemmonM.AntsaklisP.Feedback Control of Petri Nets Based on Place Invariants. Technical Report ISIS-94–002, Dept. of Electrical Engineering, University of Notre Dame, February, 1994.
17.
TarjanR. E.Enumeration of the elementary circuits of a directed graph. SIAM J. Comput.1973, 2, 211–216.
