Modular transformation methods for generalized Petri nets and their application to automated manufacturing systems

The authors present transformation methods for generalized Petri nets by introducing and using the concept of a live and bounded circuit (LB-circuit), based on fusing common paths. An LB-circuit is a generalized version of a simple elementary circuit. The authors briefly review generalized Petri nets, including their formal definitions and properties, and define an arc ratio, a remainder, and an LB-circuit. A partially overlapping relation is introduced. Using these concepts, four lemmas and three theorems which are the theoretical background for the transformation methods are presented. Reduction methods are described with examples. Synthesis methods are illustrated for a simple automated manufacturing system, a machining/assembly process with three robots and two workstations. >

[1]  Carolyn L. Beck,et al.  Synthesis of Place Transition Nets for Simulation and Control of Manufacturing Systems , 1987 .

[2]  James Lyle Peterson,et al.  Petri net theory and the modeling of systems , 1981 .

[3]  Joël Favrel,et al.  Hierarchical reduction method for analysis and decomposition of Petri nets , 1985, IEEE Transactions on Systems, Man, and Cybernetics.

[4]  Frank DiCesare,et al.  Real time control of multilevel manufacturing systems using colored Petri nets , 1988, Proceedings. 1988 IEEE International Conference on Robotics and Automation.

[5]  B. Krogh,et al.  Models for simulation and discrete control of manufacturing systems , 1986, Proceedings. 1986 IEEE International Conference on Robotics and Automation.

[6]  Ichiro Suzuki,et al.  Stepwise Refinements of Transitions and Places , 1980, Selected Papers from the First and the Second European Workshop on Application and Theory of Petri Nets.

[7]  T Murata,et al.  Reduction and expansion of live and safe marked graphs. , 1979 .

[8]  Robert Valette,et al.  Analysis of Petri Nets by Stepwise Refinements , 1979, J. Comput. Syst. Sci..

[9]  Kurt Lautenbach,et al.  The Orderly Resolution of Memory Access Conflicts Among Competing Channel Processes , 1982, IEEE Transactions on Computers.

[10]  Yadati Narahari,et al.  A Petri net approach to the modelling and analysis of flexible manufacturing systems , 1985 .

[11]  Joël Favrel,et al.  Generalized Petri Net Reduction Method , 1987, IEEE Transactions on Systems, Man, and Cybernetics.

[12]  Gérard Berthelot.  Transformations and Decompositions of Nets , 1986 .

[13]  C. Petri.  Kommunikation mit Automaten , 1962 .

[14]  N. K. Nanda,et al.  Some design aspects of databases through Petri net modeling , 1986, IEEE Transactions on Software Engineering.

[15]  MengChu Zhou,et al.  Parallel and sequential mutual exclusions for petri net modeling of manufacturing systems with shared resources , 1991, IEEE Trans. Robotics Autom..

[16]  Gérard Berthelot,et al.  Checking properties of nets using transformation , 1985, Applications and Theory in Petri Nets.

[17]  Ichiro Suzuki,et al.  A Method for Stepwise Refinement and Abstraction of Petri Nets , 1983, J. Comput. Syst. Sci..

[18]  Amir Pnueli,et al.  Marked Directed Graphs , 1971, J. Comput. Syst. Sci..

[19]  Ajoy Kumar Datta,et al.  Modular Synthesis of Deadlock-Free Control Structures , 1986, FSTTCS.

[20]  Norihisa Komoda,et al.  Liveness analysis of sequence control specifications described in capacity designated Petri net using reduction , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[21]  Michael Yoeli,et al.  Specification and verification of asynchronous circuits using marked graphs , 1987 .

[22]  P. Ladet,et al.  Modelling and validation of complex systems by coloured Petri nets; Application to a flexible manufacturing system , 1985, European Workshop on Applications and Theory in Petri Nets.

[23]  I. Koh,et al.  Transformation methods for generalized Petri nets and their applications to flexible manufacturing systems , 1990, [1990] Proceedings. Rensselaer's Second International Conference on Computer Integrated Manufacturing.

[24]  Bruce H. Krogh,et al.  Essentially decision free Petri nets for real-time resource allocation , 1987, Proceedings. 1987 IEEE International Conference on Robotics and Automation.

[25]  Tadao Murata,et al.  Petri nets: Properties, analysis and applications , 1989, Proc. IEEE.

[26]  Y. Narahari,et al.  On the invariants of coloured Petri nets , 1985, Applications and Theory in Petri Nets.

[27]  Tilak Agerwala,et al.  A Synthesis Rule for Concurrent Systems , 1978, 15th Design Automation Conference.