Frank DiCesare

A hybrid methodology for synthesis of Petri net models for manufacturing systems

Beginning with a bounded (safe), live, or reversible Petri net as a first-level net model for a system, Petri nets are synthesized by first refining operation places through basic design modules in top-down modular ways, then adding nonshared resource places stepwise, and finally adding shared resource places step by step in a bottom-up manner. Refinement theory is extended to include reversibility of Petri nets. Parallel and sequential mutual exclusions are used to model shared resources. Design of the first-level Petri nets is discussed, and two basic kinds of Petri nets, choice-free and choice-synchronization, are given to cope with different types of manufacturing systems. The major advantages of the method are that the modeling details can be introduced in incremental ways such that complexity can be handled, and the important properties of the resulting Petri net are guaranteed so that costly mathematical analysis for boundedness, liveness, and reversibility can be avoided. A manufacturing system consisting of four machines, one assembly cell, two shared robots, and two buffers is used to illustrate the design methodology. >

Parallel and sequential mutual exclusions for petri net modeling of manufacturing systems with shared resources

A theoretical basis for Petri net synthesis methods is provided that can be used to model systems with shared resources, and to make the resulting nets bounded, live, and reversible. Two resource-sharing concepts, parallel mutual exclusion (PME) and sequential mutual exclusion (SME), are formulated in the context of the Petri net theory. A PME models a resource shared by distinct independent processes, and an SME is a sequential composition of PMEs, modeling a resource shared by sequentially related processes. The conditions under which a net containing such structures remains bounded, live, and reversible are derived. >

Scheduling flexible manufacturing systems using Petri nets and heuristic search

Petri net modeling combined with heuristic search provides a new scheduling method for flexible manufacturing systems. The method formulates a scheduling problem with a Petri net model. Then, it generates and searches a partial reachability graph to find an optimal or near optimal feasible schedule in terms of the firing sequence of the transitions of the Petri net model. The method can handle features such as routing flexibility, shared resources, lot sizes and concurrency. By following the generated schedule, potential deadlocks in the Petri net model and the system can be avoided. Hence the analytical overhead to guarantee the liveness of the model and the system is eliminated. Some heuristic functions for efficient search are explored and the experimental results are presented. >

Generalized mutual exclusion contraints on nets with uncontrollable transitions

The authors study a class of specifications, called generalized mutual exclusion constraints, for discrete event systems modeled using place/transition nets. These specifications may be easily enforced by a set of places called monitors on a net system where all transitions are controllable. However, when some of the transitions of the net are uncontrollable, this technique is not always applicable. For some classes of nets, the authors prove that generalized mutual exclusion constraints may always be enforced by monitors, even in the presence of uncontrollable transitions.<<ETX>>

Design and implementation of a Petri net based supervisor for a flexible manufacturing system

Abstract This paper presents the design, generation and implementation of coordinating discrete-event control code using Petri nets (PNs) for an operating flexible manufacturing system (FMS). The modeling and control of manufacturing systems using PNs is discussed. PN synthesis methods for manufacturing control are briefly reviewed, including top-down, bottom-up, and a hybrid methodology combining the preceding two. The hybrid methodology and mutual exclusion theory is summarized. This synthesis method guarantees that the desirable properties of liveness, boundedness, and reversibility are present in the resulting net. A description of the FMS and the network of computers controlling the components is given. The automated production system controlled is a one-sixth scale physical model of a shop which performs both machining operations and assembly. The system contains two different machining workstations with robotic loading and unloading, a robotic assembly workstation, a materials movement system, raw material and final product inventory storage, and an automated storage and retrieval system. The hybrid methodology is illustrated to design a PN model for this manufacturing system. Examples of top-down and bottom-up synthesis and choice-synchronization structures are given. A PN description language and a PN execution algorithm that allow supervisory control are discussed. This paper shows that it is possible to synthesize a live, bounded, and reversible PN and to use that net description for the control of a medium sized FMS.

Adaptive design of Petri net controllers for error recovery in automated manufacturing systems

The concept of Petri net controllers is extended to include automatic error recovery and adaptive design. In the Petri net controller considered, a place that represents an operation or a state of a machine is attached to two functions and a constant so that it can represent a system working with both normal states and abnormal states. In addition, it is possible to detect an error with the controller using watchdog timers. Four basic Petri net augmentation methods for error recovery are investigated: input conditioning, alternate path, feedback error recovery, and forward error recovery. The authors demonstrate that when these methods are used to augment the Petri net controller, some important properties of the controller are guaranteed to be preserved. These properties include boundedness or safety, liveness, reversibility and the essentially decision-free property. An example of augmentations for error recovery for a piston insertion cell with two robots is given. >

Synthesis using resource control nets for modeling shared-resource systems

This paper proposes a general approach to synthesize a class of Petri nets that model shared-resource automated manufacturing systems. The approach imposes minimal restrictions on the interactions among subsystems initially so that the modeler is given significant freedom. To modularize the synthesis procedure, a shared-resource system is formulated from the processes. i.e., the subsystems, that control the system resources and the interactions among the processes. For modeling the processes. Resource control nets are defined as the basic generic modules. Then, the system model is built by merging these modules through their common transitions and common transition subnets, which denote the interactions among the processes. The merged net is proven to be conservative and thus bounded. An algorithm is also developed to check two sufficient conditions for structural liveness of the net. This algorithm examines only the nets structure, and appears to be more efficient than state enumeration techniques such as the reachability graph method. >

A review of synthesis techniques for Petri nets with applications to automated manufacturing systems

Research results in both bottom-up and top-down synthesis techniques for Petri net modeling are reviewed. These methods can be adopted for representing parallel and distributed application environments such as automated manufacturing systems. Bottom-up techniques, consisting of the merging of places and sharing of simple elementary paths, have the advantage of ease of system description since the modeled subsystems usually have real-life correspondences. Nevertheless, with current bottom-up techniques, the synthesized system may not exhibit the same control properties as the subsystems. Top-down methods, including refinement of transitions and refinement of places, have the advantage of viewing the system globally, which may generate more structured designs. However, it is difficult to apply these methods to the environments with highly shared resources. Examples in the context of automated manufacturing systems are given to demonstrate application of these techniques. Petri net reduction techniques and their relationship to synthesis methods are discussed. >

Petri net structural analysis for supervisory control

The primary motivation for this research is to show how Petri nets may be efficiently used within the framework of supervisory control. In particular, the paper discusses how integer programming techniques for Petri net models may be used to validate supervisors for the control of discrete event systems. We consider a class of place/transition nets, called elementary composed state machines. The reachability problem for this class can be solved by a modification of classical incidence matrix analysis. In fact it is possible to derive a set of linear inequalities that exactly defines the set of reachable markings. Finally, we show how important properties of discrete event systems, such as the absence of blocking states or controllability, may be analyzed by integer programming techniques. >

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. >