Synthesis of Liveness-Enforcing Petri Net Supervisors Based on a Think-Globally-Act-Locally Approach and a Structurally Minimal Method for Flexible Manufacturing Systems

This paper proposes a deadlock prevention policy for flexible manufacturing systems (FMSs) based on a think-globally-act-locally approach and a structurally minimal method. First, by using the think-globally-act-locally approach, a global idle place is temporarily added to a Petri net model with deadlocks. Then, at each iteration, an integer linear programming problem is formulated to design a minimal number of maximally permissive control places. Therefore, a supervisor with a low structural complexity is obtained since the number of control places is greatly compressed. Finally, by adding the designed supervisor, the resulting net model is optimally or near-optimally controlled. Three examples from the literature are used to illustrate the proposed method

Strict Minimal Siphon-Based Colored Petri Net Supervisor Synthesis for Automated Manufacturing Systems With Unreliable Resources

Various deadlock control policies for automated manufacturing systems with reliable and shared resources have been developed, based on Petri nets. In practical applications, a resource may be unreliable. Thus, the deadlock control policies proposed in previous studies are not applicable to such applications. This paper proposes a two-step robust deadlock control strategy for systems with unreliable and shared resources. In the first step, a live (deadlock-free) controlled system that does not consider the failure of resources is derived by using strict minimal siphon control. The second step deals with deadlock control issues caused by the failures of the resources. Considering all resource failures, a common recovery subnet based on colored Petri nets is proposed for all resource failures in the Petri net model. The recovery subnet is added to the derived system at the first step to make the system reliable. The proposed method has been tested using an automated manufacturing system deployed at King Saud University.publishedVersio

Deadlock Prevention Policy with Behavioral Optimality or Suboptimality Achieved by the Redundancy Identification of Constraints and the Rearrangement of Monitors

This work develops an iterative deadlock prevention method for a special class of Petri nets that can well model a variety of flexible manufacturing systems. A deadlock detection technique, called mixed integer programming (MIP), is used to find a strict minimal siphon (SMS) in a plant model without a complete enumeration of siphons. The policy consists of two phases. At the first phase, SMSs are obtained by MIP technique iteratively and monitors are added to the complementary sets of the SMSs. For the possible existence of new siphons generated after the first phase, we add monitors with their output arcs first pointed to source transitions at the second phase to avoid new siphons generating and then rearrange the output arcs step by step on condition that liveness is preserved. In addition, an algorithm is proposed to remove the redundant constraints of the MIP problem in this paper. The policy improves the behavioral permissiveness of the resulting net and greatly enhances the structural simplicity of the supervisor. Theoretical analysis and experimental results verify the effectiveness of the proposed method

Computationally Improved Optimal Control Methodology for Linear Programming Problems of Flexible Manufacturing Systems

Deadlock prevention policies are used to solve the deadlock problems of FMSs. It is well known that the theory of regions is the efficient method for obtaining optimal (i.e., maximally permissive) controllers. All legal and live maximal behaviors of Petri net models can be preserved by using marking/transition-separation instances (MTSIs) or event-state-separation-problem (ESSP) methods. However, they encountered great difficulties in solving all sets of inequalities that is an extremely time consuming problem. Moreover, the number of linear programming problems (LPPs) of legal markings is also exponential with net size when a plant net grows exponentially. This paper proposes a novel methodology to reduce the number of MTSIs/ESSPs and LPPs. In this paper, we used the well-known reduction approach Murata (1989) to simply the construct of system such that the problem of LPPs can then be reduced. Additionally, critical ones of crucial marking/transition-separation instances (COCMTSI) are developed and used in our deadlock prevention policy that allows designers to employ few MTSIs to deal with deadlocks. Experimental results indicate that the computational cost can be reduced. To our knowledge, this deadlock prevention policy is the most efficient policy to obtain maximal permissive behavior of Petri net models than past approaches

Scheduling and discrete event control of flexible manufacturing systems based on Petri nets

A flexible manufacturing system (FMS) is a computerized production system that can simultaneously manufacture multiple types of products using various resources such as robots and multi-purpose machines. The central problems associated with design of flexible manufacturing systems are related to process planning, scheduling, coordination control, and monitoring. Many methods exist for scheduling and control of flexible manufacturing systems, although very few methods have addressed the complexity of whole FMS operations. This thesis presents a Petri net based method for deadlock-free scheduling and discrete event control of flexible manufacturing systems. A significant advantage of Petri net based methods is their powerful modeling capability. Petri nets can explicitly and concisely model the concurrent and asynchronous activities, multi-layer resource sharing, routing flexibility, limited buffers and precedence constraints in FMSs. Petri nets can also provide an explicit way for considering deadlock situations in FMSs, and thus facilitate significantly the design of a deadlock-free scheduling and control system. The contributions of this work are multifold. First, it develops a methodology for discrete event controller synthesis for flexible manufacturing systems in a timed Petri net framework. The resulting Petri nets have the desired qualitative properties of liveness, boundedness (safeness), and reversibility, which imply freedom from deadlock, no capacity overflow, and cyclic behavior, respectively. This precludes the costly mathematical analysis for these properties and reduces on-line computation overhead to avoid deadlocks. The performance and sensitivity of resulting Petri nets, thus corresponding control systems, are evaluated. Second, it introduces a hybrid heuristic search algorithm based on Petri nets for deadlock-free scheduling of flexible manufacturing systems. The issues such as deadlock, routing flexibility, multiple lot size, limited buffer size and material handling (loading/unloading) are explored. Third, it proposes a way to employ fuzzy dispatching rules in a Petri net framework for multi-criterion scheduling. Finally, it shows the effectiveness of the developed methods through several manufacturing system examples compared with benchmark dispatching rules, integer programming and Lagrangian relaxation approaches

Process Completing Sequences for Resource Allocation Systems with Synchronization

This paper considers the problem of establishing live resource allocation in workflows with synchronization stages. Establishing live resource allocation in this class of systems is challenging since deciding whether a given level of resource capacities is sufficient to complete a single process is NP-complete. In this paper, we develop two necessary conditions and one sufficient condition that provide quickly computable tests for the existence of process completing sequences. The necessary conditions are based on the sequence of completions of � subprocesses that merge together at a synchronization. Although the worst case complexity is O(2�), we expect the number of subprocesses combined at any synchronization will be sufficiently small so that total computation time remains manageable. The sufficient condition uses a reduction scheme that computes a sufficient capacity level of each resource type to complete and merge all � subprocesses. The worst case complexity is O(�⋅�), where � is the number of synchronizations. Finally, the paper develops capacity bounds and polynomial methods for generating feasible resource allocation sequences for merging systems with single unit allocation. This method is based on single step look-ahead for deadly marked siphons and is O(2�). Throughout the paper, we use a class of Petri nets called Generalized Augmented Marked Graphs to represent our resource allocation systems

Verification of Nonblockingness in Bounded Petri Nets With Minimax Basis Reachability Graphs

This paper proposes a semi-structural approach to verify the nonblockingness of a Petri net. We construct a structure, called minimax basis reachability graph (minimax-BRG): it provides an abstract description of the reachability set of a net while preserving all information needed to test if the net is blocking. We prove that a bounded deadlock-free Petri net is nonblocking if and only if its minimax-BRG is unobstructed, which can be verified by solving a set of integer constraints and then examining the minimax-BRG. For Petri nets that are not deadlock-free, one needs to determine the set of deadlock markings. This can be done with an approach based on the computation of maximal implicit firing sequences enabled by the markings in the minimax-BRG. The approach we developed does not require the construction of the reachability graph and has wide applicability.Comment: This work has been submitted to the IEEE for possible publication. Copyright may be transferred without notice, after which this version may no longer be accessibl