Analysis of Petri net models using transitive matrix

In this paper, we study the scheduling problem with resource constraints using the Petri nets based on the transitive matrix P-invariant. This work focuses on the analysis of a cyclic schedule for the determination of the optimal cycle time and minimization of work-in-process. Especially, this paper deals with product FMS cyclic scheduling problem with each other products using the transitive matrix. The time Petri net slice is applied to analyze this FMS model. We can divide the original system into subsystems using the transitive matrix and permutate these sub-nets for analyzing the optimal scheduling.

Deadlock/livelock problems can cause catastrophic results in flexible manufacturing systems (FMS) by forcing them to stop production processes at an unpredictable stage of production. Therefore, they must be handled properly in order to obtain flawless production in FMS. Petri net (PN) based deadlock/livelock studies for FMS have been widely carried out to obtain live PN models. When a PN model is live, this ensures that the modelled FMS is deadlock-free. Firstly, an uncontrolled (plant) PN model is constructed for the FMS suffering from deadlocks/livelocks. Then reachability graph (RG) analysis of this PN model is carried out to provide all possible reachable states of the modelled system. An RG of a PN model of an FMS suffering from deadlock/livelock problems can be split into the live zone (LZ) and the deadlock zone (DZ). The former is the set of system states considered to be legal (good), while the latter is the set of system states regarded to be illegal (bad). The LZ represents the optimal (maximally permissive) system behavior that must be provided by an optimal control policy. Generally, in PN based liveness studies, a liveness enforcing supervisor (LES) consisting of a set of control places (CP) is computed. Then the controlled (closed-loop) PN model is obtained by merging the plant PN model and the LES. If the number of reachable live states of the controlled PN model is the same as the ones that exist in the LZ, then the controlled model is optimal. Otherwise, it is suboptimal. The greater the number of live reachable states of the RG, the more products to be produced within the FMS. Therefore, the number of reachable live states of the controlled PN model is considered as a quality measure. It defines the behavioral permissiveness of the controlled model. In the literature, to verify the behavioral permissiveness of the PN models, the PN tool called INA (Integrated Net Analyzer) has been widely used. Recently, by means of INA, a method was proposed to compute the number of states within the LZ and the DZ of a given PN model suffering from deadlocks/livelocks. Unfortunately, INA cannot compute RGs of large PNs having a few millions of states. Therefore, in this paper by means of TINA (TIme petri Net Analyzer), an alternative faster and much more efficient method is proposed for the computation of the number of states within the LZ and the DZ for PN models with large RGs. In addition, in order to enable the development of new PN based deadlock prevention methods, further computations are also proposed. These include the computation of the set of states in the DZ, LZ and first met bad markings (FBMs) for a given PN model suffering from deadlocks/livelocks. The applicability and the effectiveness of the proposed methods are demonstrated by considering several well-known examples of FMS from the relevant literature.INDEX TERMS Flexible manufacturing systems (FMS), deadlock, deadlock prevention, Petri Nets (PN), liveness enforcing supervisor (LES), PN computation tools.

The aim of this invited survey is to introduce Computer science/Petri nets specialists to the basic system level issues brought up by the development of Flexible Manufacturing and how Petri nets are used to aid the production engineers in their work. After some terminology concerning production engineering, the hierarchical decision and control level is briefly reviewed. Finally, the role and the presence of nets in CAE (Computer Aided Engineering) and in CAM (Computer Aided Manufacturing) for FMSs (Flexible Manufacturing Systems) are considered. From the design point of view, the use of nets have many advantages in modeling, qualitative analysis, performance evaluation and code generation. From the control of the plant perspective, scheduling on nets models, the coordination of the plant (global and partial) and the presence of nets in the local control level are discussed.Petri nets theory presents a relatively mature body, nevertheless efficient performance evaluation (even for P/T net models) and qualitative analysis of high-level net models still requires important developments. Moreover, the impression that the Petri net newcomer may have looking at the many variants of high-level-nets formalisms may initially produce some kind of rejection. In any case, it is our opinion that Petri nets appears as a key formalism to describe, analyze and implement the control of FMSs. The merging of Petri nets and knowledge based techniques seems to be very promising to deal with large complex discrete event dynamic systems such as FMSs.KeywordsFlexible Manufacture SystemDiscrete Event SystemProgrammable Logic ControllerComputer Integrate ManufactureMarked GraphThese keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Artificial neural networks (ANN's) are highly parallel and distributed computational structures that can learn from experience and perform inferences. Petri nets, on the other hand, provide an effective modeling framework for distributed systems. The basic concepts of Petri net are utilized to develop ANN-like multilayered Petri net architectures of distributed intelligence having learning ability. A Petri net model of single neuron is presented. A two-layer Petri net model-neural Petri net (NPN)-that uses this neuron model as a building block is described. A new class of Petri nets called the fuzzy neural Petri net (FNPN) is defined. The FNPN can be used for representing a fuzzy knowledge base and for fuzzy reasoning. Some application examples for the two Petri net based models are given. >

In this paper a hybrid approach is proposed for supervisory control of discrete event systems (DES) subject to forbidden states. Assuming that an uncontrolled bounded Petri net (PN) model of a (plant) DES and a set of forbidden state specifications are given, the proposed approach computes a maximally permissive and nonblocking closed-loop hybrid model. The first step is to simplify the given PN model by means of PN reduction rules. The simplified model and the specifications are then represented as buffers, and supervisory control theory (SCT) is applied to obtain a Ramadge–Wonham (RW) supervisor in the form of an automaton. After reduction of the latter’s state size by a ‘control congruence’, the simplified RW supervisor is represented by a so-called auto-net and coupled to the given uncontrolled PN plant model by means of inhibitor arcs to represent the disabling actions. The plant model and supervisor auto-net run concurrently, synchronizing on shared events. This procedure provides a maximally permissive and nonblocking ‘hybrid’ (mixed PN/automaton) closed-loop controlled system. The method is straightforward logically, graphically, and technologically. Its applicability is shown by two examples, one of them a workcell from the PN control literature.

Petri net extensions for the development of MIMO net models of automated manufacturing systems

Individuals, populations and fluid approximations: A Petri net based perspective

Nowadays, Petri net models have been used as a very promising modelling tool for systems and it presents randomness, concurrency, and synchronisation. Many researchers give attention to Petri nets because of its wide utilization. Therefore, reusability, sharing, and standardization are three functions that Petri nets must have. To actualized this concept, Semantic Web technologies can be implemented. One of the Semantic Web technologies is Ontology. In this paper, a formal approach for representing a business process in Petri nets into Ontologies is proposed. Firstly, a business process in Petri nets is presented. Then, formal definitions of Petri nets and OWL DL ontologies are introduced. Next step, converting a business process in Petri nets into OWL DL ontologies. Finally, using SPARQL Query in OWL DL ontologies to make sure that the relations of the business process in Petri nets are the same as the relations of the business process in OWL DL ontologies.

Modelling and analysis of kanban-controlled (just-in-time) production systems under realistic assumptions presents a number of challenges, including the ability to conduct both qualitative and quantitative analysis, and the ability to model control policies. These challenges are due, in part, to station interdependence, blocking and starvation due to limited buffer spaces, and the necessity of modelling both material and kanban flows. Petri nets (PNs) have recently emerged as a promising approach for modelling manufacturing systems. PNs are a graphical and mathematical technique useful for modelling concurrent, asynchronous, distributed, parallel, non-deterministic and stochastic systems. PN models can be analysed to determine both their qualitative and quantitative properties. In this paper, we develop stochastic, coloured PN (SCPN) models of a JIT system utilizing two different kanban control policies: a traditional kanban system (TKS) policy and a flexible kanban system (FKS) policy. The resulting models can be used to represent JIT systems of arbitrary size, producing single or multiple types of products, with fixed order points 1. The models are shown to be live and bounded, and can be simulated to produce quantitative results. Sample simulation results are presented to illustrate the models' capabilities.

This paper deals with the modeling and control of discrete event robotic manufacturing cells using Petri nets, and proposes a methodology of model based design and implementation of hierarchical and distributed control. Hierarchical Petri net models are adopted; conceptual Petri net model and detailed Petri net model. The overall detailed Petri net model is decomposed into local Petri net models which are used by the local machine controllers. The upper level station controller coordinates the distributed local controllers so that the aggregate behavior of decomposed subnets is the same as that of the original Petri net. The overall control system is implemented using multithreaded programming based on Petri net based multitask processing. Simulation experiments show that the distributed Petri net model based control system can perform the overall multitask processing control by coincidence of the behavior of the real system with the local Petri net models.

The work undertaken in this thesis is about the integration of two well-known methodologies: Petri net (PN) model Ii ng/analysis of industrial production processes and Artificial Intelligence (AI) optimisation search techniques. The objective of this integration is to demonstrate its potential in solving a difficult and widely studied problem, the scheduling of Flexible Manufacturing Systems (FIVIS). This work builds on existing results that clearly show the convenience of PNs as a modelling tool for FIVIS. It addresses the problem of the integration of PN and Al based search methods. Whilst this is recognised as a potentially important approach to the scheduling of FIVIS there is a lack of any clear evidence that practical systems might be built. This thesis presents a novel scheduling methodology that takes forward the current state of the art in the area by: Firstly presenting a novel modelling procedure based on a new class of PN (cb-NETS) and a language to define the essential features of basic FIVIS, demonstrating that the inclusion of high level FIVIS constraints is straight forward. Secondly, we demonstrate that PN analysis is useful in reducing search complexity and presents two main results: a novel heuristic function based on PN analysis that is more efficient than existing methods and a novel reachability scheme that avoids futile exploration of candidate schedules. Thirdly a novel scheduling algorithm that overcomes the efficiency drawbacks of previous algorithms is presented. This algorithm satisfactorily overcomes the complexity issue while achieving very promising results in terms of optimality. Finally, this thesis presents a novel hybrid scheduler that demonstrates the convenience of the use of PN as a representation paradigm to support hybridisation between traditional OR methods, Al systematic search and stochastic optimisation algorithms. Initial results show that the approach is promising.

Aim To research the application of Petri net's theoretical method in the concurrent asynchronous communications control, find out the detect arithmetic of system's deadlock, and analyze the system's liveness. Methods A detect method of deadlock for information net based Petri net is proposed in this paper. The main method is as follows: After standardize the information systems and extract its mathematical model used the Petri net theory, and then standardize this model. On the basis of model's analysis, find out the loca where system is deadness. Results After the statistical analysis of application result, this method can be effectively applied in the information systems' plan, it will reduce the times of deadlock number above 89%. Conclusion This method can be applied in the system which have the transmission of concurrent asynchronous information, provide the theory basis which have important reference value for finding the fault and repair system. The main problem is the search ergodic process of Petri net's data structure is quite time consuming, so it can be combined with experience and man-machine interactive in application, to improve the efficiency.

This paper presents an approach to perform Activity Based Costing (ABC) with Petri nets. ABC is a powerful methodology to calculate various of discrete event systems (e.g. production systems). Petri net models of discrete event systems are easy to create, comprehend, and to perform analysis, the mathematics behind Petri nets is also easy to grasp. This paper shows how ABC can be performed with Petri nets, so that various involved in a discrete event system can be easily measured with the help of the Petri net model. After a short introduction to ABC and Petri nets, this paper shows the approach which basically embeds various cost drivers as firing costs and firing times of transitions in a Petri net model. This work also presents a case study that is done with GPenSIM, a toolbox realized with this approach.

In this work, a novel hybrid modeling approach for HVAC control system design in Intelligent Buildings is introduced. In order to achieve building system integration, a characterization of HVAC system as hybrid is required. The proposed approach is a top-down modeling method based on Petri net. Starting from abstract models designed using the Production Flow Schema, Petri net based models are built by successive refinements. The discrete part of the system is modeled using Place-Transition Petri nets and the continuous part is modeled using differential equation systems. The interface between these two parts is provided by Differential Predicate Transition Petri nets.

To simulate and debug or diagnose manufacturing systems is always challenging. This paper presents a hybrid PLC-controlled and PC Visual Basic (VB)-based Human-Machine Interface (HMI) platform based on Petri net (PN) theory for Manufacturing Systems. An augmented PN model was adopted to design and simulate the operational sequence of the Flexible Manufacturing System (FMS) at the National Kaohsiung First University of Science and Technology (NKFUST). With the simulated PN model, the control sequences were quickly translated into PLC programs. A PC-based HMI monitoring system based on the PN model was developed to provide an intuitive offline simulation and online diagnostic tools for the FMS. This hybrid system shows many of advantages by using the economical discrete control unit with PLC, and PC-based HMI using PN model as a base. The discrete event control sequence of an FMS can be easily modeled and evaluated before its build-up. More importantly, it can be diagnosed online when the system is malfunctioning. That is, the presented system provides an adequate means for offline system design, simulation, performance evaluation, and quick online system diagnostic.