A Study on Flexible Manufacturing Systems using Petri Net Reduction

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.

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.

In this paper, we use Petri nets to analyse flexible manufacturing systems (FMS) to achieve the following objectives. The first objective is to derive a theorem for checking the buffer overflows in an FMS. The second objective is to schedule the earliest starting times for a sequence of operations in an FMS by the timed Petri net. The FMS may involve many part types, machines, pallets and so on. The third objective is to detect the deadlock phenomenon by a corrected algorithm of the P-invariant theory for Petri nets. This method will enable us to know whether there exists any deadlock in an FMS. The algorithm is implemented in the Turbo Pascal language. The fourth objective is to search for the optimal scheduling rule in an FMS. The search procedure is also implemented in the Turbo Pascal language¨ The optimal machine scheduling rule can result in a better throughput.

Solving the deadlocks avoidance problem in Resource Allocation Systems (RAS) in Discrete-Event Systems (DES) is a rife problem, especially in Flexible Manufacturing Systems (FMS), alias Automated Manufacturing Systems (AMS). Petri Nets (PN) are an effectual tool often used at this procedure. In principle, there are two basic approaches how to deal with deadlocks in RAS based on PN. They are listed and illustrated here. First of the approaches is realized by means of the supervisor based on P-invariants of PN, while the second one is realized by means of the supervisor based on PN siphons. While the first approach needs to know the reachability graph/tree (RG/RT) expressing the causality of the development of the PN model of RAS, in order to find (after its thorough analysis) the deadlocks, the second approach needs the thorough analysis of the PN model structure by means of finding siphons and traps. Next, both approaches will be applied on the same PN model of RAS and the effectiveness of the achievement of their results will be compared and evaluated. Several simple illustrative examples will be introduced. For the in-depth analysis of the problem of deadlock avoiding, next Part 2 of this paper is prepared, where the newest research will be introduced and illustrated on more complicated examples. If necessary (because of the limited length of particular papers), also the third part – Part 3, will be prepared.

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.

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.

This paper is concerned with fault detection and location of discrete event systems (DES) modeled using interpreted Petri nets (IPN). The approach held deals with IPN models in which the marking is partially known. A diagnosis scheme that tracks the DES inputs and outputs is proposed; it allows detecting and locating an unexpected behavior within the DES. The diagnoser handles a monitoring model, expressed also as an IPN, which is computed from the DES model through an induced conservative marking law.

The use of shared resources is a major problem occurring in discrete event (DE) systems, including manufacturing systems, computer systems, communication systems, highway/vehicle systems, and others. The issues involve problems of assignment of resources when the same resources are simultaneously requested by more than one job. Failure to suitably assign, or dispatch, resources in such situations can have serious deleterious effects on system performance, resulting in extreme cases in system deadlock [7]. Computer operating systems engineers and industrial engineers have used the concepts of circular wait (CW) and circular blocking in analysis of such phenomena [41, 24]. Various concepts in Petri nets (PN) are extremely useful for dealing with deadlock and a great deal of research has been done from the PN point of view (see references, especially [11, 14, 19]). The PN approaches are often based on the notion of the siphon, which indeed is called a “deadlock” in some works [26]. Unfortunately, it is known that many problems in scheduling, dispatching, and deadlock analysis are NP-hard [12], so that significant increases in computing power do not significantly improve computational ability. Neither PN nor CW approaches have addressed this issue.

The behavior mapping of systems has undergone rapid change with advances in technology. The representation has become digital with state description of the behavior. This manifestation is called Discrete Event Systems (DES), exhibiting properties such as non – determinism, conflict and parallelism[1]-[3]. Supervisory Control Theory (SCT)[8],[9] is chosen as a modeling paradigm and Programmable Logic Controllers (PLC) [10] – [12] as an implementation tool for DES. This work investigates the use of Fuzzy Petri nets in supervisory control and suggests a modified and improved version called Fuzzy Automation Petri net (FAPN) as a modeling tool. It presents a systematic approach to the synthesis of Fuzzy Petri net based supervisor for the forbidden state problem using supervisory design procedure. The controlled model of the system can be constructed from this FAPN net structure. The implementation is using Flexible Manufacturing System (FMS) as an example of DES. The results can be interpreted and applied to high level manufacturing systems, where the role of the supervisor is to coordinate the control of multiple machines or to low level manufacturing systems, where the control function is to switch ON/OFF with respect to the dynamics between different valves.

This paper describes the ways of using program tools for design and simulation of flexible manufacturing systems (FMS) for the purpose of teaching the undergraduate course Flexible Manufacturing Systems. The concept of the course is based on the synergism of theoretical knowledge and practical hands-on experience gained by studying numerous problem cases, using common tools for description of FMS (Petri nets, max-plus algebra and matrix modeling) and by working with more specialized program tools for FMS design and simulation. An emphasis is given to the description o the program tool FlexMan that enables elegant setting of an FMS configuration, supports automatic generation of a matrix-based FMS description and consequently, enables effective off-site design and simulation of the FMS by using virtual reality models and Internet-related technologies.

A GSPN-Based automatic analysis tool for discrete event systems

Many technological, industrial or economical systems are described by discrete event system (DES) models. The decision making processes that arise in the design and operation of this kind of systems can be afforded by means of algorithmic methodologies. A large range of approaches based on the simulation of the behavior of the system have been reported to answer this problem. Their main advantage consists of being applicable to most of the systems. An important drawback is the significant computational resources required to perform an exhaustive exploration of the state space due to the combinatorial explosion. A manual choice of a reduced set of configurations to be simulated can be improved by the use of parametric Petri nets and a metaheuristic search of the most promising ones. In this paper, a review of some definitions of parametric Petri net found in the literature is presented, as well as a definition for the general framework of stating optimization problems of both, the operation and the design of the model of the DES. Moreover, a methodology to obtain such a parametric Petri net, called compound Petri net, from an easier-to-obtain set of alternative Petri nets is proposed and an application example is given.

This paper presents a heuristic search approach for scheduling flexible manufacturing systems (FMS) with due dates based on the Petri net state equation. It is known that the state equation of a Petri net has a solution if the goal marking can be reached from the initial marking. In terms of scheduling, this denotes that the costs of jobs can be obtained from the solution. In this paper, the idea of jobwise Petri nets is introduced. A jobwise net is a part of the model of an FMS. It is only associated with one job and the resources that the job uses. A model of N jobs can be split into N jobwise net models. We combine jobwise Petri nets and the state equations to implement the search algorithm. The objective is to minimize weighted tardiness (lateness), which is the difference of the completion time of a job and its due date. In order to show that this scheduling method can get near-optimal solutions, we compare it with some commonly used dispatching rules by simulations.

Modelling Flexible Manufacturing Systems Based on Petri Nets

Secret inference and attacktability analysis of discrete event systems