Petri Net Paradigm Research Articles

Maximally Permissive Robustness Analysis of Automated Manufacturing Systems With Multiple Unreliable Resources

For real-world automated manufacturing systems (AMSs), the failures of multiple unreliable resources are very common. Maximal permissiveness is a key aspect for evaluating the performance of robust control strategies of failure-prone AMSs. However, there exist fewer works in the existing literature that can achieve maximally permissive robustness analysis. This may impede the applicability of existing robust control strategies in realistic AMSs. This article tackles the issue in the paradigm of Petri nets (PNs). We present an innovative mechanism to formalize unreliable resource failures by preventing all ingoing transitions of unreliable resource places from firing. Both reachability graph-based and integer linear programming-based methods are proposed to analyze the robustness of AMSs with either single or multiple unreliable resources. Several examples are proposed to illustrate the approach.

Robustness Analysis of Automated Manufacturing Systems With Uncontrollable Events Using Petri Nets

In this paper, we address the robustness analysis problem of automated manufacturing systems with uncontrollable events in the paradigm of Petri nets (PNs). First, we formalize unreliable resource failures as the removal of all ingoing transitions of unreliable resource places (denoted by unreliable transitions hereafter). Second, we obtain a necessary and sufficient condition to check the robustness of markings, so called robustness controllability theorem (abbreviated as RCT hereafter) in the paradigm of reduced reachability graph (abbreviated as R2G hereafter). All markings involved in the R2G of a PN are equivalent to that of its reachability graph, except that all arcs associated to unreliable transitions are removed from R2G. Based on RCT, the robustness of all markings in an R2G can be determined. An example is proposed to illustrate the approach. Note to Practitioners—In reality, it is an urgent issue to analyze the behaviors of automated manufacturing systems (AMSs) so as to guarantee their stable operation against resource failures, e.g., the missing of a signal or the failure of a sensor. In this connection, different methods are proposed to deal with the robustness analysis and control problem of AMSs with unreliable resources. The objective is to avoid any deadlock in the AMSs or to ensure the liveness of the subsystems that require only reliable resources when there exist resource failures. Due to limited actuating and sensing abilities, AMSs may be partially controlled, i.e., there exist events whose firing may not be inhibited by an external action. However, fewer research works consider this practical situation when handling robustness analysis and control issue, which renders the existing approaches impracticable. In this paper, we solve the robustness analysis problem of AMSs with uncontrollable events by using Petri nets. A necessary and sufficient condition is proposed to check the robustness of markings, called robustness controllability theorem (abbreviated as RCT hereafter) in the paradigm of reduced reachability graph. With the aid of RCT, the robustness of all markings can be determined so as to guarantee the flexibility of AMSs.

Robustness Analysis of Automated Manufacturing Systems With Unreliable Resources Using Petri Nets

This paper studies the maximally permissive robustness analysis of automated manufacturing systems (AMSs) with unreliable resources in the paradigm of Petri nets (PNs). Two types of robust markings, i.e., strongly robust markings and weakly robust markings, are defined in this paper. We propose robustness equivalence and non-robustness equivalence to characterize the markings that exhibit the same robustness and non-robustness, respectively. Reachability graph (or RG hereafter) is directly used to determine the robustness of markings; however, it is difficult to use in large-scale systems due to formidable computational difficulty. As an alternative, we present a reduced reachability graph (or R2G hereafter) based necessary and sufficient condition to check the robustness of markings, in terms of the liveness analysis of markings in R2G. We show that all safe markings of an R2G correspond to strongly robust markings of the corresponding RG, and deadlock markings as well as their bad markings and livelock markings as well as their bad markings of an R2G correspond to non-robust markings and weakly robust markings of the corresponding RG, respectively. Hence, the robustness of markings in an RG can be determined effectively and efficiently through the liveness analysis of markings in the corresponding R2G. Note to Practitioners—In practical manufacturing scenarios, it is urgent to analyze and control the automated manufacturing systems (AMSs) so as to ensure their continual production against any resource failure. If the failures of an AMS are not handled gracefully, the whole system may fall into a blocking. As a consequence, system production does not meet rapid manufacturing goals and objectives. In this paper, we focus on the maximally permissive robustness analysis of AMSs with unreliable resources in the paradigm of Petri nets. We define two types of robustness in terms of markings, i.e., strong robustness and weak robustness. From the viewpoint of reachability graph, we propose robustness equivalence and non-robustness equivalence among markings and present the procedures to check the robustness of markings. Furthermore, a set of necessary and sufficient conditions are established to provably ensure that the robustness of markings can be determined through liveness analysis in a reduced reachability graph. Therefore, the robustness of markings can be determined in a computationally efficient way.

Maximally Permissive Deadlock and Livelock Avoidance for Automated Manufacturing Systems via Critical Distance

The problem under consideration in this paper is how to avoid deadlocks and livelocks in the paradigm of Petri nets (PNs). Although deadlock and livelock avoidance has been extensively studied in existing literature, fewer results can be applied to practical automated manufacturing systems (AMSs) due to expensive computations and reduced permissiveness. In this paper, we propose an efficient and maximally permissive control scheme to avoid deadlocks and livelocks by using critical distance. From the perspective of the reachability graph of a PN, critical distance is equal to the maximum number of transitions among all transition sequences from any critical state to its corresponding deadlock or livelock state. First, we show how to calculate the critical distance of a PN in an efficient way by using a portion of reachable states. Then, local reachability graphs are established based on critical distance to avoid deadlocks and livelocks. The provided policy is maximally permissive since only the necessary minimum number of illegal transitions are forbidden at each state. Several representative examples are presented to illustrate our approach. Note to Practitioners—Deadlock and livelock avoidance is a crucial problem in automated manufacturing systems (AMSs). Various methods have been proposed to deal with deadlocks and livelocks by researchers and practitioners. However, there exist fewer works that focus on deep exploration regarding how long a deadlock or livelock will occur from a safe state. As a consequence, the existing works suffer from the disadvantages of being too aggressive or conservative, i.e., checking the whole state space or forbidding many acceptable states when avoiding deadlocks and livelocks. Through the analysis of a partial of reachable states, this paper derives the critical distance of Petri nets modeling AMSs, which is equal to the maximum number of transitions among all transition sequences from any critical marking to its corresponding deadlock or livelock marking. All deadlocks and livelocks, if exist, can be detected at any given marking within the critical distance. Our approach not only is maximally permissive but also explores only a partial of states, thereby mitigating state explosion problem.

From strong to exact Petri net computers

Petri net paradigm of computing is concerned discussing basic types of Petri net computers and their relations. We developed a technique of parametric specification of Petri nets, built of a few connected components which are repeated depending on a parameter or a set of parameters, and composition of software to generate automatically the corresponding models in a vivid graphical form. We construct explicitly a Petri net that is a strong computer of double exponent after R.J. Lipton. Its nondeterministic computation is represented by a Petri net reachability graph to which a successful branch belongs. Then we minimise and transform the net to obtain twice smaller construct than the original one. Moreover, the obtained net possesses such a marvellous property that addingto it four priority arcs makes it an exact (deterministic) computer having a single firable sequence only. Same as the Lipton’s net, the minimized net allows the proof that the Petri net reachability problem is exponential in space. Besides, it represents an example when simple transformations allow guessing the successful branch of a nondeterministic computation. The practical significance of the approach in applications consists in a state-of-art heuristic technique of solving some NP problems in polynomial time.

Fault-Recovery and Robust Deadlock Control of Reconfigurable Multi-Unit Resource Allocation Systems Using Siphons

A multi-unit resource allocation system usually contains several processes and a number of resources with multiple units. Due to the competition for shared resources in these systems, deadlocks may occur. Recently, researchers have shown an increased awareness in deadlock control strategies for such a kind of systems without considering the dynamic changes such as processing failures and rework by using the Petri net paradigm. This article reports a new strategy for deadlock analysis and control in reconfigurable multi-unit resource systems (MRSs). We discuss a generalized class of Petri nets in which each stage of a process may require a number of units of different types of resources to perform a task. In this way, we can model more complex real systems. Thanks to a generalized class of Petri nets, i.e., the system of sequential systems with shared resources (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> R), this article proposes an effective integrated strategy for designing robust supervisors for reconfigurable MRSs, and improves an S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> R model to achieve a new model, namely a system of sequential systems with shared resources and part-re-entry (S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> RP), which represents the procedure that a flawed product re-enters a system and is re-processed. We use a siphon-based max-controllability deadlock prevention policy (DPP) to supervise the evolution of the S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> RP, and present a comprehensive analysis to demonstrate that the controlled S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> RP is free of deadlocks. A net analysis tool (INA) is used to test and validate the resulting S <sup xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">4</sup> RP.

Optimal enforcement of liveness for decentralized systems of flexible manufacturing systems using Petri nets

The decentralized supervisory structure has drawn much attention in recent years. Many studies are reported in the paradigm of automata while few can be found in the Petri net model. This paper proposes a new method for decentralized supervisory control using the Petri net paradigm. Two efficient Algorithms are developed in the proposed method. Algorithm 1 is used to compute decentralized working zones from the given LS3PR Petri net model for flexible manufacturing systems. Algorithm 2 is used to compute the decentralized controllers that enforced liveness to the decentralized working zones. The sequential assembling is used to reconnect and controlled the working zones via decentralized controllers. The decentralized controller is added to the decentralized working zones that have common elements, that is, common transitions. The proposed method has the following advantages: (i) it can be applied to a complex Petri net model for flexible manufacturing systems, (ii) the proposed methods has less computational complexity when compared with the previous methods, (iii) the proposed method can obtain a minimal number of decentralized controllers that enforce liveness of the uncontrolled Petri net model. Experimental examples are presented to explore the applicability of the proposed methods.

Global Supervisory Structure for Decentralized Systems of Flexible Manufacturing Systems Using Petri Nets

Decentralized supervisory structure has drawn much attention in recent years to address the computational complexity in designing supervisory structures for large Petri net model. Many studies are reported in the paradigm of automata while few can be found in the Petri net paradigm. The decentralized supervisory structure can address the computational complexity, but it adds the structural complexity of supervisory structure. This paper proposed a new method of designing a global controller for decentralized systems of a large Petri net model for flexible manufacturing systems. The proposed method can both reduce the computational complexity by decomposition of large Petri net models into several subnets and structural complexity by designing a global supervisory structure that can greatly reduce the cost at the implementation stage. Two efficient algorithms are developed in the proposed method. Algorithm 1 is used to compute decentralized working zones from the given Petri net model for flexible manufacturing systems. Algorithm 2 is used to compute the global controller that enforces the liveness to the decentralized working zones. The ring assembling method is used to reconnect and controlled the working zones via a global controller. The proposed method can be applied to large Petri nets size and, in general, it has less computational and structural complexity. Experimental examples are presented to explore the applicability of the proposed method.

Plausible Petri nets as self‐adaptive expert systems: A tool for infrastructure asset monitoring

AbstractThis article provides a computational framework to model self‐adaptive expert systems using the Petri net (PN) formalism. Self‐adaptive expert systems are understood here as expert systems with the ability to autonomously learn from external inputs, like monitoring data. To this end, the Bayesian learning principles are investigated and also combined with the Plausible PNs (PPNs) methodology. PPNs are a variant within the PN paradigm, which are efficient to jointly consider the dynamics of discrete events, like maintenance actions, together with multiple sources of uncertain information about a state variable. The manuscript shows the mathematical conditions and computational procedure where the Bayesian updating becomes a particular case of a more general basic operation within the PPN execution semantics, which enables the uncertain knowledge being updated from monitoring data. The approach is general, but here it is demonstrated in a novel computational model acting as expert system for railway track inspection management taken as a case study using published data from a laboratory simulation of train loading on ballast. The results reveal self‐adaptability and uncertainty management as key enabling aspects to optimize inspection actions in railway track, only being adaptively and autonomously triggered based on the actual learnt state of track and other contextual issues, like resource availability, as opposed to scheduled periodic maintenance activities.

On simulating Turing machines with inhibitor Petri nets

An inhibitor Petri net is constructed that simulates an arbitrary given Turing machine. The tape of the Turing machine, its program, and internal states are encoded by the marking of nine dedicated places of the Petri net. The rules of Turing machine work are encoded by a single control flow represented by a token passage within the inhibitor Petri net composed of the sequence, branch, and loop operators. Subnets that implement arithmetic, comparison, and copying operations are employed. In the Petri net paradigm of computation, a Petri net that simulates Turing machines provides the compatibility of concepts. It is a prototype of a co‐processor supplementary to the basic processor of Petri nets. © 2017 Institute of Electrical Engineers of Japan. Published by John Wiley &amp; Sons, Inc.

Supervisor Synthesis and Performance Improvement for Automated Manufacturing Systems by Using Petri Nets

For event-driven systems like automated manufacturing systems (AMSs), intelligent part dispatching, i.e., to assign various parts to proper processing routes, is crucial to gain high resource utilization and production efficiency. This work proposes an innovative dispatching mechanism, which can better these metrics by minimizing the cycle time, i.e., the mean time to produce a product, while avoiding any deadlock, i.e., no part can proceed due to circuit wait. Its prerequisite is liveness supervision; however, temporal information is associated to certain operation stages for the sake of performance evaluation and throughput maximization, i.e., to maximize the finished-part quantity per time unit. In the paradigm of Petri nets, we show the criticality to prioritize certain activities locally. Our method can well design ratio parameters among distinct processes to improve system productivity.

Simulation-based optimization of discrete event systems with alternative structural configurations using distributed computation and the Petri net paradigm

Decision-making on discrete event systems with alternative structural configurations is a field with application to the efficient design and operation of many systems, ranging from manufacturing facilities to communication networks. The solution of this problem may be afforded by its transformation into an optimization problem. A variety of statements for this optimization problem can be presented by using different formalisms able to describe the model of the system. These different statements allow developing diverse optimization algorithms for solving the problem, which may be very demanding for a computer. In this paper, several approaches are presented in order to reduce the computing requirements needed by the mentioned algorithms, some of them are implemented in one processor and others are based on distributed computing. In particular, this paper presents a new distributed methodology, which associates sets of alternative structural configurations of the system to different alternative aggregation Petri net (AAPNs), regarding the number of available processors. Under certain conditions, this methodology alleviates the computational requirements for every processor and speeds up the optimization process. A case-study is presented and different techniques are applied to solve it, for illustrating diverse distributed and non-distributed methodologies, regarding the available processors, as well as for comparing their relative performance.

Generalised Batches Petri Net: Hybrid Model For High SpeedSystems With Variable Delays

Recently, the possibility of associating both discrete events and continuous time behaviour in the same formalism has generated a considerable interest in the Petri net paradigm. A central issue in this field is the concept of Hybrid Petri net which consists in continuous transitions and places holding non negative real number, and discrete transitions and places holding integer tokens. By adding a new type of nodes, batch transitions and batch places, Batches Petri nets have been defined. A batch node combines both a discrete event and a linear continuous dynamic behaviour in a single structure. Batches Petri nets can then be used in the control design and performance analysis of high-speed systems composed of continuous transfer elements which introduce variable delays on continuous flows. In this paper, the complete formalism of Generalised Batches Petri nets is given through the definition of the model, the enabling and firing rules, the time analysis methods, and two examples illustrate these notions.

A Formalisation of Automation Petri Nets for Control and Marked Matrix Logic Controllers

Abstract Grafcet, and more recently IEC1131-3 SFC, have sought to provide a standardised, easy to interpret graphical programming technique for programming Programmable Logic Controllers (PLCs). Both techniques represent attempts to modify Petri nets to make them applicable to sequential control tasks. However, both depart significantly from the Petri net paradigm. In this paper Automation Petri Nets for Control (APNC) are defined which retain more of the features of generalised Petri nets. Marked Matrix Equations are presented for APNCs which naturally generate Marked Metric Logic Controllers. These are easily implemented on industrial and embedded PC's in high level programming languages.

An integrated object-oriented Petri net paradigm for manufacturing control systems

A new manufacturing control software development methodology called IOPN (integrated object-oriented Petri net paradigm) is presented. The IOPN consists of four phases: (1) static analysis; (2) dynamic analysis; (3) integration; and (4) implementation. In the static analysis phase, all possible object classes required by the manufacturing control software, and the static relationships among these object classes are identified. In the dynamic phase, the objectoriented Petri net (OPN) control model is derived according to both the dynamic behaviour of shop floor operations and the desired control logic. After the control logic specified by the OPN model is analysed and there is proven to be no deadlock, the required control decision/knowledge (e.g. scheduling/ dispatching knowledge) must be included in the OPN model. Finally, the manufacturing control system is implemented directly from the specification of the OPN model by applying a number of transformation rules. Since the IOPN approach not only possesses the characteristics of object-oriented methods and Petri nets, but also provides a straightforward mapping between the high-level specification of the control logic and the code of the control software, the time required for developing a new control software or modifying an existing control software to accommodate to the operational changes will be greatly reduced.