Petri Net Controller Research Articles

Guest editorial: hybrid systems, part II

We consider it a great privilege to introduce this two-part issue on Hybrid Systems to Discrete Event Dynamic Systems: Theory and Applications. Hybrid dynamical systems constitute an abstract modeling framework for systems with bi-layer dynamics: time-driven dynamics at the lower layer, and discrete-event dynamics at the upper layer. This framework provides useful analysis techniques and simulation tools for planning and control of systems in several application areas such as mobile robotics, automotive powertrains, switching circuits, manufacturing, and telecommunications. Consequently, hybrid systems have been extensively investigated by our research community, with emphases on the problems of stability, observability, control, and optimization. The hybrid-systems framework is diverse and includes linear and nonlinear models, deterministic and stochastic systems, and centralized systems as well as distributed networks. One of their unifying themes is the bi-level structure of their dynamics, and the exploration of the interactions between their time-driven dynamics and discrete-event dynamics has been a focus of extensive research. The purpose of this special issue is to bring together papers representing some of the main standing problems in the area of hybrid systems. The contributions comprising the first part of the special issue are summarized in the following paragraphs. The first paper in this issue, On Fluidization of Discrete Event Models: Observation and Control of Continuous Petri Nets, by M. Silva, J. Julvez, C. Mahulea, and C.R. Vazquez, provides a survey of hybrid Petri networks. It starts with a tutorial on the broad topic of fluidization of discrete event dynamic systems and its use in circumventing the problem of the state-space explosion. It then considers Petri networks in detail, where it describes how fluid and hybrid models can be used in

Control of continuous Petri nets using ON/OFF based method

Continuous Petri Nets (CPN) can be used to approximate classical discrete Petri nets which suffer from the state explosion problem. In this paper we focus on the control of timed CPN (TCPN), aiming to drive the system from an initial state to a desired final one. This problem is similar to the set-point control problem in a general continuous-state system. In a previous work, a simple and efficient ON/OFF controller was proposed for structurally persistent nets, and it is proved to be minimum-time. In this work the ON/OFF controller is extended to general TCPN, but in this case, the minimum-time evolution is not guaranteed. Two extensions are proposed, both of them are based on the ON/OFF strategy. Some comparisons of different control methods are given in terms of their applications to an assembly system.

Supervisory control of Petri nets using polyhedral regions

We propose to use polyhedral computations to check the reachability and co-reachability of Petri nets, and design supervisors enforcing polyhedral invariance. To this aim, we first state a semi-algebraic behavioral model for Petri nets, derived from the marking equation. From it, we derive explicit characterizations of the sets of k-reachable marking vectors, in terms of polyhedral regions of a real vector space. This permits to calculate the region of reachable marking vectors, when the considered Petri net is bounded, as the projection of an integral polyhedron. The polyhedron is computed using the Γ-algorithm, in polynomial time. We propose an algorithm to this computation. We adapt the method to further compute the polytope of reachable, co-reachable and safe marking vectors, meeting a given set of polyhedral constraints, and finally apply it to design a supervising controller. We illustrate the method on the supervisor design of a simple AGV system.

Petri Net and GA Based Method for JSP Optimization with Dual-Objective

A new dual-objective scheduling method based on the controlled Petri net and GA is proposed to the job-shop scheduling problem (JSP) constrained by machines, workers. Firstly, a detailed analysis of supervisory control for Petri net with uncontrollable transitions, especially important, for OR-logics linear constraint, a new method for constructing a Petri net feedback controller based on monitor and inhibitor arcs is presented. The Petri net model is constructed based on above method in flexible JSP. Then, the genetic algorithm (GA) is applied based on the controlled Petri net model and Pareto. Function objectives of the proposed method are to minimize the completion time and the total expense of machines and workers. Finally, Scheduling example is employed to illustrate the effectiveness of the method.

Controller Design for Petri Net with Uncontrollable and Unobservable Transitions

A controller design method for Petri net with uncontrollable and unobservable transitions that enforces the conjunction of a set of linear inequalities on the Parikh vector is proposed. The method is based on the theory that each place can be described with a Parikh vector inequality. Constraints are classified into admissible and inadmissible constraints. An inadmissible constraint cannot be directly enforced on a plant because of the uncontrollability or unobservability of certain transitions. Construct the controller though transforming the inadmissible constraint into admissible one. The method eases the design of controller, because it is based on part net design, and it only considers the direct or indirect transitions related to the constraints. So the computation required to find the Petri net controller is quite simple. Finally, the method is proved to be simple and efficient through one example.

On fluidization of discrete event models: observation and control of continuous Petri nets

As a preliminary overview, this work provides first a broad tutorial on the fluidization of discrete event dynamic models, an efficient technique for dealing with the classical state explosion problem. Even if named as continuous or fluid, the relaxed models obtained are frequently hybrid in a technical sense. Thus, there is plenty of room for using discrete, hybrid and continuous model techniques for logical verification, performance evaluation and control studies. Moreover, the possibilities for transferring concepts and techniques from one modeling paradigm to others are very significant, so there is much space for synergy. As a central modeling paradigm for parallel and synchronized discrete event systems, Petri nets (PNs) are then considered in much more detail. In this sense, this paper is somewhat complementary to David and Alla (2010). Our presentation of fluid views or approximations of PNs has sometimes a flavor of a survey, but also introduces some new ideas or techniques. Among the aspects that distinguish the adopted approach are: the focus on the relationships between discrete and continuous PN models, both for untimed, i.e., fully non-deterministic abstractions, and timed versions; the use of structure theory of (discrete) PNs, algebraic and graph based concepts and results; and the bridge to Automatic Control Theory. After discussing observability and controllability issues, the most technical part in this work, the paper concludes with some remarks and possible directions for future research.

Constraint graph-based approach for the analysis and the control of time critical systems

The increasing complexity of manufacturing systems gives rise to the development of new formal methods allowing to handle their particularities. Petri nets are a powerful formalism for the specification and verification of concurrent systems including sequential systems and manufacturing systems. To deal with systems whose time issues become fundamental, different time Petri nets extensions have been developed in the literature, each one being dependent on the application considered. For the time critical systems, their correctness depends not only on the logic correctness but also on the time constraints. Timing issues are essential. In this paper, a new method of analysis and control for P-time Petri nets is proposed. It is based on the firing instant notion and exploits a constraint graph approach.

Synthesis a Petri net based control model for a FMS cell

Petri nets have been recognised as a high level formal and graphical specification language for modelling, analysis, and control of concurrent asynchronous distributed systems. This paper presents a PN model, synthesised by an extended version of the knitting synthesis technique. This method, as an incremental design approach, establishes the conditions under which the fundamental behavioural properties of the synthesised systems are fulfilled and preserved. That is, the synthesised models are live, bounded, and reversible (cyclic). A Petri net with the aforementioned properties is called a well-behaved Petri net system which is guaranteed to operate in a deadlock-free, stable, and cyclic fashion. Well-behaved Petri net models, synthesised using the proposed method can be compiled into control codes and implemented as real-time controllers for flexible manufacturing systems. The significance of this paper is due to the application of an extended version of knitting synthesis technique to a real life example of a flexible manufacturing system.

A modular-coordinated control for continuous Petri nets

AbstractTimed continuous Petri net (TCPN) systems are piecewise-linear models with input constraints that can approximate the dynamical behavior of a class of timed discrete-event systems. This work is devoted to the synthesis of a coordinated control strategy for large TCPN systems that can be seen as a set of T-disjoint TCPN modules interconnected by places. The goal of the control scheme is to transfer the system in such a way that each module reaches a desired marking. The resulting scheme consists of a set of affine local controllers, one per module, and a coordinator that receives and sends information to the local controllers.

A Robust Neural Fuzzy Petri Net Controller For A Temperature Control System

Temperature control systems have the characteristics of non-linearity, large inertia, and time variance. It is difficult to overcome the effects of these factors and get a reasonable results with the use of conventional controllers such as PID. So, temperature control by a robust neural fuzzy Petri net (RNFPN) controller based on an indirect forward control structure is proposed in this paper. After offline learning to get the initial weights, the RNFPN is online constructed by concurrent structure/parameter learning. The RNFPN has many advantages when applied to temperature control plants such as: high learning ability which reduces the controller training time, no a priori knowledge of the plant is required which simplifies the design task, and lastly the high control performance. The simulation results showed that the RNFPN intelligent controller has a reasonable robustness against disturbance, rapidity and good dynamic performance.

VHDL-based FPGA Implementation of C/E System

Petri Net is an important tool to model discrete event system. In this paper, Hardware Description Language VHDL is used to implement C/E System, a subclass of Petri Net. Firstly, C/E System is used to model the problem. The model is then analyzed and controlled. Secondly, Petri Net control model is described by VHDL and the VHDL source file is generated. Finally, the VHDL code is compiled, simulated, fit design and downloaded to the Programmable Logic Device FPGA through EDA software MAX PLUSII. Hardware experiment is performed with GW48-CK. A sample C/E System for the philosopher dining problem is presented in the paper using the proposed method. Simulation wave and hardware experiment further verify the correctness of the method. The VHDL-based FPGA implementation method is of great significance to the design of parallel controller based on C/E System.

Decision-making and controlling for products collaborative design implement process based on fuzzy Petri net

In order to solve the controlling problems with multiple design tasks and uncertain dynamic design process, a model of manufacture collaborative design process based on process control Petri nets is proposed by introducing decision rules information place and decision transmission. Fuzzy Petri net theory is adopted to descript fuzzy logic and knowledge expression appearing in the collaborative design process control. Synchronously, deducing knowledge-base with rules for collaborative design is built up. Two parameters are set: deterministic factor is used to express confidence degree of fuzzy rules while reliability value is used to express the reliability degree of storing proposition in decision information place. In addition, the implementation process for manufacture collaborative design is fuzzily deducted by FPN algorithm. According to the deduction result, the implementation flow of collaborative design process is decided. Finally, the presented approach is tested to be validity by control instance of driving system for chain conveyor in collaborative design process.

Модифіковані мережі Петрі (Petri netze) для формування паралельних процесів у системах управління

The problems of detecting errors in the design of complex control systems. Offered as a reference model for verification of a software system using a model based on control of Petri nets

Robustness analysis of non-ordinary Petri nets for flexible assembly systems

Non-ordinary controlled Petri nets (NCPNs) have the advantages to model flexible assembly systems in which multiple identical resources may be required to perform an operation. However, existing studies on NCPNs are still limited. For example, the robustness properties of NCPNs have not been studied. This motivates us to develop an analysis method for NCPNs. Robustness analysis concerns the ability for a system to maintain operation in the presence of uncertainties. It provides an alternative way to analyse a perturbed system without reanalysis. In our previous research, we have analysed the robustness properties of several subclasses of ordinary controlled Petri nets. To study the robustness properties of NCPNs, we augment NCPNs with an uncertainty model, which specifies an upper bound on the uncertainties for each reachable marking. The resulting PN models are called non-ordinary controlled Petri nets with uncertainties (NCPNU). Based on NCPNU, the problem is to characterise the maximal tolerable uncertainties for each reachable marking. The computational complexities to characterise maximal tolerable uncertainties for each reachable marking grow exponentially with the size of the nets. Instead of considering general NCPNU, we limit our scope to a subclass of PN models called non-ordinary controlled flexible assembly Petri net with uncertainties (NCFAPNU) for assembly systems and study its robustness. We will extend the robustness analysis to NCFAPNU. We identify two types of uncertainties under which the liveness of NCFAPNU can be maintained.

Elementary Petri net inside RFID distributed database (PNRD)

Usually, a Petri net is applied as an RFID model tool. This paper, otherwise, presents another approach to the Petri net concerning RFID systems. This approach, called elementary Petri net inside an RFID distributed database, or PNRD, is the first step to improve RFID and control systems integration, based on a formal data structure to identify and update the product state in real-time process execution, allowing automatic discovery of unexpected events during tag data capture. There are two main features in this approach: to use RFID tags as the object process expected database and last product state identification; and to apply Petri net analysis to automatically update the last product state registry during reader data capture. RFID reader data capture can be viewed, in Petri nets, as a direct analysis of locality for a specific transition that holds in a specific workflow. Following this direction, RFID readers storage Petri net control vector list related to each tag id is expected to be perceived. This paper presents PNRD cornerstones and a PNRD implementation example in software called DEMIS–Distributed Environment in Manufacturing Information Systems.

Linear programming techniques for analysis and control of batches Petri nets

In this paper we consider Generalised Batches Petri nets (GBPN) and develop new linear algebraic techniques for the analysis of this model. Two main contributions are presented. The first contribution lies in the fact that although we consider the same GBPN model that has already be presented in the literature, we associate to this model a different semantics considering that the instantaneous firing flow of continuous and batch transitions are control variables that can take an arbitrary value provided they satisfy given constraints. The second contribution consists in the analysis of the steady state behavior of GBPN. We show that under the assumption that no discrete transition fires, a steady state can be characterized by solving a linear programming problem that takes into account the net structure and the initial marking.

Comparison of Petri Net and Finite State Machine Discrete Event Control of Distributed Surveillance Network

Wireless sensor networks are an important military technology with civil and scientific applications. In this article, we derive a discrete event controller system for distributed surveillance networks that consists of three interacting hierarchies—sensing, communications, and command. Petri Net representations of the hierarchies provide plant models of resource contention and internal consistency. Control specifications are derived that enforce consistency across the hierarchies. Three controllers are created using different methodologies to satisfy these specifications. The methods used are Petri Net, finite state automata using the Ramadge and Wonham approach, and vector addition control using the Wonham and Li approach. We use the controllers derived to contrast the design methodologies. Our results find these three approaches to be roughly equivalent. Each method has advantages and disadvantages.

On suboptimal supervisory control of Petri nets in the presence of uncontrollable transitions via monitor places

Recently, a study has been presented for suboptimal supervisory control of Petri nets via monitor (control) places in the presence of uncontrollable transitions. To enforce a generalized mutual exclusion constraint (GMEC) suboptimally on a plant Petri net with uncontrollable transitions, a set of monitor places has been provided to choose from. There are two main results of this study, the first of which is that “there is not an optimal solution to the problem of computing a monitor-based controller to enforce a GMEC on a plant net in the presence of uncontrollable transitions”. The second result deals with the computation of monitor places for the suboptimal supervisory control in such Petri nets. In this paper, it is shown that there may be an optimal solution to the problem of computing a monitor-based controller to enforce a GMEC on a plant net in the presence of uncontrollable transitions. To do this, an example Petri net is considered and then two different optimal (maximally permissive) solutions are provided for this Petri net.

A hybrid approach to design deadlock-free Petri net controller for discrete event systems

The issue of supervisory control of discrete event systems (DES) based on Petri nets (PN) has been investigated by using various methods. However, there exists a problem that the supervisor, introduced to enforce the given specification, causes a deadlock in the closed-loop system, especially when the deadlock occurs in the closed-loop system in which the original plant model is live. To address this problem, we propose a hybrid approach to design a deadlock-free PN controller for DES with given specification. The approach mainly consists of two stages. Firstly, a supervisor is designed to enforce the given specification using the reported place invariants method. Then, we regard the obtained closed-loop system with deadlock introduced by the supervisor as a new plant net and adopt the theory of regions to design a deadlock-free PN controller. The controller designed by our approach is guaranteed to be maximally permissive when the original plant PN is fully controllable and observable. Even for partially controllable and observable plant PN, it is possible to obtain a suboptimal solution.

Wafer Sojourn Time Fluctuation Caused by Activity Time Variation in DualArm Cluster Tools

With wafer residency time constraints, wafer sojourn time in a processing module should be carefully controlled such that it is in a permissive range. Activity time variation often results in wafer sojourn time fluctuation and makes an originally feasible schedule infeasible. Thus, it is very important to know how the wafer sojourn time changes when activity time varies. With proposed Petri net (PN) model and real-time control policy, this paper analyzes the effect of activity time variation on wafer sojourn time delay and presents its upper bounds in dual-arm cluster tools.