Modeling Of Discrete Event Systems Research Articles

Fault diagnosis in discrete time hybrid systems – A case study

A method of analysing diagnosability of discrete time hybrid systems (DTHS), which are similar to the simple n-rate timed automata [R. Alur, C. Courcoubetis, T.A. Henzinger, P. Ho, Hybrid automata: an algorithmic approach to the specification and verification of hybrid systems, in: Hybrid Systems, LNCS 736, Springer Verlag, 1993, pp. 209–229], has been proposed. A state based fault modeling formalism is used. The properties of the DTHS model, under measurement limitations due to inadequacy or non-availability of sensors, are discussed. A definition of diagnosability for DTHS models has been adopted from the one proposed in [M. Sampath, R. Sengupta, S. Lafortune, K. Sinnamohideen, D. Teneketzis, Diagnosability of discrete-event systems, IEEE Transactions on Automatic Control 40 (9) (1995) 1555–1575] for discrete-event system (DES) models. Based on the measurement limited DTHS models, an algorithm for construction of a diagnoser is presented. It is next demonstrated through an example of a chemical reaction chamber that the diagnosability condition (over the diagnoser), which has been shown to be necessary and sufficient for DES diagnosability, fails to hold for many systems. This is so because the abstraction employed in DES modeling obliterates an important feature of the transitions namely fairness. Exploiting the explicit continuous dynamics of the DTHS models, the fairness of transitions is identified and used to demonstrate diagnosability. The diagnosability condition over the diagnoser is suitably modified to encompass the situations typified by the example.

Laws of Large Numbers and Functional Central Limit Theorems for Generalized Semi-Markov Processes

Because of the fundamental role played by generalized semi-Markov processes (GSMPs) in the modeling and analysis of complex discrete-event stochastic systems, it is important to understand the conditions under which a GSMP exhibits stable long-run behavior. To this end, we review existing work on strong laws of large numbers (SLLNs) and functional central limit theorems (FCLTs) for GSMPs; our discussion highlights the role played by the theory of both martingales and regenerative processes. We also sharpen previous limit theorems for finite-state irreducible GSMPs by establishing a SLLN and FCLT under the “natural” requirements of finite first (resp., second) moments on the clock-setting distribution functions. These moment conditions are comparable to the minimal conditions required in the setting of ordinary semi-Markov processes (SMPs). Corresponding discrete-time results for the underlying Markov chain of a GSMP are also provided. In contrast to the SMP setting, limit theorems for finite-state GSMPs require additional structural assumptions beyond irreducibility, due to the presence of multiple clocks. In our new limit theorems, the structural assumption takes the form of a “positive density” condition for specified clock-setting distributions. As part of our analysis, we show that finite moments for new clock readings imply finite moments for the od-regenerative cycles of both the GSMP and its underlying chain.

Modelling and control of discrete event systems using switching max-plus-linear systems

In this paper we consider the modelling and control of discrete event systems using switching max-plus-linear systems. In switching max-plus-linear systems we can switch between different modes of operation. In each mode the discrete event system is described by a max-plus-linear state space model with different system matrices for each mode. The switching allows us to change the structure of the system, to break synchronization and to change the order of events. We will give some examples of this type of systems. We define the model predictive control design problem for this type of discrete event system, and we show that solving this problem in general leads to a mixed integer optimization problem.

Performance evaluation of communication networks for distributed systems

Distributed control systems are used to monitor and control distributed equipment. With the growth of communication networks, severe congestion problems appeared. To avoid dropping packets and then guarantee the needs of distributed systems in terms of performances and of quality service, some algorithms were put into Transport Control Protocol (TCP). This paper focused on network modelling, study of network dynamic behaviour and of congestion avoidance. It is possible with this network modelling to determine the influence of communication networks on the transmission of control signals. The paper also presents the modelling of a communication line in internet environment. The behaviour of the communication line is modelled as a continuous system. The behaviour of the TCP protocols is seen as a Discrete Event System (DES) model. We choose hybrid Petri Nets (PNs) as a unique modelling tool, as it gives accurate models of the complex functions found in internet connections.

A hybrid approach to supervisory control of discrete event systems coupling RW supervisors to Petri nets

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.

Modular Fault Diagnosis Based on Discrete Event Systems

An awareness of failure type and location is an indispensable requirement for the establishment of adequate recovery strategies and the maintenance of Factory Automation and Process Control systems. The failure diagnosis methodology presented in this paper is based on Discrete Event Systems models and in the diagnoser concept, which enable the off-line and on-line analysis of systems failures. We present an approach for models and associated diagnosers based on a modular decomposition of the global system, with the aim of avoiding problems of exponential explosion in the number of states and computational complexity of the diagnosis process.

DEVSpecL: DEVS specification language for modeling, simulation and analysis of discrete event systems

Discrete EVent Systems Specification (DEVS) formalism supports specification of discrete event models in a hierarchical modular manner. This paper proposes a DEVS modeling language called DEVS Specification Language (DEVSpecL) based on which discrete event systems are modeled, simulated and analyzed within a DEVS-based framework for seamless systems design. Models specified in DEVSpecL can be translated in different forms of codes by code generators, which are executed with various tools for models verification, logical analysis, performance evaluation, and others.

Safe diagnosability for fault-tolerant supervision of discrete-event systems

The problem of achieving fault-tolerant supervision of discrete-event systems is considered from the viewpoint of safe and timely diagnosis of unobservable faults. To this end, the new property of safe diagnosability is introduced and studied. Standard definitions of diagnosability of discrete-event systems deal with the problem of detecting the occurrence of unobservable fault events using model-based inferencing from observed sequences of events. In safe diagnosability, it is required in addition that fault detection occur prior to the execution of a given set of forbidden strings in the failed mode of operation of the system. For instance, this constraint could be required to prevent local faults from developing into failures that could cause safety hazards. If the system is safe diagnosable, reconfiguration actions could be forced upon the detection of faults prior to the execution of unsafe behaviour, thus achieving the objective of fault-tolerant supervision. Necessary and sufficient conditions for safe diagnosability are derived. In addition, the problem of explicitly considering safe diagnosability in controller design, termed “active safe diagnosis problem”, is formulated and solved. A brief discussion of safe diagnosability for timed models of discrete-event systems is also provided.

Building reduced petri net models of discrete manufacturing systems

This paper is concerned with building reduced interpreted Petri net (IPN) models of discrete event systems (DES). It introduces two results. The first one is a new modelling methodology and the second one is the definition of transformation matrices used to obtain equivalent IPN. The modelling methodology is based on building binary IPN for the system state variables and deriving a global model using the synchronic and the novel permissive compositions. One advantage of this approach is that the combinatorial tuning phase, used by other methodologies is no longer needed. On the other hand, the transformation matrices are used to obtain reduced IPN versions of the binary IPN obtained with our modelling methodology. The reduced IPN are no longer binary and have a less number of nodes. Since the reachability graph of a reduced IPN is the same that the original net and also the input/output behavior are identical, consequentely all properties of a reduced IPN are the same than the original net; this fact is shown regarding the observability property.

PARAMETERS ESTIMATION FOR TIMED AND CONTINUOUS PETRI NETS: APPLICATION TO THE IDENTIFICATION AND MONITORING OF HYBRID SYSTEMS

ABSTRACT Petri net (PN) models are useful tools for the modeling of discrete event systems and hybrid systems. This paper is about the parameters estimation for two classes of timed PNs: T-timed PNs and continuous PNs with variable speeds. The parameters to be estimated are either incidence or temporal parameters. Data- and model-based methods are proposed. In each case, on-line and off-line implementations are detailed. As a consequence, identification and monitoring applications for hybrid systems are described.

Closed-Loop Matrix Based Model of Discrete Event Systems for Machine Logic Control Design

This paper deals with modeling, dynamic description, and control of discrete event systems (DES) for production systems and machines control logic design. The control logic of such systems is considered as DES, which is then modeled by a matrix representation of Petri net graph. The dynamics of a DES is described by a well known algebraic Petri net next-state equation and a novel logical firing event selecting equation. The control of the DES dynamics is introduced by logical signals, which represent conditions for occurrence of events. Such a presentation enables closed-loop modeling of DES, which is important for simulation of the systems and analysis of their performance before the target system is actually built. The proposed method is illustrated with a cutting machine application. Using the proposed method, the correct functionality as well as faults response can be simulated with Matlab/Simulink.

Automated synthesis of Ladder automation circuits based on state-diagrams

One area where discrete event systems are currently used is the design of control systems based on programmable logic controllers (PLCs). As the PLC technology is evolving into a family of control functions of many types at many different levels of complexity, there is an increasing need for software tools providing the systematic development of real industrial applications including modeling and control of discrete event systems. This paper describes the use of a state-diagram method in the computer aided logical synthesis and design of automation circuits. It also presents the corresponding software package developed for control logic creation. The developed software generates control logic in the form of Ladder electric circuits since they present descriptive simplicity and are widely known in the PLCs' world. The developed software package is also suitable for both industrial practice and teaching purposes.

ONLINE MONITORING OF AN AEROBIC SBR PROCESS BASED ON DISSOLVED OXYGEN MEASUREMENT

This paper presents results that enable monitoring of an aerobic sequencing batch wastewater treatment (WWT) process based on online dissolved oxygen (DO) concentration measurement. It introduces the sequential process and the DO dynamics, presents a formal discrete event system (DES) model for the traditional SBR process and a modification that enables online monitoring of the respiration rate during the reaction phase and of the oxygen transfer parameter KLa over process cycles. Finally a test method for verifying the presence of substrate in the reactor is introduced. Parts of the results have been validated with experimental data from the EOLI project.

A DISCRETE-EVENT SYSTEMS MODEL FOR CONGESTION CONTROL

This paper presents a discrete-event systems approach to the modeling of a packet-switched communication link shared by multiple users for the purpose of end-to-end congestion control. It introduces a discrete-event system model for the interaction between a shared communication link and the users, which captures the behavior that the link users receive acknowledgments for successfully transmitted packets with a delay that is proportional to the level of congestion in the link. An end-to-end congestion control scheme for this system model is presented that uses the concept of an observer from supervisory control theory. The link model and controllers are implemented in both a Java programming language simulation and the NS2 network simulation software for analysis.

Synthesis of supervisors for time-varying discrete event systems

We introduce a time-varying automaton to model discrete event systems. The structure of this time-varying automaton is very similar structure to (max,+) automaton, but allowing variable event lifetimes. Based on this time-varying automaton the design of timed supervisors is obtained by using the dioid algebra, where the languages used to describe the discrete event system as well the desired specification are replaced by matrices defined in such algebra and the supervisor synthesis is achieved through simple matrix operations. The proposed synthesis algorithm allows one to synthesize supervisors for un-timed DES, timed DES with constant event lifetime and timed DES with variable event lifetime. All these cases are treated with the same basic algorithm, the differences rely only on the definition of the event lifetime functions. The proposed algorithm presents a complexity order equal to the supervisor synthesis algorithm of un-timed discrete event systems. The proposed approach can be considered as an alternative procedure, based on a non-traditional algebraic structure, to achieve the supervisor synthesis for discrete event systems.

Petri-net based formulation and algorithm for short-term scheduling of batch plants

Effective scheduling of operations in batch plants has a great potential for high economic returns, in which the formulation and optimal solution algorithm are the main issues of study. Petri-nets have proven to be a promising technique to solve many difficult problems associated with the modeling, formal analysis, design and coordination control of discrete event systems. One of the major advantages of using a Petri-net model is that the same model can be used for the analysis of behavioral properties and performance evaluation, as well as for the systematic construction of discrete event simulators and controllers. This paper aims to present a Petri-net based approach for the scheduling of operations in batch plants. Firstly, the short-term scheduling of batch plants is formulated using timed Petri-net. Secondly, the heuristic search algorithm for scheduling of batch plants is given, which is based on generating and checking the markings in the reachability tree of the Petri-net model. Finally, the novel formulation and algorithm are tested using two simulation case studies, and compared against traditional methods.

Modeling of discrete event systems

In this article, the authors provide an alternative view on Petri nets modeling of discrete event systems. The proposed modeling procedure follows the Systems Specification guidelines underlying the well-known DEVS modeling formalism. The authors' endeavour is towards perfecting the design of reusable Petri nets-based models by searching for a good primitive for a modular model construction and the introduction of coupling templates as standardised means to couple building block components. Assuming that the real-world system to be modeled has been analyzed in depth beforehand through a suitable system analysis method (which itself is beyond the scope of the article), we present a systematic step-by-step approach to construct a model in the Petri nets domain together with its experimental frame. The construction adheres to well-defined rules, which enable computer-based model construction. The input for this systematic bottom-up construction of Petri nets-models is information (about, e.g., primitive system components, entity flows, routing constructs) gathered from the top-down system analysis. In the article, attention is also paid to the algebraic backgrounds underlying the proposed model construction. These provide the basis for formal correctness proofs, mapping Petri nets onto DEVS-models, and complexity reduction of the found Petri nets-models. By offering to the model builder the possibility to handle multiple abstraction levels and by addressing important issues related to the interfacing question of coupled models and model components described in Petri nets and DEVS formalism, the authors' work addresses two of the main research directions of Computer Automated Multi-Paradigm Modeling ([Mosterman and Vangheluwe 2002]): <i>model abstraction</i> and <i>multiformalism modeling</i>. The article concludes with an illustrative application example.

Modelling and control of discrete event systems using switching max-plus-linear systems

In this paper we consider the modelling and control of discrete event systems using switching max-plus-linear systems. In switching max-plus-linear systems we can switch between different modes of operation. In each mode the discrete event system is described by a max-plus-linear state equation with different system matrices for each mode. The switching allows us to change the structure of the system, to break synchronization and to change the order of events. We will give some examples of this type of system.We define the model predictive control design problem for this type of discrete event system, and we show that solving this problem in general leads to a mixed integer optimization problem.

A Remark on Inseparability of Min–Max Systems

Min-max systems, or min-max-plus systems are algebraic models of discrete-event dynamic systems. They are nonlinear extensions of the well known linear max-plus system models. The structural property "inseparability" of min-max systems was proposed by us in a recent paper. It turns out that inseparability is equivalent to the property of "irreducibility" proposed recently by van der Woude and Subiono, although the two properties appear in very different forms. We will prove this fact here.

Discrete Event Systems with Guards

This work presents a model of discrete event systems (DES) consisted of a synchronized deterministic finite automaton with a data structure. The model, denominated DES with guards is realized through automata with guards, where the habilitation of each group of synchronized events may be conditioned to the satisfaction of a predicate related to the discrete state of the automata and to the defined variables by data structure. The most important characteristics of DES with guards are the expression of non-regular behaviors and, depending on the structural properties of the components of the system, the construction of generic models through the parametrization of initial values, final values, etc.