Discrete Event Dynamic Systems Research Articles

Modelling and simulation of manufacturing systems with first-order hybrid Petri nets

First-order hybrid Petri nets are models that consist of continuous places holding fluid, discrete places containing a non-negative integer number of tokens, and transitions, either discrete or continuous. In the first part of the paper, we provide a framework to describe the overall hybrid net behaviour that combines both time-driven and event-driven dynamics. The resulting model is a linear discrete-time, time-varying state variable model that can be directly used by an efficient simulation tool. In the second part of the paper, we focus on manufacturing systems. Manufacturing systems are discrete-event dynamic systems whose number of reachable states is typically very large, hence approximating fluid models have often been used in this context. We describe the net models of the elementary components of a flexible manufacturing system (machines and buffers) and we show in a final example how these modules can be put together in a bottom-up fashion.

Model matching for finite-state machines

The problem of model matching for finite state machines (FSMs) consists of finding a controller for a given open-loop system so that the resulting closed-loop system matches a desired input-output behavior. In this paper, a set of model matching problems is addressed: strong model matching (where the reference model and the plant are deterministic FSMs and the initial conditions are fixed), strong model matching with measurable disturbances (where disturbances are present in the plant), and strong model matching with nondeterministic reference model (where any behavior out of those in the reference model has to be matched by the closed-loop system). Necessary and sufficient conditions for the existence of controllers for all these problems are given. A characterization of all feasible control laws is derived and an efficient synthesis procedure is proposed. Further, the well-known supervisory control problem for discrete-event dynamical systems (DEDSs) formulated in its basic form is shown to be solvable as a strong model matching problem with measurable disturbances and nondeterministic reference model.

On Hybrid Petri Nets

Petri nets (PNs) are widely used to model discrete event dynamic systems (computer systems, manufacturing systems, communication systems, etc). Continuous Petri nets (in which the markings are real...

A new uncertainty measure for belief networks with applications to optimal evidential inferencing

We are concerned with the problem of measuring the uncertainty in a broad class of belief networks, as encountered in evidential reasoning applications. In our discussion, we give an explicit account of the networks concerned, and call them the Dempster-Shafer (D-S) belief networks. We examine the essence and the requirement of such an uncertainty measure based on well-defined discrete event dynamical systems concepts. Furthermore, we extend the notion of entropy for the D-S belief networks in order to obtain an improved optimal dynamical observer. The significance and generality of the proposed dynamical observer of measuring uncertainty for the D-S belief networks lie in that it can serve as a performance estimator as well as a feedback for improving both the efficiency and the quality of the D-S belief network-based evidential inferencing. We demonstrate, with Monte Carlo simulation, the implementation and the effectiveness of the proposed dynamical observer in solving the problem of evidential inferencing with optimal evidence node selection.

Non-autonomous coloured Petri net-based methodology for the dispatching process of urban fire-fighting

This paper presents the main features of our approach to the study of the dispatching process of urban fire-fighting. A new non-autonomous coloured Petri net (NCPN) method is developed and a corresponding simulation experiment is also carried out towards the practical process. Based on an extensive analysis of the urban fire-fighting process, the basic concept of discrete event dynamic systems as well as Petri net theory is introduced. In this way, the NCPN method is extended and applied to set up systematic simulation model. It enables the modelling and simulation analysis for the dispatching process of the Shanghai 119 Command Center. Statistical analysis has also been completed involving the three aspects “object, resource and activity” for 13563 fires which took place in the Shanghai Municipality from 1992 to 1997. It furnishes the corresponding key parameters and key random variable models. Under a background of the practical dispatching process of fire-fighting in the Shanghai Municipality, the relevant simulation system is built up by means of software development. The simulation experiments are made to analyze systematically the simulation environment and the model behaviour of the dispatching process. Various sorts of residential fire objects have been tested, in which the Zhenru Fire Station is taken as the fire-fighting force and residential fire cases are randomly generated in the simulation experiment

A novel supervisory control approach to switching operations for hybrid wind/diesel/battery/mains energy systems

Hybrid energy systems, integrating renewable energy technologies with diesel generators, batteries and inverters, can provide 24 h grid quality power to remote communities. Work in the Centre for Renewable Energy Systems Technology Australia (CRESTA) has been carried out to develop a new hybrid/wind/diesel/battery/mains energy system. In the system, the switching operations of different modes play an important role in the proper running of the system. From the view of discrete event dynamic systems, a novel supervisory control approach for the switching operations of modes has been explored, in which the switching actions are defined as events, switching modes as states and events take the system from one state to another. The supervisory controller for a prototype of the hybrid wind/diesel/battery/mains energy system has been designed and it has been simulated in PSCAD/EMTDC. The results reveal that this technique could facilitate the analysis and design of supervisory controllers for switching operations, particularly in the complicated hybrid energy systems.

Automatic Solving the Problem of Control Synthesis for Manufacturing Systems

A new view on manufacturing systems (MS) modelling and control synthesis is presented. MS are understood to be a kind of discrete event dynamic systems (DEDS). Petri nets (PN), frequently used for DEDS modelling, are replaced by corresponding oriented graphs (OG). The OG nodes are represented by the PN places and the OG edges involve the PN transitions. The adjacency matrix of such a graph is utilized in the DEDS control synthesis procedure. It makes possible to generate both the straight-lined systenl development (from an initial state to a prescribed terminal one) and the backtracking one (from the terminal state to the initial one). The combination both of kinds of the model development is used to find the sequence of the DEDS control vectors. Rule-based knowledge about the control task specification can be utilized in order to choose unique (the most suitable) solution.

Arithmetic State Based Computer Aided Control System Design Tool for Discrete Event Dynamic Systems

This paper presents a new computer aided control system design tool for modelling, analysing and designing discrete event dynamic systems. Characteristic for the new design tool is a technique, which results in untimed discrete event models represented by arithmetic algebra. Thus, discrete event models are represented in the same fonnalism as traditional models of systems of continuous time or discrete time nature.

Supervisory Control of Discrete Event Systems and Its Solution with the Petri Net P-Invariants

This paper deals with the supervisory control of the discrete event dynamic systems (DEDS). It contains descriptions of the different approaches to the supervisory control synthesis, their comparison and analysis. Further and implementation of the method based on the place invariants of a Petri net is described. It also outlines possibilities for further enhancements of the considered methods.

Perturbation analysis via coupling

Perturbation analysis is an efficient method for performance analysis of discrete event dynamic systems. It yields gradient information from only one sample path observation. Over the last two decades, various perturbation analysis techniques have been developed to handle a large class of problems. Coupling is a method of generating multiple random samples. It has wide range of applications in applied probability. The paper is concerned with perturbation analysis via coupling. This approach offers a great versatility of the form of gradient estimators, which is potentially useful for variance reduction and for efficient implementation. Several known perturbation analysis techniques can be reviewed as special ways of coupling. The coupling method is further applied to gradient estimation of Markov chains. The method is used not only in deriving a gradient estimator but also in its implementation. It is proved that the estimator is strongly consistent. Finally, different coupling schemes are compared using an illustrative example.

Modelling and Control of Discrete Event Dynamic Systems

Discrete event dynamic systems (DEDS) in general are <br />investigated as to their analytical models most suitable for control<br />purposes and as to the analytical methods of the control synthesis.<br /> The possibility of utilising both the selected kind of Petri nets<br />and the oriented graphs on this way is pointed out. Because many<br />times the control task specifications (like criteria, constraints, <br />special demands, etc.) are given only verbally or in another form of<br />non analytical terms, a suitable knowledge representation about<br />the specifications is needed. Special kinds of Petri nets (logical,<br />fuzzy) are suitable on this way too. Hence, the knowledge-based<br />control synthesis of DEDS can also be examined. The developed<br />graphical tools for model drawing and testing as well as for the<br />automated knowledge-based control synthesis are described and<br />illustratively presented.<br />Two approaches to modelling and control synthesis based on<br />oriented graphs are developed. They are suitable when the <br />system model is described by the special kind of Petri nets - state<br />machines. At the control synthesis the first of them is straightforward<br /> while the second one combines both the straight-lined model<br />dynamics development (starting from the given initial state <br />towards the prescribed terminal one) and the backtracking model<br />dynamics development.

Solving Transient Scheduling Problems with Constraint Programming

We are interested in Discrete Event Dynamic Systems and especially in Flexible Manufacturing Systems (FMS) and their production management. In order to master the combinatorial complexity, we adopt steady, repetitive and deterministic schedule. We have already determined an approach to compute this cyclic schedule (which corresponds to the steady state) while optimizing quantitative and qualitative performance criteria: cycle time (throughput), Work In Process, simplicity of the schedule. In order to apply this schedule we consider and compute the transient periods to start and end the production. In a previous paper [9], we gave a preliminary study ofthe transient states. We computed upper and lower bounds for the transient state, the steady state and the makespan then we established a method to optimize the makespan. In this paper, we recall some necessary assumptions and definitions for the study of the transient states then we give a heuristic for the computation and optimization of the makespan.

Fault-tolerant supervisory control under C, D observability and its application

In this paper, a discrete-event dynamical system (DEDS) approach is employed to build a fault-tolerant system under partial observation with some diagnostic schemes. We address the issue of detectability for state identification and observability for achievable legal languages in DEDSs. Especially, we introduce C, D-observability conditions to determine the observability in view of supervisor synthesis. Based upon these, we study the diagnostic problems and the construction of fault-tolerant supervisory control systems with partial observations through the behavioural analysis upon a discrete-event model. A case study of a plasma etching system is described to illustrate the proposed approach.

Triggered Concurrent Batch Arrivals and Batch Departuresin Queueing Networks

We consider a queueing network with concurrent batch arrivals and batch services. In addition to the batch movement assumptions made in the regular queueing literature, in this paper we assume that the batch movement can also be triggered by arrivals and /or departures. Specifically, an arriving or departing batch may induce another event to occur before they are routed. This triggered event may either be the addition of a batch of customers to the network, or the removal of a batch of customers from the network. This special feature makes it useful in the study of discrete event dynamic systems with concurrent or simultaneous sequential activities. By assuming that there is an additional arrival process to the network, we show that its stationary distribution has a product form, which depends on a set of non-standard nonlinear traffic equations. Furthermore, this simple product form solution is a stochastic upper bound for the network without the additionally introduced arrivals. Besides, we show that the network satisfies a class of non-standard local balance equations.

The use of simulation in discrete-event dynamic systems design

The use of simulation as a tool to design complex stochastic systems is often inhibited by cost. We present a procedure for estimating a value for the controllable input parameter which generates a desirable output. Since the output has to be matched by varying the input parameter, an iterative method of solution is applied. The proposed solution algorithm is based on Newton's method using a single-run simulation approach to estimate the needed derivative. The major contribution of this paper is to provide a framework for arriving at a target value for product, process and service attributes through Monte Carlo experiments. The effectiveness of the proposed procedure is demonstrated by determining a desirable service rate in a queueing system with known analytical solution.

On-line tracing supervisory control of discrete-event dynamic systems based on outlooking

The conventional off-line approach to supervisor synthesis for discrete-event dynamic systems contains critical drawbacks in building overall automata models and calculating the complete control policy for these models. To resolve the complexity of this off-line approach, the supervisory control scheme based on limited lookahead control policies was proposed by Chung et al. and improved by Kumar et al. recently. However, these methods do not guarantee the same closed-loop behavior as an optimal off-line solution. Therefore, we propose an on-line tracing supervisory control scheme founded on component discrete-event models, which ensures the same closed-loop language as an optimal off-line scheme.

Modelling and analysis of a class of production processes with quality-checking

In this paper, the production processes with quality-checking are considered as a class of nondeterministic Discrete Event Dynamic Systems (DEDS) where point probability distributions are assumed, and studied in a generalized temporal logic framework. Based on the temporal model(TM), the reachability and qualitative properties of the TM are analyzed, and the synthesis problem of TMs is also discussed. The plant, controller, and the desired closed system behavior are specified in temporal logic formulas, and the problem is verified that the specifications of the desired closed loop system behavior can be deduced from the descriptions of the plant and the controller.

Design, simulation, and optimal control for the Fab 30 wafer fabrication facility

The paper introduces a methodology for the optimal control of stochastic discrete event dynamic systems (SDEDS). In this methodology, performance analysis (PA) techniques are used to design state observer of SDEDS. System identification, sensitivity analysis and predictive control techniques lead to an optimal control system design for SDEDS.

Performance Optimization of a Class of Discrete Event Dynamic Systems Using Calculus of Variations Techniques

We explore an approach involving the use of calculus of variations techniques for discrete event dynamic system (DEDS) performance optimization problems. The approach is motivated by the observation that such problems can be described by separable cost functions and recursive dynamics of the same form as that used to describe conventional discrete-time continuous-variable optimal control problems. Three important difficulties are that DEDS are generally stochastic, their dynamics typically involve max and min operations, which are not everywhere differentiable, and the state variables are often discrete. We demonstrate how to overcome these difficulties by applying the approach to a transportation problem, modeled as a polling system, where we are able to derive an explicit and intuitive analytic expression for an optimal control policy.

Discrete-event dynamic systems

The supervisory control theory of discrete-event dynamic systems (DEDS), first introduced by Ramadge and Wonham, is based on an automata concept. Given a process, the objective of this theory is to design a supervisor in such a way that the process coupled with the supervisor behaves according to various constraints. In this framework, the process is assumed to evolve spontaneously and the supervisor can only prevent some events from occurring, but cannot force them. In fact, most processes require the addition of an external control agent that forces some events to occur. This has led us to the supervised control concept where control and supervision are separated. This provides a hierarchical frame, thus enabling us to formalize and to systematize the transition from the synthesis to the implementation of the control. In the paper, Grafcet is intensively used for the supervision and the control design.