Wyniki wyszukiwania - BazTech

1

Max-plus algebra as a tool to modelling and performance analysis of manufacturing systems

Stańczyk J.

Operations Research and Decisions

|

2018

|

Vol. 28, No. 3

77--97

EN

This contribution discusses the usefulness of (max, +) algebra as a mathematical framework for a class of manufacturing systems. This class can be described as dynamic and asynchronous, where the state transitions are initiated by events that occur at di screte instants of time. An event corresponds to the start or the end of an activity. Such systems are known as discrete event systems (DES). An overview of the concepts of modelling and analysis using the (max, +) algebra approach to DES has been given. Also, examples of manufacturing systems have been provided to illustrate the potential of this approach. The type of production process used, such as serial line, assembly line, etc., influences the modelling of different basic manufacturing systems. We have also presented the impact of the capacity of interoperable buffers. Based on an analytical model, effectiveness and performance indexes have been evaluated.

2

Zastosowanie max-plus algebry w modelowaniu i analizie efektywności systemów produkcyjnych

Stańczyk J.

Zarządzanie Przedsiębiorstwem

|

2017

|

Vol. 20, nr 3

46--53

EN

In response to increased competition, manufacturing systems are becoming more complex in order to provide the flexibility and responsiveness required by the market. The increased complexity requires decision support tools that can provide insight into the effect of system changes on performance in an efficient and timely manner. This contribution discusses the usefulness of (max, +) algebra as a mathematical framework for a class of production systems. The class can be described as a dynamic and asynchronous where the state transitions are initiated by events that occur at discrete instants of time. An event corresponds to the start or the end of an activity. A common property of such examples is that the start of an activity depends on termination of several other activities. Such systems are known as discrete event systems (DES). In the paper an overview of the modeling and analysis concepts of the (max, +) algebra approach for DES is given. Also, an application examples from manufacturing systems are provided to illustrate the potential of this approach. Considered systems have been represented as (max, +) algebraic state space models. How to model different basic manufacturing systems depends on production type, like serial line, assembly line, etc. as well as impact of capacity of interoperable buffers have been presented. Based on an analytical model, effectiveness evaluation or performance indexes have been calculated for different configurations of the same production system. So, finally the best solution, for given criteria, has been obtained. All exemplary calculations have been made using the Max-Plus Algebra Toolbox for Matlab, the software package developed by author and available on his homepage.

3

Towards robust predictive fault-tolerant control for a battery assembly system

Seybold L., Witczak M., Majdzik P., Stetter R.

International Journal of Applied Mathematics and Computer Science

|

2015

|

Vol. 25, no. 4

849--862

EN

The paper deals with the modeling and fault-tolerant control of a real battery assembly system which is under implementation at the RAFI GmbH company (one of the leading electronic manufacturing service providers in Germany). To model and control the battery assembly system, a unified max-plus algebra and model predictive control framework is introduced. Subsequently, the control strategy is enhanced with fault-tolerance features that increase the overall performance of the production system being considered. In particular, it enables tolerating (up to some degree) mobile robot, processing and transportation faults. The paper discusses also robustness issues, which are inevitable in real production systems. As a result, a novel robust predictive fault-tolerant strategy is developed that is applied to the battery assembly system. The last part of the paper shows illustrative examples, which clearly exhibit the performance of the proposed approach.

4

Max-Plus linear system in control of data processing

Raszka J., Jamroż L.

Czasopismo Techniczne. Nauki Podstawowe

|

2014

|

R. 111, z. 2-NP

113--127

EN

The increasing complexity of information processing in distributed computer systems and microprocessors requires the use of time-saving devices and extended capacities of transmission channels. Processes in computers systems need effective processing time. This article describes an application of the theory of the Max Plus Linear System (MPLS) to controlling digital information processing and transmission time in information systems. System processes are described by an MPLS state equation and an MPLS output equation. The MPLS model makes use of formal mathematical methods of max-plus algebra which include maximization and addition operations in the domain of non-negative real numbers with the addition of minus infinity. The input data and the structure of the processes under consideration are represented by the Timed Event Graph (TEG) formalism constituting a special case of Timed Petri Nets. The suggested MPLS methods are useful for investigating selected properties of network models. They may be applied, among others, to evaluate performance criteria, cycle time, predictive control etc. This article presents the theoretical considerations used to determine the input signals controlling discrete processes, which are then illustrated with examples of numerical computations.

PL

Zwiększająca się złożoność procesów przetwarzania informacji w rozproszonych systemach komputerowych i mikroprocesorowych wymaga oszczędnego wykorzystania czasu pracy urządzeń i zwiększonej pojemności kanałów transmisyjnych. Procesy w systemach komputerowych potrzebują efektywnego czasu przetwarzania W niniejszym opracowaniu przedstawiono zastosowanie teorii max-plus liniowego systemu (MPLS) w sterowaniu czasem przetwarzania informacji i czasem transmisji informacji cyfrowej w systemach informatycznych. System procesów opisany jest w przestrzeni MPLS równaniem stanu i równaniem wyjścia. Model MPLS jest oparty na formalnych matematycznych metodach max plus algebry, które są wyposażone w operacje maksymalizacji i dodawania w dziedzinie nieujemnych liczb rzeczywistych rozszerzonych o minus nieskończoność. Dane wejściowe i struktura rozważanych procesów są określone przez formalizm czasowych sieci zdarzeń jako szczególnego przypadku czasowych sieci Petri’ego. Zaproponowane metody MPLS są użyteczne w badania wybranych właściwości sieci. Miedzy innymi mogą być one zastosowane do oceny wydajności, czasu cyklu, sterowania predykcyjnego, itp. W artykule zastosowano teoretyczne rozważania określające wejściowe sygnały sterujące procesem dyskretnym oraz przedstawiono przykładowy wyniki z numerycznych obliczeń.

5

Performance model of cyclic processes

Jamroż L., Raszka J.

Czasopismo Techniczne. Nauki Podstawowe

|

2010

|

R. 107, z. 1-NP

129-137

EN

This paper presents the use of both Petri nets and max-plus algebra formalism for modeling dynamic behaviour of system with cyclic processes. A cyclic processes system contains elements, which can operate in parallel while at the same time. They can have cooperative and competitive relationships. The research is focused on a design and control at the lowest operational level of the system. The considered processes are sequential and cyclic. As the performance evaluation measure the cycle time of the system is chosen.

PL

W artykule przedstawiono zastosowanie formalizmów sieci Petriego i max-plus algebry w modelowaniu systemu procesów cyklicznych. Procesy przebiegają równolegle, współpracują ze sobą lub współzawodniczą w dostępie do wspólnych zasobów. Rozważania przeprowadzono na poziomie sterowania operacyjnego. Oceny wydajności dokonano ze względu na czas cyklu pracy systemu.

6

The Performance Evaluation Tool for Automated Prototyping of Concurrent Cyclic Processes

Polak M., Majdzik P., Banaszak Z., Wójcik R.

Fundamenta Informaticae

|

2004

|

Vol. 60, nr 1-4

269--289

EN

This paper is addressing an issue of distributed systems designing aimed at automated prototyping of Cyclic Concurrent Processes Systems. In such systems concurrent processes compete for access to shared system resources. In order to ensure that a system is deadlock and starvation-free, certain conditions must be satisfied. In this paper, these conditions guarantee that for a given pair (an initial state, a set of dispatching rules) the system - belonging to a specific class - has a steady cyclic state. However, system designers are interested in values of performance indices, such as a rate of resources or processes utilization or the period of the system cycle. Nowadays, the values of performance indices are provided mainly as a result of a simulation process, which requires much more processor power than in case of an analytical method. Thus, in this paper the authors focus on providing a procedure that enables building analytical models of Cyclic Concurrent Processes Systems belonging to a system class considered in the paper. To reach this aim the max-plus algebra formalism is employed. Both the conditions ensuring a cyclic process flow and steps of the procedure are the basis of a software tool, which can be used by designers to prototype systems of desired values of the performance indices. Thanks to the computer program the designers receive a useful tool that helps to validate and allocate distributed control procedures, even in a complex system, which is a composition of simpler systems. The procedure together with the software tool is the main outcome of this paper.

7

Hybrid modelling and performance evaluation of switched discrete-event systems

Wang L.

Control and Cybernetics

|

2004

|

Vol. 33, no 2

311-321

EN

Motivated by the integrated complexity of real-time intelligent control and optimization of industrial/manufacturing processes, this paper discusses hybrid modelling and asymptotic periodic behavior of a class of switched discrete event systems, and shows how to evaluate the asymptotic performance/efficiency of such systems. We prove that, under some mild conditions, the switched discrete event system will achieve asymptotic periodic dynamics, and its performance/efficiency can be evaluated by calculating the eigenvalue of certain matrix in max-plus algebra. Illustrative examples are provided.