Modelling single-product production systems using state equations: Continuous systems and discrete systems that can be represented by continuous models

2000 ◽  
Vol 31 (12) ◽  
pp. 1627-1638
Author(s):  
Michel Ferney
Keyword(s):  
Production Systems ◽  
Discrete Systems ◽  
Continuous Systems ◽  
State Equations ◽  
Single Product ◽  
Continuous Models

scholarly journals Hidden Attractors in Discrete Dynamical Systems

Entropy ◽  
2021 ◽  
Vol 23 (5) ◽  
pp. 616
Author(s):  
Marek Berezowski ◽  
Marcin Lawnik
Keyword(s):  
Dynamical Systems ◽  
Chaos Theory ◽  
Scientific Literature ◽  
Discrete Systems ◽  
Discrete Dynamical Systems ◽  
Continuous Systems ◽  
Hidden Attractors ◽  
Negative Effects ◽  
Chemical Reactors ◽  
Points Of View

Research using chaos theory allows for a better understanding of many phenomena modeled by means of dynamical systems. The appearance of chaos in a given process can lead to very negative effects, e.g., in the construction of bridges or in systems based on chemical reactors. This problem is important, especially when in a given dynamic process there are so-called hidden attractors. In the scientific literature, we can find many works that deal with this issue from both the theoretical and practical points of view. The vast majority of these works concern multidimensional continuous systems. Our work shows these attractors in discrete systems. They can occur in Newton’s recursion and in numerical integration.

Some Possibilities of Modeling Colored Petri Nets

2021 ◽  
pp. 77-91
Author(s):  
Goharik Petrosyan ◽  
Armen Gaboutchian ◽  
Vladimir Knyaz
Keyword(s):  
Petri Nets ◽  
Petri Net ◽  
Optimal Allocation ◽  
Production Systems ◽  
Oriented Graph ◽  
Discrete Systems ◽  
Colored Petri Nets ◽  
Venn Diagram ◽  
Colored Petri Net ◽  
Language Class

Petri nets are a mathematical apparatus for modelling dynamic discrete systems. Their feature is the ability to display parallelism, asynchrony and hierarchy. First was described by Karl Petri in 1962 [1,2,8]. The Petri net is a bipartite oriented graph consisting of two types of vertices - positions and transitions connected by arcs between each other; vertices of the same type cannot be directly connected. Positions can be placed by tags (markers) that can move around the network. [2] Petri Nets (PN) used for modelling real systems is sometimes referred to as Condition/Events nets. Places identify the conditions of the parts of the system (working, idling, queuing, and failing), and transitions describe the passage from one state to another (end of a task, failure, repair...). An event occurs (a transition fire) when all the conditions are satisfied (input places are marked) and give concession to the event. The occurrence of the event entirely or partially modifies the status of the conditions (marking). The number of tokens in a place can be used to identify the number of resources lying in the condition denoted by that place [1,2,8]. Coloured Petri nets (CPN) is a graphical oriented language for design, specification, simulation and verification of systems [3-6,9,15]. It is in particular well-suited for systems that consist of several processes which communicate and synchronize. Typical examples of application areas are communication protocols, distributed systems, automated production systems, workflow analysis and VLSI chips. In the Classical Petri Net, tokens do not differ; we can say that they are colourless. Unlike standard Petri nets in Colored Petri Net of a position can contain tokens of arbitrary complexity, such as lists, etc., that enables modelling to be more reliable. The article is devoted to the study of the possibilities of modelling Colored Petri nets. The article discusses the interrelation of languages of the Colored Petri nets and traditional formal languages. The Venn diagram, which the author has modified, shows the relationship between the languages of the Colored Petri nets and some traditional languages. The language class of the Colored Petri nets includes a whole class of Context-free languages and some other classes. The paper shows modelling the task synchronization Patil using Colored Petri net, which can't be modeled using well- known operations P and V or by classical Petri network, since the operations P and V and classical Petri networks have limited mathematical properties which do not allow to model the mechanisms in which the process should be synchronized with the optimal allocation of resources.

Simulation of Multiple Cell Population Dynamics Using a 3-D Cellular Automata Model for Tissue Growth

2012 ◽  
pp. 201-220
Author(s):  
Belgacem Ben Youssef ◽  
Lenny Tang
Keyword(s):  
Population Dynamics ◽  
Cellular Automata ◽  
Temporal Dynamics ◽  
Discrete Systems ◽  
Tissue Growth ◽  
State Transitions ◽  
Extended Model ◽  
Alternative Approach ◽  
Continuous Models ◽  
Multiple Cell

In this paper, the authors describe a computational model for the growth of multicellular tissues using a discrete approach based on cellular automata to simulate the tissue growth rates and population dynamics of multiple populations of proliferating and migrating cells. Each population of cells has its own division, motion, collision, and aggregation characteristics. These random dynamic processes can be modeled by appropriately choosing the governing rules of the state transitions of each computational site. This extended model contains a number of system parameters that allow their effects on the volume coverage, the overall tissue growth rate, and some other aspects of cell behavior like the average speed of locomotion to be explored. These discrete systems provide an alternative approach to continuous models for the purpose of describing the temporal dynamics of complex systems.

Inverse Problems in Vibration

1986 ◽  
Vol 39 (7) ◽  
pp. 1013-1018 ◽  
Author(s):  
Graham M. L. Gladwell
Keyword(s):  
Inverse Problems ◽  
Eigenvalue Problems ◽  
Discrete Systems ◽  
Free Vibrations ◽  
Continuous Systems ◽  
Thin Beam ◽  
Inverse Eigenvalue Problems ◽  
Elastic Systems ◽  
Inverse Eigenvalue ◽  
Sturm Liouville

This article concerns infinitesimal free vibrations of undamped elastic systems of finite extent. A review is made of the literature relating to the unique reconstruction of a vibrating system from natural frequency data. The literature is divided into two groups—those papers concerning discrete systems, for which the inverse problems are closely related to matrix inverse eigenvalue problems, and those concerning continuous systems governed either by one or the other of the Sturm–Liouville equations or by the Euler–Bernoulli equation for flexural vibrations of a thin beam.

Non-stationary dynamic system characteristics recovery from three test signals

2020 ◽  
pp. 9-15
Author(s):  
Ilia V. Boikov ◽  
Nikolay P. Krivulin
Keyword(s):  
Dynamical Systems ◽  
Impulse Response ◽  
Discrete Systems ◽  
Exact Formula ◽  
Algebraic Expression ◽  
Continuous Systems ◽  
Exact Reconstruction ◽  
Input Signals ◽  
The Laplace Transform ◽  
System Output

Algorithms of exact restoration in an analytical form of dynamic characteristics of non-stationary dynamic systems are constructed. Non-stationary continuous dynamical systems modeled by Volterra integral equations of the first kind and non-stationary discrete dynamical systems modeled by discrete analogues of Volterra integral equations of the first kind are considered.The article consists of an introduction and three sections: 1) The exact restoration of the dynamic characteristics of continuous systems, 2) The restoration of the transition characteristics of discrete systems, 3) Conclusions. The introduction provides a statement of the problem and provides an overview of dynamical systems for which algorithms for exact reconstruction in ananalytical form of the impulse response (in the case of continuous systems) and the transition characteristic (in the case of discrete systems) are constructed. In the first section, the algorithm is constructed for the exact reconstruction of the impulse response of an non-stationary continuous dynamic system from three interconnected input signals. The first signal may be arbitrary, the second and third signals are associated with the first signal by integral operator. The exact formula for the Laplace transform of the impulse response, represented by an algebraic expression from the Laplace transform of the system output signals, is given. A model example illustrating the effectiveness of the algorithm is given. The practical application of the presented algorithm isdiscussed. In the second section, an algorithm is constructed for the exact reconstruction of the transition response of a non-stationary discrete dynamical system from three input signals that are interconnected. The first signal may be arbitrary, the second and third signals are associated with the first summing operator. The exact formula of the Z-transform of the transition characteristic is presented, which is represented by an algebraic expression from the Z-transform of the system output signals. A model example is given. The “Conclusions” section provides a summary of the results presented in the article and describes the dynamic systems to which the proposed algorithms can be extended.

Simulation of Multiple Cell Population Dynamics Using a 3-D Cellular Automata Model for Tissue Growth

2010 ◽  
Vol 1 (3) ◽  
pp. 1-18 ◽  
Author(s):  
Belgacem Ben Youssef ◽  
Lenny Tang
Keyword(s):  
Population Dynamics ◽  
Cellular Automata ◽  
Temporal Dynamics ◽  
Discrete Systems ◽  
Tissue Growth ◽  
State Transitions ◽  
Extended Model ◽  
Alternative Approach ◽  
Continuous Models ◽  
Multiple Cell

In this paper, the authors describe a computational model for the growth of multicellular tissues using a discrete approach based on cellular automata to simulate the tissue growth rates and population dynamics of multiple populations of proliferating and migrating cells. Each population of cells has its own division, motion, collision, and aggregation characteristics. These random dynamic processes can be modeled by appropriately choosing the governing rules of the state transitions of each computational site. This extended model contains a number of system parameters that allow their effects on the volume coverage, the overall tissue growth rate, and some other aspects of cell behavior like the average speed of locomotion to be explored. These discrete systems provide an alternative approach to continuous models for the purpose of describing the temporal dynamics of complex systems.

Discrete Finite Element Method Application for Analysis of Unreinforced-Masonry Underground Structures

2015 ◽  
Vol 2522 (1) ◽  
pp. 131-136 ◽  
Author(s):  
Iraj H. P. Mamaghani
Keyword(s):  
Finite Element Method ◽  
Finite Element ◽  
Discrete Systems ◽  
Unreinforced Masonry ◽  
Continuous Systems ◽  
Underground Structures ◽  
Interface Elements ◽  
Underground Openings ◽  
Discrete Finite Element ◽  
Element Method

Unreinforced-masonry underground structures are composed of a finite number of distinct interacting blocks that have length scales relatively comparable with the underground openings of interest. Therefore, these structures are ideal candidates for modeling as discrete systems instead of as continuous systems. The discrete finite element method (DFEM) developed by the author to model discontinuous media consisting of blocks of arbitrary shapes was adopted for the static analysis of unreinforced masonry underground structures. The developed DFEM was based on the principles of the finite element method incorporating contact elements. The DFEM considers blocks as subdomains and represents them by solid elements. Contact elements, which are far superior to joint or interface elements, are used to model block interactions such as sliding or separation. In this study, the DFEM is briefly reviewed; then, through some illustrative examples, the applicability of the DFEM to the analysis of unreinforced-masonry underground structures is examined and discussed. It is shown that the DFEM provides an efficient tool for researchers and practical engineers in designing, analyzing, and studying the behavior of unreinforced masonry underground structures under static loading.

scholarly journals Optimised control using proportional-integral-derivative controller tuned using internal model control

2020 ◽  
Vol 10 (3) ◽  
pp. 2452
Author(s):  
B. Mabu Sarif ◽  
D. V. Ashok Kumar ◽  
M. Venu Gopala Rao
Keyword(s):  
Pid Controller ◽  
Time Delays ◽  
Internal Model ◽  
Discrete Systems ◽  
Internal Model Control ◽  
Tuning Parameter ◽  
Continuous Systems ◽  
Proportional Integral Derivative ◽  
Proportional Integral ◽  
Model Control

Time delays are generally unavoidable in the designing frameworks for mechanical and electrical systems and so on.. In both continuous and discrete schemes, the existence of delay creates undesirable impacts on the under-thought which forces exacting constraints on attainable execution.The presence of delay confounds the design structure procedure also. It makes continuous systems boundless dimensional and also extends the readings in discrete systems fundamentally. As the Proportional-Integral-Derivative (PID) controller based on internal model control is essential and strong to address the vulnerabilities and aggravations of the model. But for an real industry process, they are less susceptible to noise than the PID controller.It results in just one tuning parameter which is the time constant of the closed-loop system λ, the internal model control filter factor.It additionally gives a decent answer for the procedure with huge time delays. The design of the PID controller based on the internal model control, with approximation of time delay using Pade’ and Taylor’s series is depicted in this paper. The first order filter used in the design provides good set-point tracking along with disturbance rejection.

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