Mathematical and computer modelling of dynamical systems pdf creator
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- Parallel Dynamical Systems over Graphs and Related Topics: A Survey
- Taylor & Francis Journals
- System dynamics
Parallel Dynamical Systems over Graphs and Related Topics: A Survey
ISSN This paper introduces a method of dynamic simulation that uses icons to represent functional elements that manage energy. Each functional element is represented by a programming object in 3D animation and is connected in the common workspace to form a diagram that automatically assembles the 3D representation of the machine that is being built. The design of machines, devices and equipment encompasses two correlated processes.
One is the calculation to determine the values of the forces, torques, speeds and functional variables involved in a system. The second is the spatial organization of the elements in a three dimensional mode. In the past, the two processes were developed independently due to the computational limits experienced at first, but it is now possible to develop both processes simultaneously and see the first approximations beginning to take place. Simulation tools for machine design optimization reduce the time required for programming and conceptual design, while at the same time allowing for a deeper analysis of dynamic behavior phenomena and maximum values for decision-making.
The following is a taxonomic analysis of those simulation tools that are more related and oriented to design optimization. Simulation started in the fifties when the development of computer tools was the task of researchers with software expertise.
This same principle is currently maintained but with greater challenges; for example, nowadays toolboxes are being developed for very specific applications. The methodology developed in the sixties by the engineering professor Jay W. The method is used to analyze simulation models in several areas Forrester, through the application of a scheme known as the Forrester diagram. This language uses multiple-object elements whose dynamic is represented by differential and algebraic equations. These programming elements allow for direct communication among them, and they offer a physical perspective that brings the user closer to reality Elmqvist, Graphic design using cable-connected functional boxes and toolboxes, where an object is passed to the design area via Drag and Drop, reduces the programming time.
This extension is characterized by a graphic programming environment of block diagrams for simulation and design based on models or systems Moler, These modern programs for graphic simulation use connected block diagrams, and they have commercial libraries with mathematical and kinematic functions, among others, which allow the development of fast prototypes and validation of different dynamic systems Tian, Sevilla, Zuo, W. Currently, Open Modelica is an open-code graphic and modeled simulation environment that is also based on Modelica.
In the last 10 years there has been a tendency to pioneer companies in the field of software design development, as well as a tendency in dynamic system simulation towards the improvement of existing software rather than the creation of new tools.
The focus of these upgrades is to meet the needs of industry and academia in order to be at the leading edge of technology and carry out the kind of specialized analysis demanded by scientific progress.
This context provides an opportunity to develop dynamic simulation alternatives focused on design methods, as well as to take advantage of the thousands of commercial items that can be used in programming objects where it is possible to simultaneously connect the mathematical model with the three-dimensional model.
This paper introduces a different approach that is oriented towards the learning of the design method. The wide array of commercial elements is arranged in functional groups. A software object is built for each element in which the mathematical model and an environment of tridimensional visualization are included.
This tool has been called Sim - Methodic. The implemented methodology is presented below and is based on the basic concepts of the object-oriented programming method. Variables of potential, flow variables, symbology classification, description of the programming objects, validation of technical systems, tridimensional model, methodology of the experiment and feedback of results are considered.
This methodology enables the usual design process which focuses on the design of elements that are to be built afterwards to be inverted. It offers the possibility of seeking commercial elements that can be integrated into a more complex sub-system. This involves the methodology of design for sub-system integration that is common for short productions and prototypes.
Representative objects of the main fields of the engineering knowledge are included in Sim-Methodic. These are customized through their mathematical model and they use tridimensional representations in a CAD file. The mathematical Model-Cad pair has parameters which correspond to commercial elements.
As shown in Figure 5, the relations between subsystems or programming objects are connected by means of information streams to form diagrams that represent complex systems. Also, an animated image of the sum of all the fundamental 3D elements is obtained, as observed in Figure 8.
Each programming object that is dragged and subsequently placed by double clicking the mouse displays several windows in which digital and graphic controls and indicators are found. In addition, a window containing the 3D individual animation of the element is displayed; from there it is possible to spatially place it and each one of them is oriented to form an entire assembly with the other elements see Table 3. Each object on the Sim-Methodic library has four dependent variables that change according to time and the type of equations implemented within the object.
There is also an independent variable: time. As a result of the growing interest in the correct use of energy, the sum of wasted energy for each element has been added. This is calculated at every instant of time according to the efficiency map.
In summary, the effect that is generated by each object on the variables is presented. To avoid the confusion that might be created by a large number of inexistent lines in a real physical system, the information is correlatedly packed into only one line of information.
Figure 1 N programming objects of generic rotational system. Color classification has been widely used in the industry for several purposes; for example, to differentiate types of fluids in piping, electric resistance values, types of gas in cylinders, and types of material, among others. It is for this reason that a color code was added to the symbology of programming objects to help the user to differentiate the type of energy that is crossing the object. The implementation of colors within the programming environment makes it possible for the user to identify the field of knowledge of the several function holders.
Object-oriented programming is characterized by a color code according to the type of energy they use. Table 1 shows the color code for the type of energy and the energy in the matter. Table 1 Color code for several types of energy and matter. Programming objects can be classified according to their function. This is how the physical laws that describe their behavior independent of the type of energy they work with are known.
The main types of function that are managed in a system are: sources of energy, energy converters, motion converters in mechanics , energy transformers, switches and transmitters. Due to the importance of the correct use of energy, in this case energy destructors brakes and anti-destructors have been introduced bearings, linear guides, ball screws, among others.
In Table 2 objects which are topologically similar are observed, but they work with different types of energy. The icon that represents a programming object is divided into two sections as shown in Figure 2. The color of section A indicates the type of energy the object is fed with. Section B serves to represent the type of energy the element delivers. Section C shows the symbolic representation of the object. A text with various letters that show the type of function of the object is overlapped in sections A and B.
For example, a two-wheel gear in section A and B only has a dark green color Table 1 , since the input and output of the element is mechanic rotational energy. In turn, section C has a symbolic representation of a pair of gears.
When the objects use two different kinds of energy, as is the case of the electrical motor which has an input of electrical energy and an output of rotational mechanical energy, section A is yellow in color Table 1 and section B is dark green, which corresponds to the type of energy that delivers the object.
Figure 2 General representation of the programming objects. Between each object and the next one there is a cluster in which information travels; among the most important information here are the variables of potential P.
V , the variables of flow F. V , and the accumulated mass or inertia. Other variables depend on the type of system. Each object, according to its nature, modifies the potential variable, but the flow variable remains constant unless it is a distributor or a collector that does the opposite.
Given that a system can have multiple interlaced cycles, there is a connection that gives feedback of the results of the iteration in order to convert them into initial values of the next iteration between the first and the last object of a cycle. The type of energy that the output terminal of an object uses should coincide with the type of energy of the input terminal of the adjacent programming object same color.
Figure 3 presents a flow chart of the procedure that follows Sim-Methodic for the design of machines or equipment. The user establishes the selection of the programming objects, initial parameters and conditions.
The relations among objects are defined through thread connections among symbolic icons used for the design of machines or equipment. Figure 3 Diagram of the process for developing a design with Sim-Methodic. The traditional design for mechanical engineers and other related programs makes use of safety factors that are empirically found and are represented in charts according to the type of work the team is conducting.
The objective is to keep a record of those dynamic loads that are not described by algebraic equations and with which the designs are measured. Due to their empirical nature, they provide low efficiency, hence the need to use modern tools.
In modern design, system modeling and simulation enable the identification of torque peaks or strength in terms of time, frequency and other relevant factors such as fatigue, which affect the load of a part or a system.
As a result, the size of the elements is set according to need, leading to a reduction in the cost of manufacturing. The goal of Sim-Methodic is to offer an innovative learning tool that supports the development of designs in the engineering field, without the need for advanced knowledge on the part of the user.
This makes it an appropriate application for undergraduate students whose detailed knowledge of technical and industrial systems is still limited.
Furthermore, the equipment that students are familiar with in university laboratories is of a generic nature. This tool provides students with the possibility to familiarize themselves with, study and interact virtually with other types of equipment that are more similar to that used in modern day industry. To illustrate, the metal-mechanic laboratories of the EAFIT University only have rotary-screw compressors; the tool we present allows the student to make designs using other types of industrial compressors such as piston compressors, centrifugal compressors and scroll-type compressors.
The implementation of this tool is directly related to the knowledge acquired through subjects that study the calculation of machine elements, material selection, dynamic systems and design method. It allows students to develop generic designs aimed at the productive and industrial sectors, facilitating analysis of how the system works and enabling students to draw their own conclusions, which leads to continuous learning.
The first stage in using this learning tool in the classroom is to deliver a general explanation of the main functional elements of a machine or piece of equipment and associate them with the Sim-Methodics programming objects.
A good example of this would be to provide the mathematical and dynamic explanation of a conveyor, a gearbox or an electric engine. Next, students join up these three programming objects and design, for example, a food conveyor and seek an optimal combination of speed versus energetic efficiency through the change of parameters in the simulation. The possibility of real-time observation of the behavior of the results of the design, depending on the change of each parameter, provides the student with an understanding of how technical systems work together and how the changes made to the system can optimize the results.
There are representative and didactic examples used in teaching machine design, which are found in most textbooks. Examples of this are the motorcycle and the car, which are very useful for studying machines with highly efficient energy converters combustion engine and because they use switches clutch.
Electric transport as a non-pollutant energy requires the design of gearboxes that include the differential transaxle. All the above-mentioned elements are included in the Sim-Methodic tool so that it is possible to develop academic examples focused on the industry. In the following exercise, Figure 4 shows how Sim-Methodic works.
An example taken from the mechanical engineering field is presented in order to look at the kinematic, dynamic relations and the parameters associated with each programming object.
A general design is validated and is connected to a common mechanism for several kinds of industrial equipment; in this case, the connecting rod, crank and slider slider crank have a dynamic behavior that provides a variable mechanical advantage regarding the turning angle.
Taylor & Francis Journals
System dynamics refers to a type of computer modeling and computer simulation created in the s by Dr. Jay W. Forrester of the Massachusetts Institute of Technology. It originally was used in management and engineering, but is now used to model all sorts of simpler or complex systems. A well know example is the Club of Rome model World model wikipedia developed for the limits to growth report by Meadows et al.
Juan A. Aledo, Silvia Martinez, Jose C. In discrete processes, as computational or genetic ones, there are many entities and each entity has a state at a given time. The update of states of the entities constitutes an evolution in time of the system, that is, a discrete dynamical system. The relations among entities are usually represented by a graph.
The paper deals with the problem of switched dynamical systems modeling especially in DC-DC converters case study consideration. It presents two approaches to describe accurately the behavior of this class of systems. A comparative study, between the obtained results and those of other techniques from the literature, is given to evaluate the performances of the studied approaches. This is a preview of subscription content, access via your institution. Rent this article via DeepDyve.
July , Volume 26, Issue 4 · Adieu and welcome · Editor's note · Modelling and analysis of haemoglobin catalytic reaction kinetic.
Submitted as: methods for assessment of models 26 Oct Estimating parameters of chaotic geophysical models is challenging due to these models' inherent unpredictability. With temporally sparse long-range observations, these models cannot be calibrated using standard least squares or filtering methods. Obvious remedies, such as averaging over temporal and spatial data to characterize the mean behavior, do not capture the subtleties of the underlying dynamics. We perform Bayesian inference of parameters in high-dimensional and computationally demanding chaotic dynamical systems by combining two approaches: i measuring model-data mismatch by comparing chaotic attractors, and ii mitigating the computational cost of inference by using surrogate models.
Flow diagrams are a common tool used to help build and interpret models of dynamical systems, often in biological contexts such as consumer-resource models and similar compartmental models. Typically, their usage is intuitive and informal. Here, we present a formalized version of flow diagrams as a kind of weighted directed graph which follow a strict grammar, which translate into a system of ordinary differential equations ODEs by a single unambiguous rule, and which have an equivalent representation as a relational database. Drawing a diagram within this strict grammar encourages a mental discipline on the part of the modeler in which all dynamical processes of a system are thought of as interactions between dynamical species that draw parcels from one or more source species and deposit them into target species according to a set of transformation rules. From these rules, the net rate of change for each species can be derived.
Dynamical systems theory is an area of mathematics used to describe the behavior of complex dynamical systems , usually by employing differential equations or difference equations. When differential equations are employed, the theory is called continuous dynamical systems. From a physical point of view, continuous dynamical systems is a generalization of classical mechanics , a generalization where the equations of motion are postulated directly and are not constrained to be Euler—Lagrange equations of a least action principle.