Search results for: integral equation.

Authors: Irena Markovska, Nikolai Zaicev, Bogdan Bogdanov, Dimitar Georgiev, Yancho Hristov

Abstract:

The present paper deals with problems related to the possibilities to use fractal systems to solve some important scientific and practical problems connected with filtering and separation of aqueous phases from organic ones. For this purpose a special separator have been designed. The reactor was filled with a porous material with fractal dimension, which is an integral part of the set for filtration and separation of emulsions. As a model emulsion hexadecan mixture with water in equal quantities (1:1) was used. We examined the hydrodynamics of the separation of the emulsion at different rates of submission of the entrance of the reactor.

Keywords: pilot reactor, fractal systems, separation, emulsions

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Authors: Aye Aye Mon

Abstract:

The application of a simple microcontroller to deal with a three variable input and a single output fuzzy logic controller, with Proportional – Integral – Derivative (PID) response control built-in has been tested for an automatic voltage regulator. The fuzzifiers are based on fixed range of the variables of output voltage. The control output is used to control the wiper motor of the auto transformer to adjust the voltage, using fuzzy logic principles, so that the voltage is stabilized. In this report, the author will demonstrate how fuzzy logic might provide elegant and efficient solutions in the design of multivariable control based on experimental results rather than on mathematical models.

Keywords: Fuzzy logic system, PID Controller, control systems, controlled A V R

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Authors: Ahmad Fahim Nasiry, Shigeo Honma

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We examine two-dimensional oil displacement by water in a petroleum reservoir. The pore fluid is immiscible, and the porous media is homogenous and isotropic in the horizontal direction. Buckley-Leverett theory and a combination of Laplacian and Darcy’s law are used to study the fluid flow through porous media, and the Laplacian that defines the dispersion and diffusion of fluid in the sand using heavy oil is discussed. The reservoir is homogenous in the horizontal direction, as expressed by the partial differential equation. Two main factors which are observed are the water saturation and pressure distribution in the reservoir, and they are evaluated for predicting oil recovery in two dimensions by a physical and mathematical simulation model. We review the numerical simulation that solves difficult partial differential reservoir equations. Based on the numerical simulations, the saturation and pressure equations are calculated by the iterative alternating direction implicit method and the iterative alternating direction explicit method, respectively, according to the finite difference assumption. However, to understand the displacement of oil by water and the amount of water dispersion in the reservoir better, an interpolated contour line of the water distribution of the five-spot pattern, that provides an approximate solution which agrees well with the experimental results, is also presented. Finally, a computer program is developed to calculate the equation for pressure and water saturation and to draw the pressure contour line and water distribution contour line for the reservoir.

Keywords: Numerical simulation, immiscible, finite difference, IADI, IADE, waterflooding.

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Authors: Mohammad Saleh Tavazoei, Mohammad Haeri

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This paper presents comparison among methods of determination of the characteristic polynomial coefficients. First, the resultant systems from the methods are compared based on frequency criteria such as the closed loop bandwidth, gain and phase margins. Then the step responses of the resultant systems are compared on the basis of the transient behavior criteria including overshoot, rise time, settling time and error (via IAE, ITAE, ISE and ITSE integral indices). Also relative stability of the systems is compared together. Finally the best choices in regards to the above diverse criteria are presented.

Keywords: Characteristic Polynomial, Transient Response, Filters, Stability.

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Authors: Tohru Kawabe

Abstract:

In this paper, a 2DOF (two degrees of freedom) PID (Proportional-Integral-Derivative) controller based on MPC (Model predictive control) algorithm fo slip suppression of EV (Electric Vehicle) under braking is proposed. The proposed method aims to improve the safety and the stability of EVs under braking by controlling the wheel slip ration. There also include numerical simulation results to demonstrate the effectiveness of the method.

Keywords: Model predictive control, PID controller, Two degrees of freedom, Electric Vehicle, Slip suppression.

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Authors: C. S. Bianca Sabrina, N. Egidio Raimundo, L. Alexandre Baratella, C. H. João Paulo

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This paper aims to present a study, with the theoretical concepts and applications of the Quadcopter, using the MATLAB simulator. In order to use this tool, the study of the stability of the drone through a Proportional - Integral - Derivative (PID) controller will be presented. After the stability study, some tests are done on the simulator and its results will be presented. From the mathematical model, it is possible to find the Newton-Euler angles, so that it is possible to stabilize the quadcopter in a certain position in the air, starting from the ground. In order to understand the impact of the controllers gain values on the stabilization of the Euler-Newton angles, three conditions will be tested with different controller gain values.

Keywords: Controllers, drones, quadcopter, stability.

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Authors: M. Giannopoulou, I. Roukounis, A. Roukouni.

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Geographical Information Systems are an integral part of planning in modern technical systems. Nowadays referred to as Spatial Decision Support Systems, as they allow synergy database management systems and models within a single user interface machine and they are important tools in spatial design for evaluating policies and programs at all levels of administration. This work refers to the creation of a Geographical Information System in the context of a broader research in the area of influence of an under construction station of the new metro in the Greek city of Thessaloniki, which included statistical and multivariate data analysis and diagrammatic representation, mapping and interpretation of the results.

Keywords: Databases, Geographical information systems (GIS), Land-use planning, Metro stations

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Authors: H. Khanfari, M. Johari Fard

Abstract:

Dealing with carbonate reservoirs can be mind-boggling for the reservoir engineers due to various digenetic processes that cause a variety of properties through the reservoir. A good estimation of the reservoir heterogeneity which is defined as the quality of variation in rock properties with location in a reservoir or formation, can better help modeling the reservoir and thus can offer better understanding of the behavior of that reservoir. Most of reservoirs are heterogeneous formations whose mineralogy, organic content, natural fractures, and other properties vary from place to place. Over years, reservoir engineers have tried to establish methods to describe the heterogeneity, because heterogeneity is important in modeling the reservoir flow and in well testing. Geological methods are used to describe the variations in the rock properties because of the similarities of environments in which different beds have deposited in. To illustrate the heterogeneity of a reservoir vertically, two methods are generally used in petroleum work: Dykstra-Parsons permeability variations (V) and Lorenz coefficient (L) that are reviewed briefly in this paper. The concept of Lorenz is based on statistics and has been used in petroleum from that point of view. In this paper, we correlated the statistical-based Lorenz method to a petroleum concept, i.e. Kozeny-Carman equation and derived the straight line plot of Lorenz graph for a homogeneous system. Finally, we applied the two methods on a heterogeneous field in South Iran and discussed each, separately, with numbers and figures. As expected, these methods show great departure from homogeneity. Therefore, for future investment, the reservoir needs to be treated carefully.

Keywords: Carbonate reservoirs, heterogeneity, homogeneous system, Dykstra-Parsons permeability variations (V), Lorenz coefficient (L).

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Authors: Andrey V. Timofeev

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The paper presents new results concerning selection of optimal information fusion formula for ensembles of C-OTDR channels. The goal of information fusion is to create an integral classificator designed for effective classification of seismoacoustic target events. The LPBoost (LP-β and LP-B variants), the Multiple Kernel Learning, and Weighing of Inversely as Lipschitz Constants (WILC) approaches were compared. The WILC is a brand new approach to optimal fusion of Lipschitz Classifiers Ensembles. Results of practical usage are presented.

Keywords: Lipschitz Classifier, Classifiers Ensembles, LPBoost, C-OTDR systems, ν-OTDR systems.

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Authors: Qingqing Wang, Shouming Zhong

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Utilizing the Lyapunov functional method and combining linear matrix inequality (LMI) techniques and integral inequality approach (IIA) to analyze the global asymptotic stability for delayed neural networks (DNNs),a new sufficient criterion ensuring the global stability of DNNs is obtained.The criteria are formulated in terms of a set of linear matrix inequalities,which can be checked efficiently by use of some standard numercial packages.In order to show the stability condition in this paper gives much less conservative results than those in the literature,numerical examples are considered.

Keywords: Neural networks, Globally asymptotic stability , LMI approach , IIA approach , Time-varying delay.

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Authors: Dominykas Broga

Abstract:

Until recently it would have been unusual to consider classifying population movements and refugees as security problem. However, efforts at shaping our world to make ourselves secure have paradoxically led to ever greater insecurity. The feeling of uncertainty, pertinent throughout all discourses of security, has led to the creation of security production into seemingly benign routines of everyday life. Yet, the paper argues, neither of security discourses accounted for, disclosed and challenged the fundamental aporias embedded in Western security narratives. In turn, the paper aims to unpick the conventional security wisdom, which is haunted with strong ontologies, embedded in the politics of Orientalism, and (in)security nexus. The paper concludes that current security affair conceals the integral impossibility of fulfilling its very own promise of assured security. The paper also provides suggestions about alternative security discourse based on mutual dialogue.

Keywords: Identity, (in)security, migration, ontology

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Authors: Jožef Ritonja, Bojan Grčar, Boštjan Polajžer

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In recent years, electricity trade between neighboring countries has become increasingly intense. Increasing power transmission over long distances has resulted in an increase in the oscillations of the transmitted power. The damping of the oscillations can be carried out with the reconfiguration of the network or the replacement of generators, but such solution is not economically reasonable. The only cost-effective solution to improve the damping of power oscillations is to use power system stabilizers. Power system stabilizer represents a part of synchronous generator control system. It utilizes semiconductor’s excitation system connected to the rotor field excitation winding to increase the damping of the power system. The majority of the synchronous generators are equipped with the conventional power system stabilizers with fixed parameters. The control structure of the conventional power system stabilizers and the tuning procedure are based on the linear control theory. Conventional power system stabilizers are simple to realize, but they show non-sufficient damping improvement in the entire operating conditions. This is the reason that advanced control theories are used for development of better power system stabilizers. In this paper, the adaptive control theory for power system stabilizers design and synthesis is studied. The presented work is focused on the use of model reference adaptive control approach. Control signal, which assures that the controlled plant output will follow the reference model output, is generated by the adaptive algorithm. Adaptive gains are obtained as a combination of the "proportional" term and with the σ-term extended "integral" term. The σ-term is introduced to avoid divergence of the integral gains. The necessary condition for asymptotic tracking is derived by means of hyperstability theory. The benefits of the proposed model reference adaptive power system stabilizer were evaluated as objectively as possible by means of a theoretical analysis, numerical simulations and laboratory realizations. Damping of the synchronous generator oscillations in the entire operating range was investigated. Obtained results show the improved damping in the entire operating area and the increase of the power system stability. The results of the presented work will help by the development of the model reference power system stabilizer which should be able to replace the conventional stabilizers in power systems.

Keywords: Power system, stability, oscillations, power system stabilizer, model reference adaptive control.

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Authors: Kho Mei Ye, Hamzah Abdul Rahman

Abstract:

This paper provides some thoughts about the lack of attentiveness of building commissioning in the construction industry and the lack of handling in project commissioning as an integral part of the project life-cycle. Many have perceived commissioning as the problem solving process of a project, rather than the start up of the equipment, or the handing over of the project to the client. Therefore, there is a lack of proper attention in the planning of commissioning as a vital part of the project life-cycle. This review paper aims to highlight the benefits of building commissioning and to propose the lacking of knowledge gap on building commissioning. Finally, this paper hopes to propose the shift of focus on this matter in future research.

Keywords: building, commissioning, construction, delay

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Authors: Kamran Turkoglu, Ugur Ozdemir, Melike Nikbay, Elbrous M. Jafarov

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In this paper, an automatic control system design based on Integral Squared Error (ISE) parameter optimization technique has been implemented on longitudinal flight dynamics of an UAV. It has been aimed to minimize the error function between the reference signal and the output of the plant. In the following parts, objective function has been defined with respect to error dynamics. An unconstrained optimization problem has been solved analytically by using necessary and sufficient conditions of optimality, optimum PID parameters have been obtained and implemented in control system dynamics.

Keywords: Optimum Design, KKT Conditions, UAV, Longitudinal Flight Dynamics, ISE Parameter Optimization.

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Authors: Shilpi Lavania, Deepak Nagaria

Abstract:

A mixed method for model order reduction is presented in this paper. The denominator polynomial is derived by matching both Markov parameters and time moments, whereas numerator polynomial derivation and error minimization is done using Genetic Algorithm. The efficiency of the proposed method can be investigated in terms of closeness of the response of reduced order model with respect to that of higher order original model and a comparison of the integral square error as well.

Keywords: Model Order Reduction (MOR), control theory, Markov parameters, time moments, genetic algorithm, Single Input Single Output (SISO).

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Authors: Some Immunological Characteristics of Tick- Borne Encephalitis in Perm Region

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It is shown that the relationship of tick-borne encephalitis virus with the human body comes in two ways, the development of acute infection with the outcome in convalescence and long stay by the virus in the body, its persistence in the nervous tissue with periodic reactivation and prolonged circulating immunoglobulin M. In spite of the fact that tick-borne encephalitis virus has a tropism for nerve tissue, involvement in the process of blood cells is an integral component of the infection. Comprehensive study of the relation of factors of innate and adaptive immunity in the tick-borne encephalitis providing insight into the features of chronic disease.

Keywords: Tick-borne encephalitis, phagocytic activity, a progressive.

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Authors: C. B. Vishwakarma

Abstract:

We elaborated the parallel and series Proportional, Integral and Derivative (PID) controllers, which are being used in industries. Various issues, which are very often faced by control engineers while designing the PID controllers for industrial systems are described. The effect of measurement noise on the actuator due to derivative term of a PID controller has been explained in detail. Similarly, proportional kick, derivative kick, saturation tendency of the actuator and reverse phenomena of an industrial process have been summarized. Moreover, we meticulously explained the remedies of the all issues of the parallel industrial PID controller.

Keywords: Band-width limited derivative control, derivative kick, proportional kick, reverse acting controller, series PID controller.

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Authors: Prodromos E. Atlamazoglou

Abstract:

The method of moments combined with the method of symmetrical components is used for the analysis of interstitial hyperthermia applicators. The basis and testing functions are both piecewise sinusoids, qualifying our technique as a Galerkin one. The dielectric coatings are modeled by equivalent volume polarization currents, which are simply related to the conduction current distribution, avoiding in that way the introduction of additional unknowns or numerical integrations. The results of our method for a four dipole circular array, are in agreement with those already published in literature for a same hyperthermia configuration. Apart from being accurate, our approach is more general, more computationally efficient and takes into account the coupling between the antennas.

Keywords: Hyperthermia, integral equations, insulated antennas, method of symmetrical components.

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Authors: Khalid Pervaiz Akhter, Mahmood Ahmad, Ghulam Murtaza, Ishrat Shafi, Zafar Javed

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The objective of this manuscript is to find area under the plasma concentration- time curve (AUC) for multiple doses of salbutamol sulphate sustained release tablets (Ventolin® oral tablets SR 8 mg, GSK, Pakistan) in the group of 18 healthy adults by using computational mathematics techniques. Following the administration of 4 doses of Ventolin® tablets 12 hourly to 24 healthy human subjects and bioanalysis of obtained plasma samples, plasma drug concentration-time profile was constructed. AUC, an important pharmacokinetic parameter, was measured using integrated equation of multiple oral dose regimens. The approximated AUC was also calculated by using computational mathematics techniques such as repeated rectangular, repeated trapezium and repeated Simpson's rule and compared with exact value of AUC calculated by using integrated equation of multiple oral dose regimens to find best computational mathematics method that gives AUC values closest to exact. The exact values of AUC for four consecutive doses of Ventolin® oral tablets were 150.5819473, 157.8131756, 164.4178231 and 162.78 ng.h/ml while the closest values approximated AUC values were 149.245962, 157.336171, 164.2585768 and 162.289224 ng.h/ml, respectively as found by repeated rectangular rule. The errors in the approximated values of AUC were negligible. It is concluded that all computational tools approximated values of AUC accurately but the repeated rectangular rule gives slightly better approximated values of AUC as compared to repeated trapezium and repeated Simpson's rules.

Keywords: Salbutamol sulphate, Area under curve (AUC), repeated rectangular rule, repeated trapezium rule, repeated Simpson's rule.

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Authors: Sheetal R. Jadhwani, Daisy Sang, Chang-Shyh Peng

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Web applications are an integral part of modem life. They are mostly based upon the HyperText Markup Language (HTML). While HTML meets the basic needs, there are some shortcomings. For example, applications can cease to work once user goes offline, real-time updates may be lagging, and user interface can freeze on computationally intensive tasks. The latest language specification HTML5 attempts to rectify the situation with new tools and protocols. This paper studies the new Web Storage, Geolocation, Web Worker, Canvas, and Web Socket APIs, and presents applications to test their features and efficiencies.

Keywords: HTML5, Web Worker, Canvas, Web Socket.

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Authors: Václav Sadílek, Miroslav Vořechovský

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The paper deals with the classical fiber bundle model of equal load sharing, sometimes referred to as the Daniels’ bundle or the democratic bundle. Daniels formulated a multidimensional integral and also a recursive formula for evaluation of the strength cumulative distribution function. This paper describes three algorithms for evaluation of the recursive formula and also their implementations with source codes in the Python high-level programming language. A comparison of the algorithms are provided with respect to execution time. Analysis of orders of magnitudes of addends in the recursion is also provided.

Keywords: Daniels bundle model, equal load sharing, Python, mpmath.

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Authors: M. Almeshal, M. O. Tokhi, K. M. Goher

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A novel design of two-wheeled robotic vehicle with moving payload is presented in this paper. A mathematical model describing the vehicle dynamics is derived and simulated in Matlab Simulink environment. Two control strategies were developed to stabilise the vehicle in the upright position. A robust Proportional- Integral-Derivative (PID) control strategy has been implemented and initially tested to measure the system performance, while the second control strategy is to use a hybrid fuzzy logic controller (FLC). The results are given on a comparative basis for the system performance in terms of disturbance rejection, control algorithms robustness as well as the control effort in terms of input torque.

Keywords: double inverted pendulum, modelling, robust control, simulation,

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Authors: Hui Liu, Haiyang Quan

Abstract:

This paper To get the angle value with a MEMS rate gyroscope in some specific field, the usual method is to make an integral operation to the rate output, which will lead the error cumulating effect. So the rate gyro is not suitable. MEMS rate integrating gyroscope (MRIG) will solve this problem. A DSP system has been developed to implement the control arithmetic. The system can measure the angle of rotation directly by the control loops that make the sensor work in whole-angle mode. Modeling the system with MATLAB, desirable results of angle outputs are got, which prove the feasibility of the control arithmetic.

Keywords: Rate gyroscope, Rate integrating gyroscope, Whole angle mode, MATLAB modeling, DSP control.

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Authors: Qamar Saeed, Vali Uddin, Reza Katebi

Abstract:

In this paper multivariable predictive PID controller has been implemented on a multi-inputs multi-outputs control problem i.e., quadruple tank system, in comparison with a simple multiloop PI controller. One of the salient feature of this system is an adjustable transmission zero which can be adjust to operate in both minimum and non-minimum phase configuration, through the flow distribution to upper and lower tanks in quadruple tank system. Stability and performance analysis has also been carried out for this highly interactive two input two output system, both in minimum and non-minimum phases. Simulations of control system revealed that better performance are obtained in predictive PID design.

Keywords: Proportional-integral-derivative Control, GeneralizedPredictive Control, Predictive PID Control, Multivariable Systems

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Authors: P. Mounnarath, U. Schmitz, Ch. Zhang

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Fragility analysis is an effective tool for the seismic vulnerability assessment of civil structures in the last several years. The design of the expansion joints according to various bridge design codes is almost inconsistent, and only a few studies have focused on this problem so far. In this study, the influence of the expansion joint clearances between the girder ends and the abutment backwalls on the seismic fragility assessment of continuous integral bridge frames is investigated. The gaps (ranging from 60 mm, 150 mm, 250 mm and 350 mm) are designed by following two different bridge design code specifications, namely, Caltrans and Eurocode 8-2. Five bridge models are analyzed and compared. The first bridge model serves as a reference. This model uses three-dimensional reinforced concrete fiber beam-column elements with simplified supports at both ends of the girder. The other four models also employ reinforced concrete fiber beam-column elements but include the abutment backfill stiffness and four different gap values. The nonlinear time history analysis is performed. The artificial ground motion sets, which have the peak ground accelerations (PGAs) ranging from 0.1 g to 1.0 g with an increment of 0.05 g, are taken as input. The soil-structure interaction and the P-Δ effects are also included in the analysis. The component fragility curves in terms of the curvature ductility demand to the capacity ratio of the piers and the displacement demand to the capacity ratio of the abutment sliding bearings are established and compared. The system fragility curves are then obtained by combining the component fragility curves. Our results show that in the component fragility analysis, the reference bridge model exhibits a severe vulnerability compared to that of other sophisticated bridge models for all damage states. In the system fragility analysis, the reference curves illustrate a smaller damage probability in the earlier PGA ranges for the first three damage states, they then show a higher fragility compared to other curves in the larger PGA levels. In the fourth damage state, the reference curve has the smallest vulnerability. In both the component and the system fragility analysis, the same trend is found that the bridge models with smaller clearances exhibit a smaller fragility compared to that with larger openings. However, the bridge model with a maximum clearance still induces a minimum pounding force effect.

Keywords: Expansion joint clearance, fiber beam-column element, fragility assessment, time history analysis.

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Authors: Evgeniy Burlutskiy

Abstract:

The paper presents a numerical investigation on the rapid gas decompression in pure nitrogen which is made by using the one-dimensional (1D) and three-dimensional (3D) mathematical models of transient compressible non-isothermal fluid flow in pipes. A 1D transient mathematical model of compressible thermal multicomponent fluid mixture flow in pipes is presented. The set of the mass, momentum and enthalpy conservation equations for gas phase is solved in the model. Thermo-physical properties of multicomponent gas mixture are calculated by solving the Equation of State (EOS) model. The Soave-Redlich-Kwong (SRK-EOS) model is chosen. This model is successfully validated on the experimental data [1] and shows a good agreement with measurements. A 3D transient mathematical model of compressible thermal single-component gas flow in pipes, which is built by using the CFD Fluent code (ANSYS), is presented in the paper. The set of unsteady Reynolds-averaged conservation equations for gas phase is solved. Thermo-physical properties of single-component gas are calculated by solving the Real Gas Equation of State (EOS) model. The simplest case of gas decompression in pure nitrogen is simulated using both 1D and 3D models. The ability of both models to simulate the process of rapid decompression with a high order of agreement with each other is tested. Both, 1D and 3D numerical results show a good agreement between each other. The numerical investigation shows that 3D CFD model is very helpful in order to validate 1D simulation results if the experimental data is absent or limited.

Keywords: Mathematical model, Rapid Gas Decompression

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Authors: Sheren H. Salah, Ahmed Y. Ben Sasi

Abstract:

The inverted pendulum system is a classic control problem that is used in universities around the world. It is a suitable process to test prototype controllers due to its high non-linearities and lack of stability. The inverted pendulum represents a challenging control problem, which continually moves toward an uncontrolled state. This paper presents the possibility of balancing an inverted pendulum system using sliding mode control (SMC). The goal is to determine which control strategy delivers better performance with respect to pendulum’s angle and cart's position. Therefore, proportional-integral-derivative (PID) is used for comparison. Results have proven SMC control produced better response compared to PID control in both normal and noisy systems.

Keywords: Inverted pendulum (IP) proportional-integralderivative (PID), sliding mode control (SMC).

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Authors: N. Z. Azlan, H. Yamaura

Abstract:

The experimental study of position control of a light weight and small size robotic finger during non-contact motion is presented in this paper. The finger possesses fingertip pinching and self adaptive grasping capabilities, and is made of a seven bar linkage mechanism with a slider in the middle phalanx. The control system is tested under the Proportional Integral Derivative (PID) control algorithm and Recursive Least Square (RLS) based Feedback Error Learning (FEL) control scheme to overcome the uncertainties present in the plant. The experiments conducted in Matlab Simulink and xPC Target environments show that the overall control strategy is efficient in controlling the finger movement.

Keywords: Anthropomorphic finger, position control, feedback error learning, experimental study

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Authors: K. Venclova, H. Urbancova, H. Vostra Vydrova

Abstract:

In current global economics the application of Business Continuity Management is the prerequisite for sustainable competitive advantage in an organization. Business Continuity Management is a managerial which identifies the potential impact of losses in an organization. The aim of this paper is to identify and critically evaluate the relative advantages and disadvantages of deploying Business Continuity Management in an organization on the basis of seven criteria. The strongest advantage of Business Continuity Management is in its capacity to identify a crisis situation and help the organization to flexibly and also to keep the critical knowledge within the organization. By contrast the main disadvantage is that establishing Business Continuity Management in an organization is time-consuming and its implementation as an integral part of the organizational culture present significant difficulties.

Keywords: Business continuity management, criteria, advantages, disadvantages, organisations, survey.

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Authors: Rudolf Csikja, Janos Toth

Abstract:

Methods to detect and localize time singularities of polynomial and quasi-polynomial ordinary differential equations are systematically presented and developed. They are applied to examples taken form different fields of applications and they are also compared to better known methods such as those based on the existence of linear first integrals or Lyapunov functions.

Keywords: blow up, finite escape time, polynomial ODE, singularity, Lotka–Volterra equation, Painleve analysis, Ψ-series, global existence

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