Search results for: test stability

Authors: Karel Frajtak, Miroslav Bures, Ivan Jelinek

Abstract:

Software testing is important stage of software development cycle. Current testing process involves tester and electronic documents with test case scenarios. In this paper we focus on new approach to testing process using automated test case generation and tester guidance through the system based on the model of the system. Test case generation and model-based testing is not possible without proper system model. We aim on providing better feedback from the testing process thus eliminating the unnecessary paper work.

Keywords: Model based testing, test automation, test generating, tester support.

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Authors: Asfar Ali Khan

Abstract:

Analytical expression for maximum power transfer through a transmission line limited by voltage stability has been formulated using exact representation of transmission line with ABCD parameters. The expression has been used for plotting PV curve at different power factors of a radial transmission line. Limiting values of reactive power have been obtained.

Keywords: Power Transfer, PV Curve, Voltage Stability.

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Authors: T. H. Young, S. J. Huang, Y. S. Chiu

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This paper investigates the parametric stability of an axially moving web subjected to non-uniform in-plane edge excitations on two opposite, simply-supported edges. The web is modeled as a viscoelastic plate whose constitutive relation obeys the Kelvin-Voigt model, and the in-plane edge excitations are expressed as the sum of a static tension and a periodical perturbation. Due to the in-plane edge excitations, the moving plate may bring about parametric instability under certain situations. First, the in-plane stresses of the plate due to the non-uniform edge excitations are determined by solving the in-plane forced vibration problem. Then, the dependence on the spatial coordinates in the equation of transverse motion is eliminated by the generalized Galerkin method, which results in a set of discretized system equations in time. Finally, the method of multiple scales is utilized to solve the set of system equations analytically if the periodical perturbation of the in-plane edge excitations is much smaller as compared with the static tension of the plate, from which the stability boundaries of the moving plate are obtained. Numerical results reveal that only combination resonances of the summed-type appear under the in-plane edge excitations considered in this work.

Keywords: Axially moving viscoelastic plate, in-plane periodic excitation, non-uniformly distributed edge tension, dynamic stability.

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Authors: Changjin Xu

Abstract:

In this paper, a delayed prototype model is studied. Regarding the delay as a bifurcation parameter, we prove that a sequence of Hopf bifurcations will occur at the positive equilibrium when the delay increases. Using the normal form method and center manifold theory, some explicit formulae are worked out for determining the stability and the direction of the bifurcated periodic solutions. Finally, Computer simulations are carried out to explain some mathematical conclusions.

Keywords: Prototype model, Stability, Hopf bifurcation, Delay, Periodic solution.

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Authors: P. Naderi, S.M.T. Bathaee, R. Hoseinnezhad, R. Chini

Abstract:

Using electrical machine in conventional vehicles, also called hybrid vehicles, has become a promising control scheme that enables some manners for fuel economy and driver assist for better stability. In this paper, vehicle stability control, fuel economy and Driving/Regeneration braking for a 4WD hybrid vehicle is investigated by using an electrical machine on each non-driven wheels. In front wheels driven vehicles, fuel economy and regenerative braking can be obtained by summing torques applied on rear wheels. On the other hand, unequal torques applied to rear wheels provides enhanced safety and path correction in steering. In this paper, a model with fourteen degrees of freedom is considered for vehicle body, tires and, suspension systems. Thereafter, powertrain subsystems are modeled. Considering an electrical machine on each rear wheel, a fuzzy controller is designed for each driving, braking, and stability conditions. Another fuzzy controller recognizes the vehicle requirements between the driving/regeneration and stability modes. Intelligent vehicle control to multi objective operation and forward simulation are the paper advantages. For reaching to these aims, power management control and yaw moment control will be done by three fuzzy controllers. Also, the above mentioned goals are weighted by another fuzzy sub-controller base on vehicle dynamic. Finally, Simulations performed in MATLAB/SIMULINK environment show that the proposed structure can enhance the vehicle performance in different modes effectively.

Keywords: Hybrid, pitch, roll, regeneration, yaw.

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Authors: Petr Šimek, Kamil Kostruk

Abstract:

This paper deals with the problem of testing the Electronic Control Unit (ECU) for the specified function validation. Modern ECUs have many functions which need to be tested. This process requires tracking between the test and the specification. The technique discussed in this paper explores the system for automating this process. The paper focuses on the introduction to the problem in general, then it describes the proposed test system concept and its principle. It looks at how the process of the ECU interface specification file for automated interface testing and test tracking works. In the end, the future possible development of the project is discussed.

Keywords: Electronic control unit testing, embedded system, test generate, test automation, process automation, CAN bus, Ethernet.

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Authors: Liping Zhang, Kelin Li

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In this paper, a class of impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms is formulated and investigated. By establishing a delay differential inequality and M-matrix theory, some sufficient conditions ensuring the existence, uniqueness and global exponential stability of equilibrium point for impulsive BAM fuzzy cellular neural networks with time delays in the leakage terms are obtained. In particular, a precise estimate of the exponential convergence rate is also provided, which depends on system parameters and impulsive perturbation intention. It is believed that these results are significant and useful for the design and applications of BAM fuzzy cellular neural networks. An example is given to show the effectiveness of the results obtained here.

Keywords: Global exponential stability, bidirectional associative memory, fuzzy cellular neural networks, leakage delays, impulses.

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Authors: M. Baghdasaryan, A. Sukiasyan

Abstract:

An algorithm for estimating the stable operation conditions of the synchronous motor of the ore mill electric drive is proposed. The stable operation conditions of the synchronous motor are revealed, taking into account the estimation of the q angle change and the technological factors. The stability condition obtained allows to ensure the stable operation of the motor in the synchronous mode, taking into account the nonlinear character of the mill loading. The developed algorithm gives an opportunity to present the undesirable phenomena, arising in the electric drive system. The obtained stability condition can be successfully applied for the optimal control of the electromechanical system of the mill.

Keywords: Electric drive, synchronous motor, ore mill, stability, technological factors.

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Authors: Lili Wang

Abstract:

By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and  effectiveness of the results.

Keywords: Almost periodic solution, Exponential stability, Neural networks, Impulses.

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Authors: E. Ansari-Piri, N. Eghbali

Abstract:

Let A and B be two linear algebras. A linear map ϕ : A → B is called an n-homomorphism if ϕ(a1...an) = ϕ(a1)...ϕ(an) for all a1, ..., an ∈ A. In this note we have a verification on the behavior of almost n-multiplicative linear maps with n > 2 in the fuzzy normed spaces

Keywords: Almost multiplicative maps, n-homomorphism maps, almost n-multiplicative maps, fuzzy normed space, stability.

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Authors: K. Saravanan

Abstract:

An electrical power system has some negative aspects such as flickering and deviations of voltage/power. This can be eliminated using energy storage devices that will provide a backup energy at the time of voltage/power deviations. Energy-storage devices get charging when system voltage/power is higher than reference value and discharging when system voltage/power is lower than reference value, it is acting as catalysts to provide energy boost. In this paper, a dynamic control of Unified Power Flow Controller (UPFC) integrated with superconducting magnetic energy storage (SMES) is developed to improve the power quality, power oscillation damping, and dynamic voltage stability through the transmission line. UPFC inter-connected to SMES through an interface with DC-DC chopper. This inter-connected system is capable of injecting (absorbing) the real and reactive power into (from) the system at the beginning of stability problems. In this paper, the simulation results of UPFC integrated with SMES and UPFC integrated with fuel cells (FCs) are compared using MATLAB/Simulink software package.

Keywords: UPFC, SMES, power system stability, flexible ac transmission systems, fuel cells, chopper.

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Authors: Dae-Hee Son, Soon-Ryul Nam

Abstract:

The power system frequency falls when disturbance such as rapid increase of system load or loss of a generating unit occurs in power systems. Especially, increase in the number of renewable generating units has a bad influence on the power system because of loss of generating unit depending on the circumstance. Conventional technologies use frequency droop control battery output for the frequency regulation and balance between supply and demand. If power is supplied using the fast output characteristic of the battery, power system stability can be further more improved. To improve the power system stability, we propose battery output control using ROCOF (Rate of Change of Frequency) in this paper. The bigger the power difference between the supply and the demand, the bigger the ROCOF drops. Battery output is controlled proportionally to the magnitude of the ROCOF, allowing for faster response to power imbalances. To simulate the control method of battery output system, we develop the user defined model using PSS/E and confirm that power system stability is improved by comparing with frequency droop control.

Keywords: PSS/E user defined model, power deviation, frequency droop control, ROCOF, rate of change of frequency.

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Authors: Adil K. Tamimi, Tarig Ali, Rawan Anoohi, Ahmed Rajput, Kaltham Alkamali

Abstract:

3D concrete printing is one of the most innovative and modern techniques in the field of construction that achieved several milestones in that field for the following advantages: saving project’s time, ability to execute complicated shapes, reduce waste and low cost. However, the concept of 3D printing in UAE is relatively new where construction teams, including clients, consultants, and contractors, do not have the required knowledge and experience in the field. This is the most significant obstacle for the construction parties, which make them refrained from using 3D concrete printing compared to conventional concreting methods. This study shows the historical development of the 3D concrete printing, its advantages, and the challenges facing this innovation. Concrete mixes and materials have been proposed and evaluated to select the best combination for successful 3D concrete printing. The main characteristics of the 3D concrete printing in the fresh and hardened states are considered, such as slump test, flow table, compressive strength, tensile, and flexural strengths. There is need to assess the structural stability of the 3D concrete by testing the bond between interlayers of the concrete.  

Keywords: 3D printing, concrete mixes, workability, compressive strength, slump test, tensile strength, flexural strength.

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Authors: Mahmoud A. Mahmoud, Ashraf Osman

Abstract:

In this study, the different approaches currently followed by design codes to assess the stability of buildings utilizing concrete moment resisting frames structural system are evaluated. For such purpose, a parametric study was performed. It involved analyzing group of concrete moment resisting frames having different slenderness ratios (height/width ratios), designed for different lateral loads to vertical loads ratios and constructed using ordinary reinforced concrete and high strength concrete for stability check and overall buckling using code approaches and computer buckling analysis. The objectives were to examine the influence of such parameters that directly linked to frames’ lateral stiffness on the buildings’ stability and evaluates the code approach in view of buckling analysis results. Based on this study, it was concluded that, the most susceptible buildings to instability and magnification of second order effects are buildings having high aspect ratios (height/width ratio), having low lateral to vertical loads ratio and utilizing construction materials of high strength. In addition, the study showed that the instability limits imposed by codes are mainly mathematical to ensure reliable analysis not a physical ones and that they are in general conservative. Also, it has been shown that the upper limit set by one of the codes that second order moment for structural elements should be limited to 1.4 the first order moment is not justified, instead, the overall story check is more reliable.

Keywords: Buckling, lateral stability, p-delta, second order.

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Authors: M. Battira, R. Bessaih

Abstract:

We numerically study the three-dimensional magnetohydrodynamics (MHD) stability of oscillatory natural convection flow in a rectangular cavity, with free top surface, filled with a liquid metal, having an aspect ratio equal to A=L/H=5, and subjected to a transversal temperature gradient and a uniform magnetic field oriented in x and z directions. The finite volume method was used in order to solve the equations of continuity, momentum, energy, and potential. The stability diagram obtained in this study highlights the dependence of the critical value of the Grashof number Grcrit , with the increase of the Hartmann number Ha for two orientations of the magnetic field. This study confirms the possibility of stabilization of a liquid metal flow in natural convection by application of a magnetic field and shows that the flow stability is more important when the direction of magnetic field is longitudinal than when the direction is transversal.

Keywords: Natural convection, Magnetic field, Oscillatory, Cavity, Liquid metal.

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Authors: Raluca Iulia Iulian

Abstract:

The question of interethnic and interreligious conflicts in ex-Yugoslavia receives much attention within the framework of the international context created after 1991 because of the impact of these conflicts on the security and the stability of the region of Balkans and of Europe. This paper focuses on the rationales leading to the declaration of independence by Kosovo according to ethnic and religious criteria and analyzes why these same rationales were not applied in Bosnia and Herzegovina. The approach undertaken aims at comparatively examining the cases of Kosovo, and Bosnia and Herzegovina. At the same time, it aims at understanding the political decision making of the international community in the case of Kosovo. Specifically, was this a good political decision for the security and the stability of the region of Balkans, of Europe, or even for global security and stability? This research starts with an overview on the European security framework post 1991, paying particular attention to Kosovo and Bosnia and Herzegovina. It then presents the theoretical and methodological framework and compares the representative cases. Using the constructivism issue and the comparative methodology, it arrives at the results of the study. An important issue of the paper is the thesis that this event modifies the principles of international law and creates dangerous precedents for regional stability in the Balkans.

Keywords: Interethnic and interreligious conflict, security andstability, superpower.

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Authors: H. C. Chinwenyi, H. D. Ibrahim, J. O. Adekunle

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The incubation period is defined as the time from infection with a microorganism to development of symptoms. In this research, two disease models: one with incubation period and another without incubation period were studied. The study involves the use of a  mathematical model with a single incubation period. The test for the existence and stability of the disease free and the endemic equilibrium states for both models were carried out. The fourth order Runge-Kutta method was used to solve both models numerically. Finally, a computer program in MATLAB was developed to run the numerical experiments. From the results, we are able to show that the endemic equilibrium state of the model with incubation period is locally asymptotically stable whereas the endemic equilibrium state of the model without incubation period is unstable under certain conditions on the given model parameters. It was also established that the disease free equilibrium states of the model with and without incubation period are locally asymptotically stable. Furthermore, results from numerical experiments using empirical data obtained from Nigeria Centre for Disease Control (NCDC) showed that the overall population of the infected people for the model with incubation period is higher than that without incubation period. We also established from the results obtained that as the transmission rate from susceptible to infected population increases, the peak values of the infected population for the model with incubation period decrease and are always less than those for the model without incubation period.

Keywords: Asymptotic stability, incubation period, Routh-Hurwitz criterion, Runge Kutta method.

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Authors: Yanhui Jia, Ning Guo, Juan Li, Yunkui Sun, Wei Yang, Tianping Zhang, Lin Ma, Wei Meng, Hai Geng

Abstract:

The current statuses of lifetime test of LaB6 hollow cathode at the Lanzhou Institute of Physics (LIP), China, was described. 5A LaB6 hollow cathode was design for LIPS-200 40mN Xenon ion thruster, and it could be used for LHT-100 80 mN Hall thruster, too. Life test of the discharge and neutralizer modes of LHC-5 hollow cathode were stared in October 2011, and cumulative operation time reached 17,300 and 16,100 hours in April 2015, respectively. The life of cathode was designed more than 11,000 hours. Parameters of discharge and key structure dimensions were monitored in different stage of life test indicated that cathodes were health enough. The test will continue until the cathode cannot work or operation parameter is not in normally. The result of the endurance test of cathode demonstrated that the LaB6 hollow cathode is satisfied for the required of thruster in life and performance.

Keywords: LaB6, hollow cathode, thruster, lifetime test, electric propulsion.

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Authors: Ravindra Mallya, B. Satish Shenoy, B. Raghuvir Pai

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The study deals with the challenges in developing a test rig to test the performance of water lubricated journal bearing. The test rig is designed to simulate the working conditions of the bearing in order to understand their performance before they are put in operation. The bearing that is studied is the commercially available water lubricated bearing which has a rubber liner bonded with a rigid metal shell. The lubricant enters the bearing axially through a pressurized inlet tank and exits to an outlet tank which is at sufficiently low pressure. The load on the bearing is applied through the dead weight system which acts both in upward and downward direction so that net load acts on the bearing. The issues in feeding the lubricant into the bearing from the inlet side and preventing the leakage of the lubricant is discussed. The application of the load on the test bearing while maintaining the bearing afloat is also discussed.

Keywords: Axial groove, hydrodynamic pressure, journal bearing, test rig, water lubrication.

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Authors: Mahawish Masud, Muhammad Iqbal, M. U. Khan, Farooque Azam

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Manual writing of test cases from functional requirements is a time-consuming task. Such test cases are not only difficult to write but are also challenging to maintain. Test cases can be drawn from the functional requirements that are expressed in natural language. However, manual test case generation is inefficient and subject to errors.  In this paper, we have presented a systematic procedure that could automatically derive test cases from user stories. The user stories are specified in a restricted natural language using a well-defined template.  We have also presented a detailed methodology for writing our test ready user stories. Our tool “Test-o-Matic” automatically generates the test cases by processing the restricted user stories. The generated test cases are executed by using open source Selenium IDE.  We evaluate our approach on a case study, which is an open source web based application. Effectiveness of our approach is evaluated by seeding faults in the open source case study using known mutation operators.  Results show that the test case generation from restricted user stories is a viable approach for automated testing of web applications.

Keywords: Automated testing, natural language, user story modeling, software engineering, software testing, test case specification, transformation and automation, user story, web application testing.

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Authors: M. Najafi, F. Rahimi Dehgolan

Abstract:

In this paper, the dynamic modeling of a single-link flexible beam with a tip mass is given by using Hamilton's principle. The link has been rotational and translational motion and it was assumed that the beam is moving with a harmonic velocity about a constant mean velocity. Non-linearity has been introduced by including the non-linear strain to the analysis. Dynamic model is obtained by Euler-Bernoulli beam assumption and modal expansion method. Also, the effects of rotary inertia, axial force, and associated boundary conditions of the dynamic model were analyzed. Since the complex boundary value problem cannot be solved analytically, the multiple scale method is utilized to obtain an approximate solution. Finally, the effects of several conditions on the differences among the behavior of the non-linear term, mean velocity on natural frequencies and the system stability are discussed.

Keywords: Non-linear vibration, stability, axially moving beam, bifurcation, multiple scales method.

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Authors: Raouf Fareh, Maarouf Saad, Sofiane Khadraoui, Tamer Rabie

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This paper presents a tracking control strategy based on Lyapunov approach for nonholonomic wheeled mobile robot. This control strategy consists of two levels. First, a kinematic controller is developed to adjust the right and left wheel velocities. Using this velocity control law, the stability of the tracking error is guaranteed using Lyapunov approach. This kinematic controller cannot be generated directly by the motors. To overcome this problem, the second level of the controllers, dynamic control, is designed. This dynamic control law is developed based on Lyapunov theory in order to track the desired trajectories of the mobile robot. The stability of the tracking error is proved using Lupunov and Barbalat approaches. Simulation results on a nonholonomic wheeled mobile robot are given to demonstrate the feasibility and effectiveness of the presented approach.

Keywords: Mobile robot, trajectory tracking, Lyapunov, stability.

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Authors: Yury Nikulin

Abstract:

A multicriteria linear programming problem with integer variables and parameterized optimality principle "from lexicographic to Slater" is considered. A situation in which initial coefficients of penalty cost functions are not fixed but may be potentially a subject to variations is studied. For any efficient solution, appropriate measures of the quality are introduced which incorporate information about variations of penalty cost function coefficients. These measures correspond to the so-called stability and accuracy functions defined earlier for efficient solutions of a generic multicriteria combinatorial optimization problem with Pareto and lexicographic optimality principles. Various properties of such functions are studied and maximum norms of perturbations for which an efficient solution preserves the property of being efficient are calculated.

Keywords: Stability and accuracy, multicriteria optimization, lexicographic optimality.

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Authors: Awatef Chniguir, Tarek Farah, Zouhair Ben Jemaa, Safya Belguith

Abstract:

Optimal routing allows minimizing energy consumption in wireless sensor networks (WSN). Clustering has proven its effectiveness in organizing WSN by reducing channel contention and packet collision and enhancing network throughput under heavy load. Therefore, nowadays, with the emergence of the Internet of Things, heterogeneity is essential. Stable election protocol (SEP) that has increased the network stability period and lifetime is the first clustering protocol for heterogeneous WSN. SEP and its descendants, namely SEP, Threshold Sensitive SEP (TSEP), Enhanced TSEP (ETSSEP) and Current Energy Allotted TSEP (CEATSEP), were studied. These algorithms’ performance was evaluated based on different metrics, especially first node death (FND), to compare their stability. Simulations were conducted on the MATLAB tool considering two scenarios: The first one demonstrates the fraction variation of advanced nodes by setting the number of total nodes. The second considers the interpretation of the number of nodes while keeping the number of advanced nodes permanent. CEATSEP outperforms its antecedents by increasing stability and, at the same time, keeping a low throughput. It also operates very well in a large-scale network. Consequently, CEATSEP has a useful lifespan and energy efficiency compared to the other routing protocol for heterogeneous WSN.

Keywords: Clustering, heterogeneous, stability, scalability, throughput, IoT, WSN.

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Authors: Sangram Keshori Mohapatra, Sidhartha Panda, Prasant Kumar Satpathy

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Power-system stability improvement by simultaneous tuning of power system stabilizer (PSS) and a Static Var Compensator (SVC) based damping controller is thoroughly investigated in this paper. Both local and remote signals with associated time delays are considered in the present study. The design problem of the proposed controller is formulated as an optimization problem, and differential evolution (DE) algorithm is employed to search for the optimal controller parameters. The performances of the proposed controllers are evaluated under different disturbances for both single-machine infinite bus power system and multi-machine power system. The performance of the proposed controllers with variations in the signal transmission delays has also been investigated. The proposed stabilizers are tested on a weakly connected power system subjected to different disturbances. Nonlinear simulation results are presented to show the effectiveness and robustness of the proposed control schemes over a wide range of loading conditions and disturbances. Further, the proposed design approach is found to be robust and improves stability effectively even under small disturbance conditions.

Keywords: Differential Evolution Algorithm, Power System Stability, Power System Stabilizer, Static Var Compensator

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Authors: Markus Mazzola, Gunther Schaaf

Abstract:

A vehicle driving with an Adaptive Cruise Control System (ACC) is usually controlled decentrally, based on the information of radar systems and in some publications based on C2X-Communication (CACC) to guarantee stable platoons. In this paper we present a Model Predictive Control (MPC) design of a centralized, server-based ACC-System, whereby the vehicular platoon is modeled and controlled as a whole. It is then proven that the proposed MPC design guarantees asymptotic stability and hence string stability of the platoon. The Networked MPC design is chosen to be able to integrate system constraints optimally as well as to reduce the effects of communication delay and packet loss. The performance of the proposed controller is then simulated and analyzed in an LTE communication scenario using the LTE/EPC Network Simulator LENA, which is based on the ns-3 network simulator.

Keywords: Adaptive Cruise Control, Centralized Server, Networked Model Predictive Control, String Stability.

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Authors: Eman Alzahrani, Hala M. Abo-Dief, Ashraf T. Mohamed

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The present work is aimed at examining carbon steel oil pipelines corrosion using three natural extracts (Eruca Sativa, Rosell and Mango peels) that are used as inhibitors of different concentrations ranging from 0.05-0.1wt. %. Two sulphur compounds are used as corrosion mediums. Weight loss method was used for measuring the corrosion rate of the carbon steel specimens immersed in technical white oil at 100ºC at various time intervals in absence and presence of the two sulphur compounds. The corroded specimens are examined using the chemical wear test, scratch test and hardness test. The scratch test is carried out using scratch loads from 0.5 Kg to 2.0 Kg. The scratch width is obtained at various scratch load and test conditions. The Brinell hardness test is carried out and investigated for both corroded and inhibited specimens. The results showed that three natural extracts can be used as environmentally friendly corrosion inhibitors.

Keywords: Inhibition, natural extract, pipelines corrosion, sulphur compounds.

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Authors: Muhammad Shahid, Nasir-uddin Khan, Mushtaq Hussain, Muhammad Liaquat Ali, Asif Mansoor

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Tuberculosis (TB) remains a leading cause of infectious mortality. It is primarily transmitted by the respiratory route, individuals with active disease may infect others through airborne particles which releases when they cough, talk, or sing and subsequently inhale by others. In order to study the effect of the Bacilli Calmette-Guerin (BCG) vaccine after vaccination of TB patient, a Vaccinated Susceptible Infected and Recovered (VSIR) mathematical model is being developed to achieve the desired objectives. The mathematical model, so developed, shall be used to quantify the effect of BCG Vaccine to protect the immigrant young adult person. Moreover, equations are to be established for the disease endemic and free equilibrium states and subsequently utilized in disease stability analysis. The stability analysis will give a complete picture of disease annihilation from the total population if the total removal rate from the infectious group should be greater than total number of dormant infections produced throughout infectious period.

Keywords: Bacillus Calmette-Guerin vaccine, disease-free equilibrium state, VSIR Quantification, disease stability analysis.

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Authors: Chenxue Yang, Mao Ye, Zijian Liu, Tao Li, Jiao Bao

Abstract:

Non-negative matrix factorization (NMF) is a useful computational method to find basis information of multivariate nonnegative data. A popular approach to solve the NMF problem is the multiplicative update (MU) algorithm. But, it has some defects. So the columnwisely alternating gradient (cAG) algorithm was proposed. In this paper, we analyze convergence of the cAG algorithm and show advantages over the MU algorithm. The stability of the equilibrium point is used to prove the convergence of the cAG algorithm. A classic model is used to obtain the equilibrium point and the invariant sets are constructed to guarantee the integrity of the stability. Finally, the convergence conditions of the cAG algorithm are obtained, which help reducing the evaluation time and is confirmed in the experiments. By using the same method, the MU algorithm has zero divisor and is convergent at zero has been verified. In addition, the convergence conditions of the MU algorithm at zero are similar to that of the cAG algorithm at non-zero. However, it is meaningless to discuss the convergence at zero, which is not always the result that we want for NMF. Thus, we theoretically illustrate the advantages of the cAG algorithm.

Keywords: Non-negative matrix factorizations, convergence, cAG algorithm, equilibrium point, stability.

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Authors: A. S. Gorobtsov, A. S. Polyanina, A. E. Andreev

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The movement of points feet of the anthropomorphous robot in space occurs along some stable trajectory of a known form. A large number of modifications to the methods of control of biped robots indicate the fundamental complexity of the problem of stability of the program trajectory and, consequently, the stability of the control for the deviation for this trajectory. Existing gait generators use piecewise interpolation of program trajectories. This leads to jumps in the acceleration at the boundaries of sites. Another interpolation can be realized using differential equations with fractional derivatives. In work, the approach to synthesis of generators of program trajectories is considered. The resulting system of nonlinear differential equations describes a smooth trajectory of movement having rectilinear sites. The method is based on the theory of an asymptotic stability of invariant sets. The stability of such systems in the area of localization of oscillatory processes is investigated. The boundary of the area is a bounded closed surface. In the corresponding subspaces of the oscillatory circuits, the resulting stable limit cycles are curves having rectilinear sites. The solution of the problem is carried out by means of synthesis of a set of the continuous smooth controls with feedback. The necessary geometry of closed trajectories of movement is obtained due to the introduction of high-order nonlinearities in the control of stabilization systems. The offered method was used for the generation of trajectories of movement of point’s feet of the anthropomorphous robot. The synthesis of the robot's program movement was carried out by means of the inverse method.

Keywords: Control, limits cycle, robot, stability.

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