Search results for: Time difference of Arrival (TDoA)

Authors: O. Soji-Omoniwa, N. O. Muhammad, L. A. Usman, B. P. Omoniwa

Abstract:

This study was conducted to investigate the effect of the leaf essential oil of C. sinensis harvested at 7.00a.m and 4.00p.m on some Liver and Kidney function indices of diabetic rats as well as investigate the effect of time of harvest on the observed effect. Experimental animals were divided into 4 groups (A, B, C and D). Diabetes mellitus was induced in all animals, except the normal control group (Group A), by injecting 150mg/kg body weight of alloxan monohydrate intraperitoneally. Group A received distilled water while group B (diabetic control group) was not treated. Group C and D were treated with leaf essential oil of C. sinensis harvested at 7.00 a.m and 4.00p.m respectively at a dose of 110 mg/kg body weight every other day for 15 days. Alkaline phosphatase (ALP), Alanine Transaminase (ALT) and Aspartate Transaminase (AST) activity was evaluated in the serum, Liver and Kidney of studied animals. Total and Direct Bilirubin level, Total Protein and Globulin, Creatinine and Urea level were also evaluated. Result showed that creatinine and urea, serum ALP, AST and ALT levels was significantly reduced (p < 0.05), while the levels of total Protein and Globulin increased significantly (p < 0.05) for the treated animals compared to the diabetic control group. In conclusion, the leaf essential oil of Citrus sinensis ameliorated the impaired renal and liver function; however, the time of harvest of the leaf does not significantly affect its ameliorative effect.

Keywords: C. sinensis, Function indices, Harvest time, Leaf essential oil.

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Authors: Moulay A. Akhloufi

Abstract:

In recent years, we see an increase of interest for efficient tracking systems in surveillance applications. Many of the proposed techniques are designed for static cameras environments. When the camera is moving, tracking moving objects become more difficult and many techniques fail to detect and track the desired targets. The problem becomes more complex when we want to track a specific object in real-time using a moving Pan and Tilt camera system to keep the target within the image. This type of tracking is of high importance in surveillance applications. When a target is detected at a certain zone, the possibility of automatically tracking it continuously and keeping it within the image until action is taken is very important for security personnel working in very sensitive sites. This work presents a real-time tracking system permitting the detection and continuous tracking of targets using a Pan and Tilt camera platform. A novel and efficient approach for dealing with occlusions is presented. Also a new intelligent forget factor is introduced in order to take into account target shape variations and avoid learning non desired objects. Tests conducted in outdoor operational scenarios show the efficiency and robustness of the proposed approach.

Keywords: Tracking, surveillance, target detection, Pan and tilt.

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Authors: Muhammad Mujtaba Asad, Razali Bin Hassan, Fahad Sherwani

Abstract:

This paper explains about the voltage output for DC to DC boost converter between open loop, PID controller and fuzzy logic controller through Matlab Simulink. Simulink input voltage was set at 12V and the voltage reference was set at 24V. The analysis on the deviation of voltage resulted that the difference between reference voltage setting and the output voltage is always lower. Comparison between open loop, PID and FLC shows that, the open loop circuit having a bit higher on the deviation of voltage. The PID circuit boosts for FLC has a lesser deviation of voltage and proved that it is such a better performance on control the deviation of voltage during the boost mode.

Keywords: Boost Convertors, Power Electronics, PID, Fuzzy logic, Open loop.

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Authors: Alaa I. Arafa, Hemdan O. A. Said. Marwa A. M. Ali

Abstract:

This paper investigates and evaluates experimentally the structural behavior of high strength concrete (HSC) beams under fire and compares it with that of Normal strength concrete (NSC) beams. The main investigated parameters are: concrete compressive strength (300 or 600 kg/cm²); the concrete cover thickness (3 or 5 cm); the degree of temperature (room temperature or 600 ^oC); the type of cooling (air or water); and the fire exposure time (3 or 5 hours). Test results showed that the concrete compressive strength decreases significantly as the exposure time to fire increases.

Keywords: Experimental, fire, high strength concrete beams, monotonic loading.

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Authors: T. Li, J.Y. Zhang, W.H. Zhang, M.H. Zhu

Abstract:

A numerical simulation of vortex-induced vibration of a 2-dimensional elastic circular cylinder with two degree of freedom under the uniform flow is calculated when Reynolds is 200. 2-dimensional incompressible Navier-Stokes equations are solved with the space-time finite element method, the equation of the cylinder motion is solved with the new explicit integral method and the mesh renew is achieved by the spring moving mesh technology. Considering vortex-induced vibration with the low reduced damping parameter, the variety trends of the lift coefficient, the drag coefficient, the displacement of cylinder are analyzed under different oscillating frequencies of cylinder. The phenomena of locked-in, beat and phases-witch were captured successfully. The evolution of vortex shedding from the cylinder with time is discussed. There are very similar trends in characteristics between the results of the one degree of freedom cylinder model and that of the two degree of freedom cylinder model. The streamwise vibrations have a certain effect on the lateral vibrations and their characteristics.

Keywords: Fluid-structure interaction, Navier-Stokes equation, Space-time finite element method, vortex-induced vibration.

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Authors: A. Al-Mazloum, E. Omer, M. F. A. Abdullah

Abstract:

Recently many cases of missing children between ages 14 and 17 years are reported. Parents always worry about the possibility of kidnapping of their children. This paper proposes an Android based solution to aid parents to track their children in real time. Nowadays, most mobile phones are equipped with location services capabilities allowing us to get the device’s geographic position in real time. The proposed solution takes the advantage of the location services provided by mobile phone since most of kids carry mobile phones. The mobile application use the GPS and SMS services found in Android mobile phones. It allows the parent to get their child’s location on a real time map. The system consists of two sides, child side and parent side. A parent’s device main duty is to send a request location SMS to the child’s device to get the location of the child. On the other hand, the child’s device main responsibility is to reply the GPS position to the parent’s device upon request.

Keywords: Child Tracking System, Global Positioning System (GPS), SMS-based Mobile Application.

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Authors: Abd Elrahman Elgamala, N. Darwish, I. Bondouk, Sh. Hamada

Abstract:

Available experimental angular distributions for ⁶Li elastically scattered from ¹⁶O nucleus in the energy range 13.0–50.0 MeV are investigated and reanalyzed using optical model of the conventional phenomenological potential and also using double folding optical model of different interaction models: DDM3Y1, CDM3Y1, CDM3Y2, and CDM3Y3. All the involved models of interaction are of M3Y Paris except DDM3Y1 which is of M3Y Reid and the main difference between them lies in the different values for the parameters of the incorporated density distribution function F(ρ). We have extracted the renormalization factor N_R for ⁶Li+¹⁶O nuclear system in the energy range 13.0–50.0 MeV using the aforementioned interaction models.

Keywords: Elastic scattering, optical model, folding potential, density distribution.

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Authors: P. Javid, A. Aeenmehr, J. Taghavifar

Abstract:

In this paper, supply air pressure of HVAC system has been modeled with second-order transfer function plus dead-time. In HVAC system, the desired input has step changes, and the output of proposed control system should be able to follow the input reference, so the idea of using model based predictive control is proceeded and designed in this paper. The closed loop control system is implemented in MATLAB software and the simulation results are provided. The simulation results show that the model based predictive control is able to control the plant properly.

Keywords: Air conditioning system, GPC, dead time, Air supply control.

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Authors: Mira Trebar

Abstract:

Logistics processes of perishable food in the supply chain include the distribution activities and the real time temperature monitoring to fulfil the cold chain requirements. The paper presents the use of RFID (Radio Frequency Identification) technology as an identification tool of receiving and shipping activities in the cold store. At the same time, the use of RFID data loggers with temperature sensors is presented to observe and store the temperatures for the purpose of analyzing the processes and having the history data available for traceability purposes and efficient recall management.

Keywords: Logistics, warehouse, RFID device, cold chain.

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Authors: Shamsuddin Ahmed, M. G. M. Khan, Biman Prasad, Avlin Prasad

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The focus of this paper is to construct daily time series exchange rate forecast models of Samoan Tala/USD and Tala/AUD during the year 2008 to 2012 with neural network The performance of the models was measured by using varies error functions such as Root Square mean error (RSME), Mean absolute error (MAE), and Mean absolute percentage error (MAPE). Our empirical findings suggest that AR (1) model is an effective tool to forecast the Tala/USD and Tala/AUD.

Keywords: Neural Network Forecasting Model, Autoregressive time series, Exchange rate, Tala/AUD, winters model.

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Authors: Omar M. Sallabi, Younis El-Haddad

Abstract:

The Genetic Algorithm (GA) is one of the most important methods used to solve many combinatorial optimization problems. Therefore, many researchers have tried to improve the GA by using different methods and operations in order to find the optimal solution within reasonable time. This paper proposes an improved GA (IGA), where the new crossover operation, population reformulates operation, multi mutation operation, partial local optimal mutation operation, and rearrangement operation are used to solve the Traveling Salesman Problem. The proposed IGA was then compared with three GAs, which use different crossover operations and mutations. The results of this comparison show that the IGA can achieve better results for the solutions in a faster time.

Keywords: AI, Genetic algorithms, TSP.

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Authors: Ehab F. Badran, Guoxiang Gu

Abstract:

We consider optimal channel equalization for MIMO (multi-input/multi-output) time-varying channels in the sense of MMSE (minimum mean-squared-error), where the observation noise can be non-stationary. We show that all ZF (zero-forcing) receivers can be parameterized in an affine form which eliminates completely the ISI (inter-symbol-interference), and optimal channel equalizers can be designed through minimization of the MSE (mean-squarederror) between the detected signals and the transmitted signals, among all ZF receivers. We demonstrate that the optimal channel equalizer is a modified Kalman filter, and show that under the AWGN (additive white Gaussian noise) assumption, the proposed optimal channel equalizer minimizes the BER (bit error rate) among all possible ZF receivers. Our results are applicable to optimal channel equalization for DWMT (discrete wavelet multitone), multirate transmultiplexers, OFDM (orthogonal frequency division multiplexing), and DS (direct sequence) CDMA (code division multiple access) wireless data communication systems. A design algorithm for optimal channel equalization is developed, and several simulation examples are worked out to illustrate the proposed design algorithm.

Keywords: Channel equalization, Kalman filtering, Time-varying systems.

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Authors: Tahany W. Sadak

Abstract:

Presented work discusses research results concerning the effect of the heat treatment process. Thermal fatigue which expresses repeated heating and cooling processes affect the ductility or the brittleness of the material. In this research, 70 specimens of copper (1.5 mm thickness, 85 mm length, 32 mm width) are subjected to thermal fatigue at different conditions. Heating temperatures T_h are 100, 300 and 500 °C. Number of repeated cycles N is from 1 to 100. Heating time t_h =600 Sec, and Cooling time; t_C= 900 Sec.  Results are evaluated and then compared to each other and to that of specimens without subjected to thermal fatigue.

Keywords: Copper, hardness, heat treatment, thermal fatigue, thermal analysis.

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Authors: Martin Popescu D. Dana Maria

Abstract:

The aims of this research are to broaden the study on the relationship between emotional intelligence and counterproductive work behavior (CWB). The study sample consisted in 441 Romanian employees from companies all over the country. Data has been collected through web surveys and processed with SPSS. The results indicated an average correlation between the two constructs and their sub variables, employees with a high level of emotional intelligence tend to be less aggressive. In addition, labeling was considered an individual difference which has the power to influence the level of employee aggression. A regression model was used to underline the importance of emotional intelligence together with labeling as predictors of CWB. Results have shown that this regression model enforces the assumption that labeling and emotional intelligence, taken together, predict CWB. Employees, who label themselves as victims and have a low degree of emotional intelligence, have a higher level of CWB.

Keywords: Aggression, CWB, emotional intelligence, labeling.

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Authors: S.H. Khoon, G.I. Issabayeva, L.W. Lee

Abstract:

Air quality in Setapak district of Kuala Lumpur was studied by analysing the rainwater chemical composition using ion chromatography method. Twelve sampling sites were selected and 120 rainwater samples were collected in the period of 10 weeks. The results of this study were compared to the earlier published data and the evaluation showed that the NO3 - ion concentration increased from 0.41 to 3.32 ppm, while SO4 2- ion concentration increased from 0.39 to 3.26 ppm over the past two decades that is mostly due to rapid urban development of the city. However, it was found that the chemical composition for both residential and industrial areas does not have significant difference. Most of the rainwater samples showed alkaline pH (pH > 5.6). The possible factors for such alkaline pH in rainwater samples are assumed to be the marine sources, biomass burning and alkaline character of soil particles.

Keywords: acid deposition; atmospheric pollution; deposition fluxes; trajectories

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Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

Abstract:

In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays

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Authors: Le Zhao, Alain Nogaret

Abstract:

We have built universal central pattern generator (CPG) hardware by interconnecting Hodgkin-Huxley neurons with reciprocally inhibitory synapses. We investigate the dynamics of neuron oscillations as a function of the time delay between current steps applied to individual neurons. We demonstrate stimulus dependent switching between spiking polyrhythms and map the phase portraits of the neuron oscillations to reveal the basins of attraction of the system. We experimentally study the dependence of the attraction basins on the network parameters: The neuron response time and the strength of inhibitory connections.

Keywords: Central pattern generator, winnerless competition principle.

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Authors: Csaba Tóth, Éva Lakatos, László Pethő, Seoyoung Cho

Abstract:

The temperature effect on asphalt pavement structure is a crucial factor at the design stage. In this paper, by applying the German guidelines for temperature along the asphalt depth is estimated. The aim is to consider temperature profiles in different seasons in numerical modelling. The model is built with an elastic and isotropic solid element with 19 subdivisions of asphalt layers to reflect the temperature variation. Comparison with the simple three-layer pavement system (asphalt layers, base, and subgrade layers) will be followed to see the difference in result without temperature variation along with the depth. Finally, the fatigue life calculation was checked to prove the validity of the methodology of considering the temperature in the numerical modelling.

Keywords: Temperature profile, flexible pavement modelling, finite element method, temperature modelling.

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Authors: Won-Ho Kim, Nuwan Sanjeewa Rajasooriya

Abstract:

In this paper, a simple moving human detection method is proposed for video surveillance system or access monitoring system. The frame difference and noise threshold are used for initial detection of a moving human-object, and simple labeling method is applied for final human-object segmentation. The simulated results show that the applied algorithm is fast to detect the moving human-objects by performing 95% of correct detection rate. The proposed algorithm has confirmed that can be used as an intelligent video access monitoring system.

Keywords: Moving human-object detection, Video access monitoring, Image processing.

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Authors: Jong Han Joo, Jeong Hun Lee, Young Sun Kim, Jae Young Kang, Seung Ho Choi

Abstract:

In this study, we propose a novel technique for acoustic echo suppression (AES) during speech recognition under barge-in conditions. Conventional AES methods based on spectral subtraction apply fixed weights to the estimated echo path transfer function (EPTF) at the current signal segment and to the EPTF estimated until the previous time interval. However, the effects of echo path changes should be considered for eliminating the undesired echoes. We describe a new approach that adaptively updates weight parameters in response to abrupt changes in the acoustic environment due to background noises or double-talk. Furthermore, we devised a voice activity detector and an initial time-delay estimator for barge-in speech recognition in communication networks. The initial time delay is estimated using log-spectral distance measure, as well as cross-correlation coefficients. The experimental results show that the developed techniques can be successfully applied in barge-in speech recognition systems.

Keywords: Acoustic echo suppression, barge-in, speech recognition, echo path transfer function, initial delay estimator, voice activity detector.

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Authors: A. Alshebani, Y. Swesi, S. Mrayed, F. Altaher, I. Musbah

Abstract:

Cs-type nanocomposite zeolite membrane was successfully synthesized on an alumina ceramic hollow fibre with a mean outer diameter of 1.7 mm; cesium cationic exchange test was carried out inside test module with mean wall thickness of 230 μm and an average crossing pore size smaller than 0.2 μm. Separation factor of n-butane/H₂ obtained indicate that a relatively high quality closed to 20. Maxwell-Stefan modeling provides an equivalent thickness lower than 1 µm. To compare the difference an application to CO₂/N₂ separation has been achieved, reaching separation factors close to (4,18) before and after cation exchange on H-zeolite membrane formed within the pores of a ceramic alumina substrate.

Keywords: MFI membrane, nanocomposite, Ceramic hollow fibre, CO2, Ion-exchange.

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Authors: Nasir Mehmood, Jens Ogniewski, Vinodh Ravinath

Abstract:

This paper describes the design of a real-time audiorange digital oscilloscope and its implementation in 90nm CMOS FPGA platform. The design consists of sample and hold circuits, A/D conversion, audio and video processing, on-chip RAM, clock generation and control logic. The design of internal blocks and modules in 90nm devices in an FPGA is elaborated. Also the key features and their implementation algorithms are presented. Finally, the timing waveforms and simulation results are put forward.

Keywords: CMOS, VLSI, Oscilloscope, Field Programmable Gate Array (FPGA), VHDL, Video Graphics Array (VGA)

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Authors: Mahmoud Zarrini, R. N. Pralhad

Abstract:

In this paper, mathematical modeling of detonation in the ground is studied. Estimation of flow parameters such as velocity, maximum velocity, acceleration, maximum acceleration, shock pressure as a result of an explosion in the ground have been computed in an appropriate dynamic model approach. The variation of these parameters with the diameter of detonation place (L), density of earth or stone (¤ü), time decay of detonation (T), peak pressure (Pm), and time (t) have been analyzed. The model has been developed from the concept of underwater explosions [Refs. [1]-[3]] with appropriate changes to the present model requirements.

Keywords: Shock velocity, detonation, shock acceleration, shock pressure.

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Authors: G. Sokhansefat, M. Delavar, M. Banedj-Schafii

Abstract:

Recently research on human wayfinding has focused mainly on mental representations rather than processes of wayfinding. The objective of this paper is to demonstrate the rationality behind applying multi-agent simulation paradigm to the modeling of rescuer team wayfinding in order to develop computational theory of perceptual wayfinding in crisis situations using image schemata and affordances, which explains how people find a specific destination in an unfamiliar building such as a hospital. The hypothesis of this paper is that successful navigation is possible if the agents are able to make the correct decision through well-defined cues in critical cases, so the design of the building signage is evaluated through the multi-agent-based simulation. In addition, a special case of wayfinding in a building, finding one-s way through three hospitals, is used to demonstrate the model. Thereby, total rescue time for rescue operation during building fire is computed. This paper discuses the computed rescue time for various signage localization and provides experimental result for optimization of building signage design. Therefore the most appropriate signage design resulted in the shortest total rescue time in various situations.

Keywords: Multi-Agent system (MAS), Spatial Cognition, Wayfinding, Indoor Environment, Geospatial Information System (GIS).

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Authors: Sanjaykumar R. Patel, Parth R. Kayastha

Abstract:

α-lactose monohydrate is widely used in the pharmaceutical industries as an inactive substance that acts as a vehicle or a medium for a drug or other active substance. It is a byproduct of dairy industries, and the recovery of lactose from whey not only boosts the improvement of the economics of whey utilization but also causes a reduction in pollution as lactose recovery can reduce the BOD of whey by more than 80%. In the present study, levels of process parameters were kept as initial lactose concentration (30-50% w/w), sonication amplitude (20-40%), sonication time (2-6 hours), and crystallization temperature (10-20 ^oC) for the recovery of lactose in ultrasound assisted cooling crystallization. In comparison with cooling crystallization, the use of ultrasound enhanced the lactose recovery by 39.17% (w/w). The parameters were optimized for the lactose recovery using Taguchi Method. The optimum conditions found were initial lactose concentration at level 3 (50% w/w), amplitude of sonication at level 2 (40%), the sonication time at level 3 (6 hours), and crystallization temperature at level 1 (10 °C). The maximum recovery was found to be 85.85% at the optimum conditions. Sonication time and the initial lactose concentration were found to be significant parameters for the lactose recovery.

Keywords: Crystallization, Taguchi method, ultrasound, lactose.

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Authors: Vivek V, Hafeez Syed, Darren W Terrell, Harit Naik, Halliburton

Abstract:

Applying a rigorous process to optimize the elements of a supply-chain network resulted in reduction of the waiting time for a service provider and customer. Different sources of downtime of hydraulic pressure controller/calibrator (HPC) were causing interruptions in the operations. The process examined all the issues to drive greater efficiencies. The issues included inherent design issues with HPC pump, contamination of the HPC with impurities, and the lead time required for annual calibration in the USA. HPC is used for mandatory testing/verification of formation tester/pressure measurement/logging-while drilling tools by oilfield service providers, including Halliburton. After market study andanalysis, it was concluded that the current HPC model is best suited in the oilfield industry. To use theexisting HPC model effectively, design andcontamination issues were addressed through design and process improvements. An optimum network is proposed after comparing different supply-chain models for calibration lead-time reduction.

Keywords: Hydraulic Pressure Controller/Calibrator, M/LWD, Pressure, FTWD

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Authors: Rajesh Gupta, Anish Sachdeva, Arvind Bhardwaj

Abstract:

Shippers are concentrating on the core competency to stay competitive and outsourcing the logistic activities to the third party who is expert in this field. This third party logistics (3PL) is drawing the due attention at government, industrial, academicians and practitioner-s levels. If the logistics cost in India can be brought down from the current level of 13% of GDP to 9% (level in the U.S.), the savings would be around Rs 3 lakh crore approximately per annum. But the problem with the shippers is to select the suitable 3PL provider. Various criteria for selection of 3PL have been listed in the literature which are discussed in the present literature review. Every shipper will select the criteria suitable to its own requirement which have to be dynamically reviewed time to time so as to fit in the ever changing environment.

Keywords: 3PL, criteria, shipper, outsourcing

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Authors: Mohamed Azab

Abstract:

In this paper a new maximum power point tracking algorithm for photovoltaic arrays is proposed. The algorithm detects the maximum power point of the PV. The computed maximum power is used as a reference value (set point) of the control system. ON/OFF power controller with hysteresis band is used to control the operation of a Buck chopper such that the PV module always operates at its maximum power computed from the MPPT algorithm. The major difference between the proposed algorithm and other techniques is that the proposed algorithm is used to control directly the power drawn from the PV. The proposed MPPT has several advantages: simplicity, high convergence speed, and independent on PV array characteristics. The algorithm is tested under various operating conditions. The obtained results have proven that the MPP is tracked even under sudden change of irradiation level.

Keywords: Photovoltaic, maximum power point tracking, MPPT.

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Authors: Κonstantinos Kalovrektis, Chryssanthi Palazi

Abstract:

Schools today face ever-increasing demands in their attempts to ensure that students are well equipped to enter the workforce and navigate a complex world. Research indicates that computer technology can help support learning, implementation of various experiments or learning games, and that it is especially useful in developing the higher-order skills of critical thinking, observation, comprehension, implementation, comparison, analysis and active attention to activities such as research, field work, simulations and scientific inquiry. The ICT in education supports the learning procedure by enabling it to be more flexible and effective, create a rich and attractive training environment and equip the students with knowledge and potential useful for the competitive social environment in which they live. This paper presents the design, the development, and the results of the evaluation analysis of an interactive educational game which using real electric vehicles - toys (material) on a toy race track. When the game starts each student selects a specific vehicle toy. Then students are answering questionnaires in the computer. The vehicles' speed is related to the percentage of right answers in a multiple choice questionnaire (software). Every question has its own significant value depending of the different level of questionnaire. Via the developed software, each right or wrong answers in questionnaire increase or decrease the real time speed of their vehicle toys. Moreover the rate of vehicle's speed increase or decrease depends on the difficulty level of each question. The aim of the work is to attract the student’s interest in a learning process and also to improve their scores. The developed real time game was tested using independent populations of students of age groups: 8-10, 11-14, 15-18 years. Standard educational and statistical analysis tools were used for the evaluation analysis of the game. Results reveal that students using the developed real time control game scored much higher (60%) than students using a traditional simulation game on the same questionnaire. Results further indicate that student's interest in repeating the developed real time control gaming was far higher (70%) than the interest of students using a traditional simulation game.

Keywords: Real time game, sensor, learning games, LabVIEW

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Authors: T. Sakamoto, N. Hori

Abstract:

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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