Search results for: Vehicle Dynamics

Authors: T. Hussain, M. W. Siddiqi, A. Iqbal

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The study is aimed to test causal relationship between growth and unemployment, using time series data for Pakistan from 1972 to 2006. Growth is considered to be a pathway to decrease the level of unemployment. Unemployment is a social and political issue. It is a phenomenon where human resources are wasted leading to deacceleration in growth. Johanson Cointegration shows that there is long run relationship between growth and unemployment. For short run dynamics and causality, the study utilizes Vector Error Correction Model (VECM). The results of VECM indicate that there is short and long run causal relation between growth and unemployment including capital, labor and human capital as explanatory variables.

Keywords: Economic Growth, Unemployment, Cointegrationand Causality.

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Authors: Santosh Kr. Choudhary

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In this article, LQR based PID controller design for 3DOF helicopter system is investigated. The 3-DOF helicopter system is a benchmark laboratory model having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. This article first presents the mathematical model of the 3DOF helicopter system and then illustrates the basic idea and technical formulation for controller design. The paper explains the simple approach for the approximation of PID design parameters from the LQR controller gain matrix. The simulation results show that the investigated controller has both static and dynamic performance, therefore the stability and the quick control effect can be obtained simultaneously for the 3DOF helicopter system.

Keywords: 3DOF helicopter system, PID controller, LQR controller, modeling, simulation.

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Authors: Elizabeth M. Hodge, Sharon K. Collins, Eric Kisling

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Virtual environments are a hot topic in academia and more importantly in courses offered via distance education. Today-s gaming generation view virtual worlds as strong social and interactive mediums for communicating and socializing. And while institutions of higher education are challenged with increasing enrollment while balancing budget cuts, offering effective courses via distance education become a valid option. Educators can utilize virtual worlds to offer students an enhanced learning environment which has the power to alleviate feelings of isolation through the promotion of communication, interaction, collaboration, teamwork, feedback, engagement and constructivists learning activities. This paper focuses on the use of virtual environments to facilitate interaction in distance education courses so as to produce positive learning outcomes for students. Furthermore, the instructional strategies were reviewed and discussed for use in virtual worlds to enhance learning within a social context.

Keywords: Virtual Environments, Second Life, Instructional Strategies and Technology

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Authors: Chih-Hui Chiu, Chun-Hsien Lin

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In this study, a robust intelligent backstepping tracking control (RIBTC) system combined with adaptive output recurrent cerebellar model articulation control (AORCMAC) and H∞ control technique is proposed for wheeled inverted pendulums (WIPs) real-time control with exact system dynamics unknown. Moreover, a robust H∞ controller is designed to attenuate the effect of the residual approximation errors and external disturbances with desired attenuation level. The experimental results indicate that the WIPs can stand upright stably when using the proposed RIBTC.

Keywords: Wheeled inverted pendulum, backsteppingtracking control, H∞ control, adaptive output recurrentcerebellar model articulation control.

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Authors: Markus Mazzola, Gunther Schaaf

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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: Moohyun Lee, Soojung Hur, Yongwan Park

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We propose obstacle classification method based on 2D LIDAR Database. The existing obstacle classification method based on 2D LIDAR, has an advantage in terms of accuracy and shorter calculation time. However, it was difficult to classifier the type of obstacle and therefore accurate path planning was not possible. In order to overcome this problem, a method of classifying obstacle type based on width data of obstacle was proposed. However, width data was not sufficient to improve accuracy. In this paper, database was established by width and intensity data; the first classification was processed by the width data; the second classification was processed by the intensity data; classification was processed by comparing to database; result of obstacle classification was determined by finding the one with highest similarity values. An experiment using an actual autonomous vehicle under real environment shows that calculation time declined in comparison to 3D LIDAR and it was possible to classify obstacle using single 2D LIDAR.

Keywords: Obstacle, Classification, LIDAR, Segmentation, Width, Intensity, Database.

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Authors: Khin Thandar Lwin, Than Htike, Zaw Min Naing

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This paper introduces an intelligent system, which can be applied in the monitoring of vehicle speed using a single camera. The ability of motion tracking is extremely useful in many automation problems and the solution to this problem will open up many future applications. One of the most common problems in our daily life is the speed detection of vehicles on a highway. In this paper, a novel technique is developed to track multiple moving objects with their speeds being estimated using a sequence of video frames. Field test has been conducted to capture real-life data and the processed results were presented. Multiple object problems and noisy in data are also considered. Implementing this system in real-time is straightforward. The proposal can accurately evaluate the position and the orientation of moving objects in real-time. The transformations and calibration between the 2D image and the actual road are also considered.

Keywords: Motion Estimation, Image Analyses, Speed Detection

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Authors: V. Geza, J. Vencels, G. Zageris, S. Pavlovs

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One of the most perspective methods to produce SoG-Si is refinement via metallurgical route. The most critical part of this route is refinement from boron and phosphorus. Therefore, a new approach could address this problem. We propose an approach of creating surface waves on silicon melt’s surface in order to enlarge its area and accelerate removal of boron via chemical reactions and evaporation of phosphorus. A two dimensional numerical model is created which includes coupling of electromagnetic and fluid dynamic simulations with free surface dynamics. First results show behaviour similar to experimental results from literature.

Keywords: Numerical modelling, silicon refinement, surface waves, VOF method.

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Authors: Zundong Zhang, Limin Jia, Yuanyuan Chai

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Control of complex systems is one of important files in complex systems, that not only relies on the essence of complex systems which is denoted by the core concept – emergence, but also embodies the elementary concept in control theory. Aiming at giving a clear and self-contained description of emergence, the paper introduces a formal way to completely describe the formation and dynamics of emergence in complex systems. Consequently, this paper indicates the Emergence-Oriented Control methodology that contains three kinds of basic control schemes: the direct control, the system re-structuring and the system calibration. As a universal ontology, the Emergence-Oriented Control provides a powerful tool for identifying and resolving control problems in specific systems.

Keywords: Complex System Control, Emergence, Emergence- Oriented Control Methodology.

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Authors: Naohiko Honma, Kojiro Suzuki

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This paper proposes the concept of aerocapture with aerodynamic-environment-adaptive variable geometry flexible aeroshell that vehicle deploys. The flexible membrane is composed of thin-layer film or textile as its aeroshell in order to solve some problems obstructing realization of aerocapture technique. Multi-objective optimization study is conducted to investigate solutions and derive design guidelines. As a result, solutions which can avoid aerodynamic heating and enlarge the corridor width up to 10% are obtained successfully, so that the effectiveness of this concept can be demonstrated. The deformation-use optimum solution changes its drag coefficient from 1.6 to 1.1, along with the change in dynamic pressure. Moreover, optimization results show that deformation-use solution requires the membrane for which upper temperature limit and strain limit are more than 700 K and 120%, respectively, and elasticity (Young-s modulus) is of order of 106 Pa.

Keywords: Aerocapture, flexible aeroshell, optimization, response surface methodology.

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Authors: H. Bouadi, M. Bouchoucha, M. Tadjine

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In this paper; we are interested principally in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints in order to develop a new control scheme as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation. After, the use of Backstepping approach for the synthesis of tracking errors and Lyapunov functions, a sliding mode controller is developed in order to ensure Lyapunov stability, the handling of all system nonlinearities and desired tracking trajectories. Finally simulation results are also provided in order to illustrate the performances of the proposed controller.

Keywords: Dynamic modeling, nonholonomic constraints, Backstepping, sliding mode.

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Authors: Manan’Iarivo Rasolonjanahary, Chris Bingham, Nigel Schofield, Masoud Bazargan

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This paper presents the research and application of model predictive scheduled charging of electric vehicles (EV) subject to limited available power resource. To focus on algorithm and operational characteristics, the EV interface to the source is modelled as a battery state equation during the charging operation. The researched methods allow for the priority scheduling of EV charging in a multi-vehicle regime and when subject to limited source power availability. Priority attribution for each connected EV is described. The validity of the developed methodology is shown through the simulation of different scenarios of charging operation of multiple connected EVs including non-scheduled and scheduled operation with various numbers of vehicles. Performance of the developed algorithms is also reported with the recommendation of the choice of suitable parameters.

Keywords: Model predictive control, non-scheduled, power limited sources, scheduled and stop-start battery charging.

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Authors: Balsam Mustafa, Safaai Deris

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Requirements are critical to system validation as they guide all subsequent stages of systems development. Inadequately specified requirements generate systems that require major revisions or cause system failure entirely. Use Cases have become the main vehicle for requirements capture in many current Object Oriented (OO) development methodologies, and a means for developers to communicate with different stakeholders. In this paper we present the results of a laboratory experiment that explored whether different types of use case format are equally effective in facilitating high knowledge user-s understanding. Results showed that the provision of diagrams along with the textual use case descriptions significantly improved user comprehension of system requirements in both familiar and unfamiliar application domains. However, when comparing groups that received models of textual description accompanied with diagrams of different level of details (simple and detailed) we found no significant difference in performance.

Keywords: Prior knowledge, requirement specification, usecase format, user understanding.

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Authors: Mohamed Sanad, Noha Hassan

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A broadband resonant terminal antenna has been developed. It can be used in different MIMO arrangements such as 2x2, 4x4, 8x8, or even 12x12 MIMO configurations. The antenna covers the whole LTE and WiFi bands besides the existing 2G/3G bands (700-5800 MHz), without using any matching/tuning circuits. Matching circuits significantly reduce the efficiency of any antenna and reduce the battery life. They also reduce the bandwidth because they are frequency dependent. The antenna can be implemented in smartphone handsets, tablets, laptops, notebooks or any other terminal. It is also suitable for different IoT and vehicle applications. The antenna is manufactured from a flexible material and can be bent or folded and shaped in any form to fit any available space in any terminal. It is self-contained and does not need to use the ground plane, the chassis or any other component of the terminal. Hence, it can be mounted on any terminal at different positions and configurations. Its performance does not get affected by the terminal, regardless of its type, shape or size. Moreover, its performance does not get affected by the human body of the terminal’s users. Because of all these unique features of the antenna, multiples of them can be simultaneously used for MIMO diversity coverage in any terminal device with a high isolation and a low correlation factor between them.

Keywords: IOT, LTE, MIMO, terminal antenna, WiFi.

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Authors: Bahram Talebjedi, Amirmohammad Sattari, Ahmed Zoher Sihorwala, Mina Hoorfar

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Among different droplet manipulations, controlled droplet-splitting is of great significance due to its ability to increase throughput and operational capability. Furthermore, unequal droplet-splitting can provide greater flexibility and a wider range of dilution factors. In this study, we developed two-dimensional, time-dependent complex fluid dynamics simulations to model droplet formation in a flow focusing device, followed by splitting in a Y-shaped junction with sub-channels of unequal widths. From the results obtained from the numerical study, we correlated the diameters of the droplets in the sub-channels to the Weber number, thereby demarcating the droplet splitting and non-splitting regimes.

Keywords: Microfluidics, unequal droplet splitting, two phase flow, flow focusing device.

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Authors: N. Ravi Kumar, R. Kamalakannan

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The advancement of hybrid energy resources such as solar and wind power leading to the emergence of customer owned grid. It provides an opportunity to regulars to obtain low energy costs as well as enabling the power supplier to regulate the utility grid. There is a need to develop smart systems that will automatically submit energy demand schedule and monitors energy price signals in real-time without the prompt of customers. In this paper, a demand side energy management for a grid connected household and also smart preparation of electrical appliance have been presented. It also reduces electricity bill for the consumers in the grid. In addition to this, when production is high, the surplus energy fashioned in the customer owned grid is given to main grid or neighboring micro grids. The simulation of the entire system is presented using LabVIEW software.

Keywords: Distributed renewable energy resource, power storage devices, scheduling, smart meters, smart micro grid, electric vehicle.

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Authors: A. Beheshti, S. Salkhordeh, H. Amini

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Based on statistics released by Islamic Republic of Iran Police (IRIP), from among the total 9555 motorcycle accidents that happened in 2007, 857 riders died and 11219 one got injured. If we also consider the death toll and injuries of other vehicles' accidents resulted from traffic violation by motorcycle riders, then paying attention to the motorcycle accidents seems to be very necessary. Therefore, in this study we tried to investigate the traits and issues related to production, application, and training, along with causes of motorcycle accidents from 4 perspectives of road, human, environment and vehicle and also based on statistical and geographical analysis of accident-sheets prepared by Iran Road Patrol Department (IRPD). Unfamiliarity of riders with regulations and techniques of motorcycling, disuse of safety equipments, inefficiency of roads and design of junctions for safe trafficking of motorcycles and finally the lack of sufficient control of responsible organizations are among the major causes which lead to these accidents.

Keywords: Motorcycle, Motorcycle riders, Road accidents, Statistical analysis of accidents.

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Authors: Mackenzie Leake, Liyu Xia, Kamil Rocki, Wayne Imaino

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In the Hierarchical Temporal Memory (HTM) paradigm the effect of overlap between inputs on the activation of columns in the spatial pooler is studied. Numerical results suggest that similar inputs are represented by similar sets of columns and dissimilar inputs are represented by dissimilar sets of columns. It is shown that the spatial pooler produces these results under certain conditions for the connectivity and proximal thresholds. Following the discussion of the initialization of parameters for the thresholds, corresponding qualitative arguments about the learning dynamics of the spatial pooler are discussed.

Keywords: Hierarchical Temporal Memory, HTM, Learning Algorithms, Machine Learning, Spatial Pooler.

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Authors: Jolly Shah, S.S.Rattan, B.C.Nakra

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Automatic control of the robotic manipulator involves study of kinematics and dynamics as a major issue. This paper involves the forward and inverse kinematics of 2-DOF robotic manipulator with revolute joints. In this study the Denavit- Hartenberg (D-H) model is used to model robot links and joints. Also forward and inverse kinematics solution has been achieved using Artificial Neural Networks for 2-DOF robotic manipulator. It shows that by using artificial neural network the solution we get is faster, acceptable and has zero error.

Keywords: Artificial Neural Network, Forward Kinematics, Inverse Kinematics, Robotic Manipulator

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Authors: A. A. Jafari, A. M. Khoshnood, J. Roshanian

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Attitude control of aerospace system with liquid containers may face to a problem associate with fuel sloshing. The sloshing phenomena can degrade the stability of control system and in the worst case, interaction between the attitude control system and fuel vibration leading to resonance. In this paper, a full process of nonlinear dynamic modeling of an aerospace launch vehicle with fuel sloshing is given. Then, a new control system based on model reference adaptive filter is proposed and its algorithm is extracted. This controller implemented on the main attitude control system. Finally, numerical simulation of nonlinear model and control system is carried out to examine the performance of the new controller. Results of simulations show that the inconvenient effects of the fuel sloshing by augmenting this control system are reduced and attitude control system performs, satisfactorily.

Keywords: nonlinear dynamic modeling, fuel sloshing, vibration control, model reference, adaptive filter

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Authors: E. Menga, S. Hernandez

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Finite Element Models (FEMs) are widely used in order to study and predict the dynamic properties of structures and usually, the prediction can be obtained with much more accuracy in the case of a single component than in the case of assemblies. Especially for structural dynamics studies, in the low and middle frequency range, most complex FEMs can be seen as assemblies made by linear components joined together at interfaces. From a modelling and computational point of view, these types of joints can be seen as localized sources of stiffness and damping and can be modelled as lumped spring/damper elements, most of time, characterized by nonlinear constitutive laws. On the other side, most of FE programs are able to run nonlinear analysis in time-domain. They treat the whole structure as nonlinear, even if there is one nonlinear degree of freedom (DOF) out of thousands of linear ones, making the analysis unnecessarily expensive from a computational point of view. In this work, a methodology in order to obtain the nonlinear frequency response of structures, whose nonlinearities can be considered as localized sources, is presented. The work extends the well-known Structural Dynamic Modification Method (SDMM) to a nonlinear set of modifications, and allows getting the Nonlinear Frequency Response Functions (NLFRFs), through an ‘updating’ process of the Linear Frequency Response Functions (LFRFs). A brief summary of the analytical concepts is given, starting from the linear formulation and understanding what the implications of the nonlinear one, are. The response of the system is formulated in both: time and frequency domain. First the Modal Database is extracted and the linear response is calculated. Secondly the nonlinear response is obtained thru the NL SDMM, by updating the underlying linear behavior of the system. The methodology, implemented in MATLAB, has been successfully applied to estimate the nonlinear frequency response of two systems. The first one is a two DOFs spring-mass-damper system, and the second example takes into account a full aircraft FE Model. In spite of the different levels of complexity, both examples show the reliability and effectiveness of the method. The results highlight a feasible and robust procedure, which allows a quick estimation of the effect of localized nonlinearities on the dynamic behavior. The method is particularly powerful when most of the FE Model can be considered as acting linearly and the nonlinear behavior is restricted to few degrees of freedom. The procedure is very attractive from a computational point of view because the FEM needs to be run just once, which allows faster nonlinear sensitivity analysis and easier implementation of optimization procedures for the calibration of nonlinear models.

Keywords: Frequency response, nonlinear dynamics, structural dynamic modification, softening effect, rubber.

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Authors: M. Saleem Khan, Khaled Benkrid

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This paper presents the development techniques for a complete autonomous design model of an advanced train control system and gives a new approach for the implementation of multi-agents based system. This research work proposes to develop a novel control system to enhance the efficiency of the vehicles under constraints of various conditions, and contributes in stability and controllability issues, considering relevant safety and operational requirements with command control communication and various sensors to avoid accidents. The approach of speed scheduling, management and control in local and distributed environment is given to fulfill the dire needs of modern trend and enhance the vehicles control systems in automation. These techniques suggest the state of the art microelectronic technology with accuracy and stability as forefront goals.

Keywords: Multi-agents, Railway vehicle control system, autonomous design, Train management, Speed scheduling andcontrol.

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Authors: Daria N. Podvigina, Tatiana V. Chernigovskaya

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We have studied the temporal characteristics of bistable perception of the stimuli of two types: one involves alterations in a perceived depth and another one has an ambiguous content. We used the Necker lattice and lines of shadowed circles ambiguously perceived either as spheres or holes as stimuli of the first type. The Winson figure (the Eskimo/Indian picture) was a stimulus of the second type. We have analyzed how often the reversals occurred (reversal rate) and for how long each of the two interpretations, or percepts, was observed during one presentation (stability durations). For all three ambiguous images the reversal rate and the stability durations had similar values, which provide another evidence for a significant role of top-down processes in multistable perception.

Keywords: Multistable perception, perceived depth, reversal rate, top-down processes.

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Authors: Balázs Héder, Róbert Singliar, János Bitó

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The impact of rain attenuation on wireless communication signals is predominant because of the used high frequency (above 10 GHz). The knowledge of statistics of attenuation is very important for planning point-to-point microwave links operating in high frequency band. Describing the statistics of attenuation is possible for instance with fade duration or level crossing rate. In our examination we determine these statistics from one year measured data for a given microwave link, and we are going to make an attempt to transform the level crossing rate statistic to fade duration statistic.

Keywords: Rain attenuation measurement, fade duration, level crossing rate.

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Authors: M. Barański

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This article presents a new vibration diagnostic method designed to (PM) machines with permanent magnets. Those devices are commonly used in small wind and water systems or vehicles drives. The author’s method is very innovative and unique. Specific structural properties of PM machines are used in this method - electromotive force (EMF) generated due to vibrations. There was analysed number of publications which describe vibration diagnostic methods and tests of electrical PM machines and there was no method found to determine the technical condition of such machine basing on their own signals. In this article will be discussed: the method genesis, the similarity of machines with permanent magnet to vibration sensor and simulation and laboratory tests results. The method of determination the technical condition of electrical machine with permanent magnets basing on its own signals is the subject of patent application and it is the main thesis of author’s doctoral dissertation.

Keywords: Electrical vehicle, generator, permanent magnet, traction drive, vibrations.

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Authors: Thach D. Do, Juhum Kwon, Chang-Joo Moon

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A Ground Control System (GCS), which controls Unmanned Aerial Vehicles (UAVs) and monitors their missionrelated data, is one of the major components of UAVs. In fact, some traditional GCSs were built on an expensive, complicated hardware infrastructure with workstations and PCs. In contrast, a GCS on a portable device – such as an Android phone or tablet – takes advantage of its light-weight hardware and the rich User Interface supported by the Android Operating System. We implemented that kind of GCS and called it Ground System Software (GSS) in this paper. In operation, our GSS communicates with UAVs or other GSS via TCP/IP connection to get mission-related data, visualizes it on the device-s screen, and saves the data in its own database. Our study showed that this kind of system will become a potential instrument in UAV-related systems and this kind of topic will appear in many research studies in the near future.

Keywords: Android Operating System, Ground Control System, Mobile Device, Unmanned Aerial Vehicle.

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Authors: Haluk Eren, Ümit Çelik

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Recent developments in unmanned aerial vehicles (UAVs) have begun to attract intense interest. UAVs started to use for many different applications from military to civilian use. Some online retailer and logistics companies are testing the UAV delivery. UAVs have great potentials to reduce cost and time of deliveries and responding to emergencies in a short time. Despite these great positive sides, just a few works have been done for routing of UAVs for package deliveries. As known, transportation of goods from one place to another may have many hazards on delivery route due to falling hazards that can be exemplified as ground objects or air obstacles. This situation refers to wide-range insurance concept. For this reason, deliveries that are made with drones get into the scope of shipping insurance. On the other hand, air traffic was taken into account in the absence of unmanned aerial vehicle. But now, it has been a reality for aerial fields. In this study, the main goal is to conduct risk analysis of package delivery services using drone, based on delivery routes.

Keywords: Drone risk assessment, drone package delivery.

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Authors: Ghazwan Al-Haji

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Most accidents occur in urban areas, and the most related casualties are vulnerable road users (pedestrians and cyclists). The traffic calming measures (TCMs) are widely used and considered to be successful in reducing speed and traffic volume. However, TCMs create unwanted effects include: noise, emissions, energy consumption, vehicle delays and emergency response time (ERT). Different vertical and horizontal TCMs have been already applied nationally (Sweden) and internationally with different impacts. It is a big challenge among traffic engineers, planners, and policy-makers to choose and priorities the best TCMs to be implemented. This study will assess the existing guidelines for TCMs in relation to safety and ERT with focus on data from Norrkoping city in Sweden. The expected results will save lives, time, and money on particularly Swedish Roads. The study will also review newly technologies and how they can improve safety and reduce ERT.

Keywords: Traffic safety, traffic calming measures, speeding, emergency response time.

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Authors: Eshagh Rasouli Sarabi, Mir Saeed Moosavi

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In Iran, due to abundance of energy resources, energy consumption is extraordinarily higher than international standards and transportation sector is considered to be one of the major consumers of energy. Moreover, air pollution in urban areas as a result of high dependence on private vehicle and lower standards of vehicles, high subsidies spent on fuel and time waste due to traffic congestion in urban areas all have led to speculations on new strategies and policies in order to control energy consumption in transportation sector. These strategies and policies will be introduced in this paper and their consequences will be analyzed with consideration to socio-economic factors affecting the urban society of Iran. Besides, the intention is to suggest and analyze new approaches such as broader application of public transportation system, demand management in transport sector, replacement of deteriorated vehicles, quality improvement in car manufacture and introduction of substitute fuels.

Keywords: Consumption, energy, fuel, transportation.

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Authors: Sajid Iqbal, Masood Ahmed, Suhail Aftab Qureshi

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DC-DC converters are widely used in regulated switched mode power supplies and in DC motor drive applications. There are several sources of unwanted nonlinearity in practical power converters. In addition, their operation is characterized by switching that gives birth to a variety of nonlinear dynamics. DC-DC buck and boost converters controlled by pulse-width modulation (PWM) have been simulated. The voltage waveforms and attractors obtained from the circuit simulation have been studied. With the onset of instability, the phenomenon of subharmonic oscillations, quasi-periodicity, bifurcations, and chaos have been observed. This paper is mainly motivated by potential contributions of chaos theory in the design, analysis and control of power converters, in particular and power electronics circuits, in general.

Keywords: Buck converter, boost converter, period- doubling, chaos, bifurcation, strange attractor.

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