Search results for: space vector pulse width modulation.

Authors: Mei Li, Fahui Zhai

Abstract:

In this paper, the definitions of the quaternion measure and the quaternion vector measure are introduced. The relation between the quaternion measure and the complex vector measure as well as the relation between the quaternion linear functional and the complex linear functional are discussed respectively. By using these relations, the necessary and sufficient condition to determine the quaternion vector measure is given.

Keywords: Quaternion, Quaternion measure, Quaternion vector measure, Quaternion Banach space, Quaternion linear functional.

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Authors: M. Sadeghi, A.H. Jafari, S.M.P. Firoozabadi

Abstract:

Deep Brain Stimulation or DBS is the second solution for Parkinson's Disease. Its three parameters are: frequency, pulse width and voltage. They must be optimized to achieve successful treatment. Nowadays it is done clinically by neurologists and there is not certain numerical method to detect them. The aim of this research is to introduce simulation and modeling of Parkinson's Disease treatment as a computational procedure to select optimum voltage. We recorded finger tremor signals of some Parkinsonian patients under DBS treatment at constant frequency and pulse width but variable voltages; then, we adapted a new model to fit these data. The optimum voltages obtained by data fitting results were the same as neurologists- commented voltages, which means modeling can be used as an engineering method to select optimum stimulation voltages.

Keywords: modeling, Deep Brain Stimulation, Parkinson'sdisease, tremor.

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Authors: Hanifah Jambari, Naziha A. Azli, M. Afendi M. Piah

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This paper presents the generation of bipolar square wave pulses with characteristics that are suitable for liquid food sterilization using a Cascaded H-bridge Multilevel Inverter (CHMI). Bipolar square waves pulses have been reported as stable for a longer time during the sterilization process with minimum heat emission and increased efficiency. The CHMI allows the system to produce bipolar square wave pulses and yielding high output voltage without using a transformer while fulfilling the pulse requirements for effective liquid food sterilization. This in turn can reduce power consumption and cost of the overall liquid food sterilization system. The simulation results have shown that pulses with peak output voltage of 2.4 kV, pulse width of between 1 2s and 1 ms at frequencies of 50 Hz and 100 Hz can be generated by a 7-level CHMI. Results from the experimental set-up based on a 5-level CHMI has indicated the potential of the proposed circuit in producing bipolar square wave output pulses with peak values that depends on the DC source level supplied to the CHMI modules, pulse width of between 12.5 2s and 1 ms at frequencies of 50 Hz and 100 Hz.

Keywords: pulsed electric field, multilevel inverter, bipolarsquare wave, food sterilization

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Authors: Wei Zhang, Su-Yan Tang, Yi-Fan Zhu, Wei-Ping Wang

Abstract:

Support vector regression (SVR) has been regarded as a state-of-the-art method for approximation and regression. The importance of kernel function, which is so-called admissible support vector kernel (SV kernel) in SVR, has motivated many studies on its composition. The Gaussian kernel (RBF) is regarded as a “best" choice of SV kernel used by non-expert in SVR, whereas there is no evidence, except for its superior performance on some practical applications, to prove the statement. Its well-known that reproducing kernel (R.K) is also a SV kernel which possesses many important properties, e.g. positive definiteness, reproducing property and composing complex R.K by simpler ones. However, there are a limited number of R.Ks with explicit forms and consequently few quantitative comparison studies in practice. In this paper, two R.Ks, i.e. SV kernels, composed by the sum and product of a translation invariant kernel in a Sobolev space are proposed. An exploratory study on the performance of SVR based general R.K is presented through a systematic comparison to that of RBF using multiple criteria and synthetic problems. The results show that the R.K is an equivalent or even better SV kernel than RBF for the problems with more input variables (more than 5, especially more than 10) and higher nonlinearity.

Keywords: admissible support vector kernel, reproducing kernel, reproducing kernel Hilbert space, support vector regression.

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Authors: Sajid Iqbal, Masood Ahmed, Suhail Aftab Qureshi

Abstract:

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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Authors: Dana M. Ragab, Jasim A Ghaeb

Abstract:

The Voltage Unbalance Factor (VUF) index is recommended to evaluate system performance under unbalanced operation. However, its calculation requires complex algebra which limits its use in the field. Furthermore, one system cycle is required at least to detect unbalance using the VUF. Ideally unbalance mitigation must be performed within 10 ms for 50 Hz systems. In this work, a linear relation for VUF evaluation in three-phase electrical power system using space vector (SV) is derived. It is proposed to determine the voltage unbalance quickly and accurately and to overcome the constraints associated with the traditional methods of VUF evaluation. Aqaba-Qatrana-South Amman (AQSA) power system is considered to study the system performance under unbalanced conditions. The results show that both the complexity of calculations and the time required to evaluate VUF are reduced significantly.

Keywords: Power quality, space vector, unbalance evaluation.

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Authors: Robersy Sánchez, Ricardo Grau

Abstract:

A plausible architecture of an ancient genetic code is derived from an extended base triplet vector space over the Galois field of the extended base alphabet {D, G, A, U, C}, where the letter D represent one or more hypothetical bases with unspecific pairing. We hypothesized that the high degeneration of a primeval genetic code with five bases and the gradual origin and improvements of a primitive DNA repair system could make possible the transition from the ancient to the modern genetic code. Our results suggest that the Watson-Crick base pairing and the non-specific base pairing of the hypothetical ancestral base D used to define the sum and product operations are enough features to determine the coding constraints of the primeval and the modern genetic code, as well as the transition from the former to the later. Geometrical and algebraic properties of this vector space reveal that the present codon assignment of the standard genetic code could be induced from a primeval codon assignment. Besides, the Fourier spectrum of the extended DNA genome sequences derived from the multiple sequence alignment suggests that the called period-3 property of the present coding DNA sequences could also exist in the ancient coding DNA sequences.

Keywords: Genetic code vector space, primeval genetic code, power spectrum.

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Authors: G. R. Arab Markadeh, J. Soltani, N. R. Abjadi, M. Hajian

Abstract:

In this paper, a direct torque control - space vector modulation (DTC-SVM) scheme is presented for a six-phase speed and voltage sensorless induction motor (IM) drive. The decoupled torque and stator flux control is achieved based on IM stator flux field orientation. The rotor speed is detected by on-line estimating of the rotor angular slip speed and stator vector flux speed. In addition, a simple method is introduced to estimate the stator resistance. Moreover in this control scheme the voltage sensors are eliminated and actual motor phase voltages are approximated by using PWM inverter switching times and the dc link voltage. Finally, some simulation and experimental results are presented to verify the effectiveness and capability of the proposed control scheme.

Keywords: Stator FOC, Multiphase motors, sensorless.

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Authors: Hyunhee Ryu, Young Ju Jeon, Jaeuk U. Kim, Hae Jung Lee, Yu Jung Lee, Jong Yeol Kim

Abstract:

The aim of this study was to investigate the effect of blood viscosity on the radial pulse wave. For this, we obtained the radial pulse wave of 15 males with abnormal high hematocrit level and 47 males with normal hematocrit level at the age of thirties and forties. Various variables of the radial pulse wave between two groups were analyzed and compared by Student's T test. There are significant differences in several variables about height, time and area of the pulse wave. The first peak of the radial pulse wave was higher in abnormal high hematocrit group, but the third peak was higher and longer in normal hematocrit group. Our results suggest that the radial pulse wave can be used for diagnosis of high blood viscosity and more clinical application.

Keywords: Radial pulse wave, Blood viscosity, Hematocrit.

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Authors: Peter Antwi Buah, Yingbin Zhang, Jianxian He, Chenlin Xiang, Delali Atsu Y. Bakah

Abstract:

Near-fault ground motions with velocity pulses are considered to cause significant damage to structures or slopes compared to ordinary ground motions without velocity pulses. The double pulsed pulse-like ground motion is well known to be stronger than the single pulse. This research has numerically justified this perspective by studying the dynamic response of a homogeneous rock slope subjected to four pulse-like and two non-pulse-like ground motions using the Fast Lagrangian Analysis of Continua in 3 Dimensions (FLAC3D) software. Two of the pulse-like ground motions just have a single pulse. The results show that near-fault ground motions with velocity pulses can cause a higher dynamic response than regular ground motions. The amplification of the peak ground acceleration (PGA) in horizontal direction increases with the increase of the slope elevation. The seismic response of the slope under double pulse ground motion is stronger than that of the single pulse ground motion. The PGV amplification factor under the effect of the non-pulse-like records is also smaller than those under the pulse-like records. The velocity pulse strengthens the earthquake damage to the slope, which results in producing a stronger dynamic response.

Keywords: Velocity pulses, dynamic response, PGV magnification effect, elevation effect, double pulse.

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Authors: Melih Turgut, Süha Yılmaz

Abstract:

In this paper, first, a characterization of spherical Pseudo null curves in Semi-Euclidean space is given. Then, to investigate position vector of a pseudo null curve, a system of differential equation whose solution gives the components of the position vector of a pseudo null curve on the Frenet axis is established by means of Frenet equations. Additionally, in view of some special solutions of mentioned system, characterizations of some special pseudo null curves are presented.

Keywords: Semi-Euclidean Space, Pseudo Null Curves, Position Vectors.

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Authors: S. Abouda, F. Nollet, A. Chaari, N. Essounbouli, Y. Koubaa

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In this paper we propose the study of a centrifugal pump control system driven by a three-phase induction motor, which is supplied by a PhotoVoltaic PV generator. The system includes solar panel, a DC / DC converter equipped with its MPPT control, a voltage inverter to three-phase Pulse Width Modulation - PWM and a centrifugal pump driven by a three phase induction motor. In order to control the flow of the centrifugal pump, a Direct Torque Control - DTC of the induction machine is used. To illustrate the performances of the control, simulation results are carried out using Matlab/Simulink.

Keywords: Photovoltaic generators, Maximum power point tracking (MPPT), DC/DC converters, Induction motor, Direct torque control (DTC).

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Authors: Sanjay L. Kurkute, Pradeep M. Patil, Kakasaheb C. Mohite

Abstract:

An optimal control strategy based on simple model, a single phase unity power factor boost converter is presented with an evaluation of first order differential equations. This paper presents an evaluation of single phase boost converter having power factor correction. The simple discrete model of boost converter is formed and optimal control is obtained, digital PI is adopted to adjust control error. The method of instantaneous current control is proposed in this paper for its good tracking performance of dynamic response. The simulation and experimental results verified our design.

Keywords: Single phase, boost converter, Power factor correction (PFC), Pulse Width Modulation (PWM).

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Authors: P. Varalaxmi, A. Kirubakaran

Abstract:

This paper presents a thirteen-level asymmetrical cascaded H-bridge single phase inverter. In this configuration, the desired output voltage level is achieved by connecting the DC sources in different combinations by triggering the switches. The modes of operation are explained well for positive level generations. Moreover, a comparison is made with conventional topologies of diode clamped, flying capacitors and cascaded-H-bridge and some recently proposed topologies to show the significance of the proposed topology in terms of reduced part counts. The simulation work has been carried out in MATLAB/Simulink environment. The experimental work is also carried out for lower rating to verify the performance and feasibility of the proposed topology. Further the results are presented for different loading conditions.

Keywords: Multilevel inverter, pulse width modulation, total harmonic distortion, THD.

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Authors: N. Ould Cherchali, A. Tlemçani, M. S. Boucherit, A. Morsli

Abstract:

Nature-inspired metaheuristic algorithms, particularly those founded on swarm intelligence, have attracted much attention over the past decade. Firefly algorithm has appeared in approximately seven years ago, its literature has enlarged considerably with different applications. It is inspired by the behavior of fireflies. The aim of this paper is the application of firefly algorithm for solving a nonlinear algebraic system. This resolution is needed to study the Selective Harmonic Eliminated Pulse Width Modulation strategy (SHEPWM) to eliminate the low order harmonics; results have been applied on multilevel inverters. The final results from simulations indicate the elimination of the low order harmonics as desired. Finally, experimental results are presented to confirm the simulation results and validate the efficaciousness of the proposed approach.

Keywords: Firefly algorithm, metaheuristic algorithm, multilelvel inverter, SHEPWM.

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Authors: A. Yazdanpanah Goharrizi

Abstract:

An improved topology of a voltage-fed quasi-resonant soft switching LCrCdc series-parallel half bridge inverter with a constant-frequency for electronic ballast applications is proposed in this paper. This new topology introduces a low-cost solution to reduce switching losses and circuit rating to achieve high-efficiency ballast. Switching losses effect on ballast efficiency is discussed through experimental point of view. In this discussion, an improved topology in which accomplishes soft switching operation over a wide power regulation range is proposed. The proposed structure uses reverse recovery diode to provide better operation for the ballast system. A symmetrical pulse wide modulation (PWM) control scheme is implemented to regulate a wide range of out-put power. Simulation results are kindly verified with the experimental measurements obtained by ballast-lamp laboratory prototype. Different load conditions are provided in order to clarify the performance of the proposed converter.

Keywords: Electronic ballast, Pulse wide modulation (PWM) Reverse recovery diode, Soft switching.

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Authors: Guangpu Chen

Abstract:

When the failure function is monotone, some monotonic reliability methods are used to gratefully simplify and facilitate the reliability computations. However, these methods often work in a transformed iso-probabilistic space. To this end, a monotonic simulator or transformation is needed in order that the transformed failure function is still monotone. This note proves at first that the output distribution of failure function is invariant under the transformation. And then it presents some conditions under which the transformed function is still monotone in the newly obtained space. These concern the copulas and the dependence concepts. In many engineering applications, the Gaussian copulas are often used to approximate the real word copulas while the available information on the random variables is limited to the set of marginal distributions and the covariances. So this note catches an importance on the conditional monotonicity of the often used transformation from an independent random vector into a dependent random vector with Gaussian copulas.

Keywords: Monotonic, Rosenblatt, Nataf transformation, dependence concepts, completely positive matrices, Gaussiancopulas

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Authors: Fariba Haghbin, Othman Bin Ibrahim, Mohammad Reza Attarzadeh Niaki

Abstract:

With the development of virtual communities, there is an increase in the number of members in Virtual Communities (VCs). Many join VCs with the objective of sharing their knowledge and seeking knowledge from others. Despite the eagerness of sharing knowledge and receiving knowledge through VCs, there is no standard of assessing ones knowledge sharing capabilities and prospects of knowledge sharing. This paper developed a vector space model to assess the knowledge sharing prospect of VC users.

Keywords: Knowledge sharing network, Virtual community, knowledge relationship, Vector Space Model.

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Authors: Wang liguo, Wang zongmin, Kong ying

Abstract:

A novel interpolation scheme to extend usable spectrum and upconvert in high performance D/A converters is addressed in this paper. By adjusting the pulse width of cycle and the production circuit of code, the expansion code is a null code or complementary code that is interpolation process. What the times and codes of interpolation decide DAC works in one of a normal mode or multi-mixer mode so that convert the input digital data signal into normal signal or a mixed analog signal having a mixer frequency that is higher than the data frequency. Simulation results show that the novel scheme and apparatus most extend the usable frequency spectrum into fifth to sixth Nyquist zone beyond conventional DACs.

Keywords: interpolation, upconversion, modulation, switching function, duty cycle.

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Authors: A. Аndreev, Yu. Rozhdestvenskii, К. Platonov, R. Salomaa

Abstract:

This paper considers various channels of gammaquantum generation via an ultra-short high-power laser pulse interaction with different targets.We analyse the possibilities to create a pulsed gamma-radiation source using laser triggering of some nuclear reactions and isomer targets. It is shown that sub-MeV monochromatic short pulse of gamma-radiation can be obtained with pulse energy of sub-mJ level from isomer target irradiated by intense laser pulse. For nuclear reaction channel in light- atom materials, it is shown that sub-PW laser pulse gives rise to formation about million gamma-photons of multi-MeV energy.

Keywords: High power laser, short pulse, fast particles, isomertarget.

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Authors: József Valyon, Gábor Horváth

Abstract:

In comparison to the original SVM, which involves a quadratic programming task; LS–SVM simplifies the required computation, but unfortunately the sparseness of standard SVM is lost. Another problem is that LS-SVM is only optimal if the training samples are corrupted by Gaussian noise. In Least Squares SVM (LS–SVM), the nonlinear solution is obtained, by first mapping the input vector to a high dimensional kernel space in a nonlinear fashion, where the solution is calculated from a linear equation set. In this paper a geometric view of the kernel space is introduced, which enables us to develop a new formulation to achieve a sparse and robust estimate.

Keywords: Support Vector Machines, Least Squares SupportVector Machines, Regression, Sparse approximation.

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Authors: Mohamed Fathy Heweage, Xiao Wen, Ayman Mokhtar, Ahmed Eldamarawy

Abstract:

In this paper, we are interested in modeling, simulation, and measurement of the laser spot position with a quadrant detector. We enhance detection and tracking of semi-laser weapon decoding system based on microcontroller. The system receives the reflected pulse through quadrant detector and processes the laser pulses through a processing circuit, a microcontroller decoding laser pulse reflected by the target. The seeker accuracy will be enhanced by the decoding system, the laser detection time based on the receiving pulses number is reduced, a gate is used to limit the laser pulse width. The model is implemented based on Pulse Repetition Frequency (PRF) technique with two microcontroller units (MCU). MCU1 generates laser pulses with different codes. MCU2 decodes the laser code and locks the system at the specific code. The codes EW selected based on the two selector switches. The system is implemented and tested in Proteus ISIS software. The implementation of the full position determination circuit with the detector is produced. General system for the spot position determination was performed with the laser PRF for incident radiation and the mechanical system for adjusting system at different angles. The system test results show that the system can detect the laser code with only three received pulses based on the narrow gate signal, and good agreement between simulation and measured system performance is obtained.

Keywords: 4-quadrant detector, pulse code detection, laser guided weapons, pulse repetition frequency, ATmega 32 microcontrollers.

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Authors: Mohamed. A. Shrud, Ahmad H. Kharaz, Ahmed. S. Ashur, Ahmed Faris, Mustafa Benamar

Abstract:

This paper will focus on modeling, analysis and simulation of a 42V/14V dc/dc converter based architecture. This architecture is considered to be technically a viable solution for automotive dual-voltage power system for passenger car in the near further. An interleaved dc/dc converter system is chosen for the automotive converter topology due to its advantages regarding filter reduction, dynamic response, and power management. Presented herein, is a model based on one kilowatt interleaved six-phase buck converter designed to operate in a Discontinuous Conduction Mode (DCM). The control strategy of the converter is based on a voltagemode- controlled Pulse Width Modulation (PWM) with a Proportional-Integral-Derivative (PID). The effectiveness of the interleaved step-down converter is verified through simulation results using control-oriented simulator, MatLab/Simulink.

Keywords: Automotive, dc-to-dc power modules, design, interleaved, Matlab\Simulink and PID control.

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Authors: S. Nazhan, Hassan K. Al-Musawi, Khalid A. Humood

Abstract:

This paper reports on an experimental investigation into the influence of current modulation on the properties of a vertical-cavity surface-emitting laser (VCSEL) with a direct square wave modulation. The optical output power response, as a function of the pumping current, modulation frequency, and amplitude, is measured for an 850 nm VCSEL. We demonstrate that modulation frequency and amplitude play important roles in reducing the VCSEL’s power consumption for optical generation. Indeed, even when the biasing current is below the static threshold, the VCSEL emits optical power under the square wave modulation. The power consumed by the device to generate light is significantly reduced to > 50%, which is below the threshold current, in response to both the modulation frequency and amplitude. An operating VCSEL device at low power is very desirable for less thermal effects, which are essential for a high-speed modulation bandwidth.

Keywords: VCSELs, optical power generation, power consumption, square wave modulation.

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Authors: D. Liu, D. M. Donskoy

Abstract:

The vibroacoustic modulation method is based on the modulation effect of high-frequency ultrasonic wave (carrier) by low-frequency vibration in the presence of various defects, primarily contact-type such as cracks, delamination, etc. The presence and severity of the defect are measured by the ratio of the spectral sidebands and the carrier in the spectrum of the modulated signal. This approach, however, does not differentiate between amplitude and frequency modulations, AM and FM, respectfully. This paper is an attempt to explain the generation mechanisms of FM and its correlation with the flaw properties. Here we proposed two possible mechanisms leading to FM modulation based on nonlinear local defect resonance and dynamic acoustoelastic models.

Keywords: Non-destructive testing, nonlinear acoustics, structural health monitoring, acoustoelasticity, local defect resonance.

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Authors: Wilfred Fritz

Abstract:

Grid connected solar PV inverters need to be compliant to standard regulations regarding unwanted harmonic generation. This paper gives an introduction to harmonics, solar PV inverter voltage regulation and balancing through compensation and investigates the behaviour of harmonic generation at different power levels. Practical measurements of harmonics and power levels with a power quality data logger were made, on a test network at a university in Germany. The test setup and test results are discussed. The major finding was that between the morning and afternoon load peak windows when the PV inverters operate under low solar insolation and low power levels, more unwanted harmonics are generated. This has a huge impact on the power quality of the grid as well as capital and maintenance costs. The design of a single-tuned harmonic filter towards harmonic mitigation is presented.

Keywords: Harmonics, power quality, pulse width modulation, total harmonic distortion.

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Authors: A-Q. Nguyen. A. Amrhar, J. Zambrano, G. Brown, O.A. Yeste-Ojeda, R. Jr. Landry

Abstract:

Since the presence of Next Generation Air Transportation System (NextGen), Automatic Dependent Surveillance-Broadcast (ADS-B) has raised specific concerns related to the privacy and security, due to its vulnerable, low-level of security and limited payload. In this paper, the authors introduce and analyze the combination of Pulse Amplitude Modulation (PAM) and Phase Shift Keying (PSK) Modulation in conventional ADS-B, forming Secure ADS-B (SADS-B) avionics. In order to demonstrate the potential of this combination, Hardware-in-the-loop (HIL) simulation was used. The tests' results show that, on the one hand, SADS-B can offer five times the payload as its predecessor. This additional payload of SADS-B can be used in various applications, therefore enhancing the ability and efficiency of the current ADS-B. On the other hand, by using the extra phase modulated bits as a digital signature to authenticate ADS-B messages, SADS-B can increase the security of ADS-B, thus ensure a more secure aviation as well. More importantly, SADS-B is compatible with the current ADS-B In and Out. Hence, no significant modifications will be needed to implement this idea. As a result, SADS-B can be considered the most promising approach to enhance the capability and security of ADS-B.

Keywords: ADS-B authentication, ADS-B security, NextGen ADS-B, PSK signature, secure ADS-B.

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Authors: H. Sediki, S. Djennoune

Abstract:

The switching lag-time and the voltage drop across the power devices cause serious waveform distortions and fundamental voltage drop in pulse width-modulated inverter output. These phenomenons are conspicuous when both the output frequency and voltage are low. To estimate the output voltage from the PWM reference signal it is essential to take account of these imperfections and to correct them. In this paper, on-line compensation method is presented. It needs three simple blocs to add at the ideal reference voltages. This method does not require any additional hardware circuit and off- line experimental measurement. The paper includes experimental results to demonstrate the validity of the proposed method. It is applied, finally, in case of indirect vector controlled induction machine and implemented using dSpace card.

Keywords: Dead time, field-oriented control, Induction motor, PWM inverter, voltage drop.

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Authors: Shi Chen, Zi Y. Chen, Jian K. Dan, Jian F. Li

Abstract:

Evolution of one-dimensional electron system under high-energy-density (HED) conditions is investigated, using the principle of least-action and variational method. In a single-mode modulation model, the amplitude and spatial wavelength of the modulation are chosen to be general coordinates. Equations of motion are derived by considering energy conservation and force balance. Numerical results show that under HED conditions, electron density modulation could exist. Time dependences of amplitude and wavelength are both positively related to the rate of energy input. Besides, initial loading speed has a significant effect on modulation amplitude, while wavelength relies more on loading duration.

Keywords: Electron density modulation, HED, nonlinearevolution, plasmas.

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Authors: Kemal Efe, Gui-Liang Feng

Abstract:

The optimal bisection width of r-dimensional N× · · ·× N grid is known to be Nr-1 when N is even, but when N is odd, only approximate values are available. This paper shows that the exact bisection width of grid is Nr -1 N-1 when N is odd.

Keywords: Grids, Parallel Architectures, Graph Bisection, VLSI Layouts.

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