Search results for: switching function.

Authors: Neelam Bawane nee' Singhal, C. V. Srikrishna

Abstract:

Many metrics were proposed to evaluate the characteristics of the analysis and design model of a given product which in turn help to assess the quality of the product. Function point metric is a measure of the 'functionality' delivery by the software. This paper presents an analysis of a set of programs of a project developed in Cµ through Function Points metric. Function points are measured for a Data Flow Diagram (DFD) of the case developed at initial stage. Lines of Codes (LOCs) and possible errors are calculated with the help of measured Function Points (FPs). The calculations are performed using suitable established functions. Calculated LOCs and errors are compared with actual LOCs and errors found at the time of analysis & design review, implementation and testing. It has been observed that actual found errors are more than calculated errors. On the basis of analysis and observations, authors conclude that function point provides useful insight and helps to analyze the drawbacks in the development process.

Keywords: Function Points, Data Flow Diagram, Lines ofCodes.

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Authors: Essam S. Altubaishi

Abstract:

The motivation for adaptive modulation and coding is to adjust the method of transmission to ensure that the maximum efficiency is achieved over the link at all times. The receiver estimates the channel quality and reports it back to the transmitter. The transmitter then maps the reported quality into a link mode. This mapping however, is not a one-to-one mapping. In this paper we investigate a method for selecting the proper modulation scheme. This method can dynamically adapt the mapping of the Signal-to- Noise Ratio (SNR) into a link mode. It enables the use of the right modulation scheme irrespective of changes in the channel conditions by incorporating errors in the received data. We propose a Markov model for this method, and use it to derive the average switching thresholds and the average throughput. We show that the average throughput of this method outperforms the conventional threshold method.

Keywords: Adaptive modulation and coding, CDMA, Markov model.

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Authors: Vladimir S. Timofeev

Abstract:

In this article the problem of distributional moments estimation is considered. The new approach of moments estimation based on usage of the characteristic function is proposed. By statistical simulation technique author shows that new approach has some robust properties. For calculation of the derivatives of characteristic function there is used numerical differentiation. Obtained results confirmed that author’s idea has a certain working efficiency and it can be recommended for any statistical applications.

Keywords: Characteristic function, distributional moments, robustness, outlier, statistical estimation problem, statistical simulation.

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Authors: G. Bal, D. Uygun

Abstract:

This paper describes the design and modeling procedure of a novel 5-phase segment type switched reluctance motor (ST-SRM) under simultaneous two-phase (bipolar) excitation of windings. The rotor cores of ST-SRM are embedded in an aluminum block as well as to improve the performance characteristics. The magnetic circuit of the produced ST-SRM is constructed so that the magnetic flux paths are short and exclusive to each phase, thereby minimizing the commutation switching and eddy current losses in the laminations. The design and simulation principles presented apply primarily to conventional SRM and ST-SRM. It is proved that the novel 5-phase switched reluctance motor under two-phase excitation is superior among the criteria used in comparison. The purposed model is particularly well suited for high torque and weight constrained applications such as automobiles, aerospace and military applications.

Keywords: Segmental Rotor Pairs, Two-phase Excitation, Commutation Switching, Aluminum Block.

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Authors: A. Faruk Bakan, İsmail Aksoy, Nihan Altintaş

Abstract:

In this paper, half bridge DC-DC converters with transformer isolation presented in the literature are analyzed for highcurrent and low-voltage applications under the same operation conditions, and compared in terms of losses and efficiency. The conventional and improved half-bridge DC-DC converters are simulated, and current and voltage waveforms are obtained for input voltage Vdc=500V, output current IO=450A, output voltage VO=38V and switching frequency fS=20kHz. IGBTs are used as power semiconductor switches. The power losses of the semiconductor devices are calculated from current and voltage waveforms. From simulation results, it is seen that the capacitor switched half bridge converter has the best efficiency value, and can be preferred at high power and high frequency applications.

Keywords: Isolated half bridge DC-DC converter, high-current low-voltage applications, soft switching, high efficiency.

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Authors: Rashidah Omar, Suzeini Abdul Halim, Aini Janteng

Abstract:

The coefficients estimate problem for Taylor-Maclaurin series is still an open problem especially for a function in the subclass of bi-univalent functions. A function f ϵ A is said to be bi-univalent in the open unit disk D if both f and f^-1 are univalent in D. The symbol A denotes the class of all analytic functions f in D and it is normalized by the conditions f(0) = f’(0) – 1=0. The class of bi-univalent is denoted by  The subordination concept is used in determining second and third Taylor-Maclaurin coefficients. The upper bound for second and third coefficients is estimated for functions in the subclasses of bi-univalent functions which are subordinated to the function φ. An analytic function f is subordinate to an analytic function g if there is an analytic function w defined on D with w(0) = 0 and |w(z)| < 1 satisfying f(z) = g[w(z)]. In this paper, two subclasses of bi-univalent functions associated with Hohlov operator are introduced. The bound for second and third coefficients of functions in these subclasses is determined using subordination. The findings would generalize the previous related works of several earlier authors.

Keywords: Analytic functions, bi-univalent functions, Hohlov operator, subordination.

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Authors: Z. Altawallbeh

Abstract:

In this paper, an explicit homotopic function is constructed to compute the Hochschild homology of a finite dimensional free k-module V. Because the polynomial algebra is of course fundamental in the computation of the Hochschild homology HH and the cyclic homology CH of commutative algebras, we concentrate our work to compute HH of the polynomial algebra, by providing certain homotopic function.

Keywords: Exterior algebra, free resolution, free and projective modules, Hochschild homology, homotopic function, symmetric algebra.

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Authors: Kourosh Parand, Jamal Amani Rad

Abstract:

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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Authors: Sergey M. Karabanov, Dmitry V. Suvorov

Abstract:

Magnetically controlled microelectromechanical system (MCMEMS) switches is one of the directions in the field of micropower switching technology. MCMEMS switches are a promising alternative to Hall sensors and reed switches. The most important parameter for MCMEMS is the contact resistance, which should have a minimum value and is to be stable for the entire duration of service life. The value and stability of the contact resistance is mainly determined by the contact coating material. This paper presents the research results of a contact coating based on nanoscale ruthenium films obtained by electrolytic deposition. As a result of the performed investigations, the deposition modes of ruthenium films are chosen, the regularities of the contact resistance change depending on the number of contact switching, and the coating roughness are established. It is shown that changing the coating roughness makes it possible to minimize the contact resistance.

Keywords: Contact resistance, electrode coating, electrolythic deposition, magnetically controlled MEMS.

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Authors: E. Assareh, M.A. Behrang, M. Ghalambaz, A.R. Noghrehabadi, A. Ghanbarzadeh

Abstract:

In this paper, a new approach is introduced to solve Blasius equation using parameter identification of a nonlinear function which is used as approximation function. Bees Algorithm (BA) is applied in order to find the adjustable parameters of approximation function regarding minimizing a fitness function including these parameters (i.e. adjustable parameters). These parameters are determined how the approximation function has to satisfy the boundary conditions. In order to demonstrate the presented method, the obtained results are compared with another numerical method. Present method can be easily extended to solve a wide range of problems.

Keywords: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

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Authors: Norlyda Mohamed, Daud Mohamad, Shaharuddin Cik Soh

Abstract:

Let Gα ,β (γ ,δ ) denote the class of function f (z), f (0) = f ′(0)−1= 0 which satisfied e δ {αf ′(z)+ βzf ′′(z)}> γ i Re in the open unit disk D = {z ∈ı : z < 1} for some α ∈ı (α ≠ 0) , β ∈ı and γ ∈ı (0 ≤γ <α ) where δ ≤ π and α cosδ −γ > 0 . In this paper, we determine some extremal properties including distortion theorem and argument of f ′( z ) .

Keywords: Argument of f ′(z) , Carathéodory Function, Closeto- convex Function, Distortion Theorem, Extremal Properties

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Authors: R. Srinivasa Rao, S. V. L. Narasimham

Abstract:

This paper presents a novel approach for optimal reconfiguration of radial distribution systems. Optimal reconfiguration involves the selection of the best set of branches to be opened, one each from each loop, such that the resulting radial distribution system gets the desired performance. In this paper an algorithm is proposed based on simple heuristic rules and identified an effective switch status configuration of distribution system for the minimum loss reduction. This proposed algorithm consists of two parts; one is to determine the best switching combinations in all loops with minimum computational effort and the other is simple optimum power loss calculation of the best switching combination found in part one by load flows. To demonstrate the validity of the proposed algorithm, computer simulations are carried out on 33-bus system. The results show that the performance of the proposed method is better than that of the other methods.

Keywords: Distribution system, network reconfiguration, powerloss reduction, radial network, heuristic technique.

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Authors: Sudha Bansal, Lalit Mohan Saini, Dheeraj Joshi

Abstract:

The controller is used to improve the dynamic performance of DC-DC converter by achieving a robust output voltage against load disturbances. This paper presents the performance of PI and Fuzzy controller for a phase- shifted zero-voltage switched full-bridge PWM (ZVS FB- PWM) converters with a closed loop control. The proposed converter is regulated with minimum overshoot and good stability. In this paper phase-shift control method is used as an effective tool to reduce switching losses and duty cycle losses. A 1kW/100KHz dc/dc converter is simulated and analyzed using MATLAB. The circuit is simulated for static and dynamic load (DC motor). It has been observed that performance of converter with fuzzy controller is better than that of PI controller. An efficiency comparison of the converter with a reported topology has also been carried out.

Keywords: Full-bridge converter, phase-shifted, synchronous rectifier (SR), zero-voltage switching (ZVS).

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Authors: Maha Sliti, Walid Abdallah, Noureddine Boudriga

Abstract:

In the frame of this work, we present an optical multicasting approach based on optical code-words. Our approach associates, in the edge node, an optical code-word to a group multicast address. In the core node, a set of tunable decoders are used to send a traffic data to multiple destinations based on the received code-word. The use of code-words, which correspond to the combination of an input port and a set of output ports, allows the implementation of an optical switching matrix. At the reception of a burst, it will be delayed in an optical memory. And, the received optical code-word is split to a set of tunable optical decoders. When it matches a configured code-word, the delayed burst is switched to a set of output ports.

Keywords: Optical multicast, optical burst switching networks, optical code-words, tunable decoder, virtual optical memory.

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Authors: Maha Sliti, Walid Abdallah, Noureddine Boudriga

Abstract:

In the frame of this work, we present an optical multicasting approach based on optical code-words. Our approach associates, in the edge node, an optical code-word to a group multicast address. In the core node, a set of tunable decoders are used to send a traffic data to multiple destinations based on the received code-word. The use of code-words, which correspond to the combination of an input port and a set of output ports, allows the implementation of an optical switching matrix. At the reception of a burst, it will be delayed in an optical memory. And, the received optical code-word is split to a set of tunable optical decoders. When it matches a configured code-word, the delayed burst is switched to a set of output ports.

Keywords: Optical multicast, optical burst switching networks, optical code-words, tunable decoder, virtual optical memory.

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Authors: Peichen Zhao

Abstract:

In this paper, we extend the compound binomial model to the case where the premium income process, based on a binomial process, is no longer a linear function. First, a mathematically recursive formula is derived for non ruin probability, and then, we examine the expected discounted penalty function, satisfy a defect renewal equation. Third, the asymptotic estimate for the expected discounted penalty function is then given. Finally, we give two examples of ruin quantities to illustrate applications of the recursive formula and the asymptotic estimate for penalty function.

Keywords: Discounted penalty function, compound binomial process, recursive formula, discrete renewal equation, asymptotic estimate.

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Authors: Pallav Roxy, Durga Toshniwal

Abstract:

Clustering unstructured text documents is an important issue in data mining community and has a number of applications such as document archive filtering, document organization and topic detection and subject tracing. In the real world, some of the already clustered documents may not be of importance while new documents of more significance may evolve. Most of the work done so far in clustering unstructured text documents overlooks this aspect of clustering. This paper, addresses this issue by using the Fading Function. The unstructured text documents are clustered. And for each cluster a statistics structure called Cluster Profile (CP) is implemented. The cluster profile incorporates the Fading Function. This Fading Function keeps an account of the time-dependent importance of the cluster. The work proposes a novel algorithm Clustering n-ary Merge Algorithm (CnMA) for unstructured text documents, that uses Cluster Profile and Fading Function. Experimental results illustrating the effectiveness of the proposed technique are also included.

Keywords: Clustering, Text Mining, Unstructured TextDocuments, Fading Function.

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Authors: Saleem Z. Ramadan, Gürsel A. Süer

Abstract:

In this paper a genetic algorithm (GA) with dual-fitness function is proposed and applied to solve the deterministic identical machine scheduling problem. The mating fitness function value was used to determine the mating for chromosomes, while the selection fitness function value was used to determine their survivals. The performance of this algorithm was tested on deterministic identical machine scheduling using simulated data. The results obtained from the proposed GA were compared with classical GA and integer programming (IP). Results showed that dual-fitness function GA outperformed the classical single-fitness function GA with statistical significance for large problems and was competitive to IP, particularly when large size problems were used.

Keywords: Machine scheduling, Genetic algorithms, Due dates, Number of tardy jobs, Number of early jobs, Integer programming, Dual Fitness functions.

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Authors: Minh T. N. Le, Cathleen Teh, Ng Shyh-Chang, Vladimir Korzh, Harvey F. Lodish, Bing Lim

Abstract:

MicroRNAs are an important class of gene expression regulators that are involved in many biological processes including embryogenesis. miR-125b is a conserved microRNA that is enriched in the nervous system. We have previously reported the function of miR-125b in neuronal differentiation of human cell lines. We also discovered the function of miR-125b in regulating p53 in human and zebrafish. Here we further characterize the brain defects in zebrafish embryos injected with morpholinos against miR-125b. Our data confirm the essential role of miR-125b in brain morphogenesis particularly in maintaining the balance between proliferation, cell death and differentiation. We identified lunatic fringe (lfng) as an additional target of miR-125b in human and zebrafish and suggest that lfng may mediate the function of miR-125b in neurogenesis. Together, this report reveals new insights into the function of miR- 125b during neural development of zebrafish.

Keywords: microRNA, miR-125b, neurogenesis, zebrafish.

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Authors: Yuan Zheng

Abstract:

3D model-based vehicle matching provides a new way for vehicle recognition, localization and tracking. Its key is to construct an evaluation function, also called fitness function, to measure the degree of vehicle matching. The existing fitness functions often poorly perform when the clutter and occlusion exist in traffic scenarios. In this paper, we present a practical and efficient fitness function. Unlike the existing evaluation functions, the proposed fitness function is to study the vehicle matching problem from both local and global perspectives, which exploits the pixel gradient information as well as the silhouette information. In view of the discrepancy between 3D vehicle model and real vehicle, a weighting strategy is introduced to differently treat the fitting of the model’s wireframes. Additionally, a normalization operation for the model’s projection is performed to improve the accuracy of the matching. Experimental results on real traffic videos reveal that the proposed fitness function is efficient and robust to the cluttered background and partial occlusion.

Keywords: 3D-2D matching, fitness function, 3D vehicle model, local image gradient, silhouette information.

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Authors: M. Suresh Kumar, K. Ramani

Abstract:

This paper proposed the comparison made between Multi-Carrier Pulse Width Modulation, Sinusoidal Pulse Width Modulation and Selective Harmonic Elimination Pulse Width Modulation technique for minimization of Total Harmonic Distortion in Cascaded H-Bridge Multi-Level Inverter. In Multicarrier Pulse Width Modulation method by using Alternate Position of Disposition scheme for switching pulse generation to Multi-Level Inverter. Another carrier based approach; Sinusoidal Pulse Width Modulation method is also implemented to define the switching pulse generation system in the multi-level inverter. In Selective Harmonic Elimination method using Genetic Algorithm and Particle Swarm Optimization algorithm for define the required switching angles to eliminate low order harmonics from the inverter output voltage waveform and reduce the total harmonic distortion value. So, the results validate that the Selective Harmonic Elimination Pulse Width Modulation method does capably eliminate a great number of precise harmonics and minimize the Total Harmonic Distortion value in output voltage waveform in compared with Multi-Carrier Pulse Width Modulation method, Sinusoidal Pulse Width Modulation method. In this paper, comparison of simulation results shows that the Selective Harmonic Elimination method can attain optimal harmonic minimization solution better than Multi-Carrier Pulse Width Modulation method, Sinusoidal Pulse Width Modulation method.

Keywords: Multi-level inverter, Selective Harmonic Elimination Pulse Width Modulation, Multi-Carrier Pulse Width Modulation, Total Harmonic Distortion, Genetic Algorithm.

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Authors: L. Moussaoui, L. Rahmani

Abstract:

This paper deals with the direct torque control (DTC) of the induction motor. This type of control allows decoupling control between the flux and the torque without the need for a transformation of coordinates. However, as with other hysteresis-based systems, the classical DTC scheme represents a high ripple, in both the electromagnetic torque and the stator flux and a distortion in the stator current. As well, it suffers from variable switching frequency. To solve these problems various modifications, in conventional DTC scheme, have been made during the last decade. Indeed the DTC based on space vector modulation (SVM) has proved to generate very low ripples in torque and flux with constant switching frequency. It also shows almost the same dynamic performances as the classical DTC system. On the other hand, fuzzy logic is considered as an interesting alternative approach for its advantages: Analysis close to the exigencies of user, ability of nonlinear systems control, best dynamic performances and inherent quality of robustness.

Therefore, two fuzzy direct torque control approaches, for the induction motor fed by SVM-voltage source inverter, are proposed in this paper. By using these two approaches of DTC, the advantages of fuzzy logic control, space vector modulation, and direct torque control method are combined. The performances of these DTC schemes are evaluated through digital simulation using Matlab/Simulink platform and fuzzy logic tools. Simulation results illustrate the effectiveness and the superiority of the proposed Fuzzy DTC-SVM schemes in comparison to the classical DTC.

Keywords: Direct torque control, Fuzzy logic control, Induction motor, Switching frequency, Space vector modulation, Torque and flux ripples.

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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: S. Massoum, A. Bentaallah, A. Massoum, F. Benaimeche, P. Wira, A. Meroufel

Abstract:

This paper presents a speed fuzzy sliding mode controller for a vector controlled induction machine (IM) fed by a voltage source inverter (PWM). The sliding mode based fuzzy control method is developed to achieve fast response, a best disturbance rejection and to maintain a good decoupling. The problem with sliding mode control is that there is high frequency switching around the sliding mode surface. The FSMC is the combination of the robustness of Sliding Mode Control (SMC) and the smoothness of Fuzzy Logic (FL). To reduce the torque fluctuations (chattering), the sign function used in the conventional SMC is substituted with a fuzzy logic algorithm. The proposed algorithm was simulated by Matlab/Simulink software and simulation results show that the performance of the control scheme is robust and the chattering problem is solved.

Keywords: IM, FOC, FLC, SMC, and FSMC.

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Authors: Abdul Rashid Husain, Mohamad Noh Ahmad, Abdul Halim Mohd Yatim

Abstract:

In this paper, a few chattering-free Sliding Mode Controllers (SMC) are proposed to stabilize an Active Magnetic Bearing (AMB) system with gyroscopic effect that is proportional to the rotor speed. The improved switching terms of the controller inherited from the saturation-type function and boundary layer control technique is shown to be able to achieve bounded and asymptotic stability, respectively, while the chattering effect in the input is attenuated. This is proven to be advantageous for AMB system since minimization of chattering results in optimized control effort. The performance of each controller is demonstrated via result of simulation in which the measurement of the total consumed energy and maximum control magnitude of each controller illustrates the effectiveness of the proposed controllers.

Keywords: Active Magnetic Bearing (AMB), Sliding Mode Control (SMC), chattering-free SMC.

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Authors: E. E. El-Kholy, Ahamed Kalas, Mahmoud Fauzy, M. El-Shahat Dessouki, Abdou. M. El-Refay, Mohammed El-Zefery

Abstract:

Direct Torque Control (DTC) is an AC drive control method especially designed to provide fast and robust responses. In this paper a progressive algorithm for direct torque control of threephase induction drive system supplied by photovoltaic arrays using voltage source inverter to control motor torque and flux with maximum power point tracking at different level of insolation is presented. Experimental results of the new DTC method obtained by an experimental rapid prototype system for drives are presented. Simulation and experimental results confirm that the proposed system gives quick, robust torque and speed responses at constant switching frequencies.

Keywords: Photovoltaic (PV) array, direct torque control (DTC), constant switching frequency, induction motor, maximum power point tracking (MPPT).

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Authors: V. Joshi Manohar, P. Sujatha, K. S. R. Anjaneyulu

Abstract:

Nowadays Multilevel inverters are widely using in various applications. Modulation strategy at fundamental switching frequency like, SHEPWM is prominent technique to eliminate lower order of harmonics with less switching losses and better harmonic profile. The equations which are formed by SHE are highly nonlinear transcendental in nature, there may exist single, multiple or even no solutions for a particular MI. However, some loads such as electrical drives, it is required to operate in whole range of MI. In order to solve SHE equations for whole range of MI, intelligent techniques are well suited to solve equations so as to produce lest %THDV. Hence, this paper uses Continuous genetic algorithm for minimising harmonics. This paper also presents wavelet based analysis of harmonics. The developed algorithm is simulated and %THD from FFT analysis and Wavelet analysis are compared. MATLAB programming environment and SIMULINK models are used whenever necessary.

Keywords: Cascade H-Bridge Inverter (CHB), Continuous Genetic Algorithm (C-GA), Selective Harmonic Elimination Pulse Width Modulation (SHEPWM), Total Harmonic Distortion (%THDv), Wavelet Transform (WT).

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Authors: Aziza Benaboud, Alfred Rufer

Abstract:

In this paper the authors propose a flexible electronic solution, to improve the energetic efficiency of a thermo plant. This is achieved by replacing the mechanical gear box, placed traditionally between a gas turbine and a synchronous generator; by a power electronic converter. After reminding problematic of gear boxes and interest of a proposed electronic solution in high power plants, the authors describe a new control strategy for an indirect frequency converter, which is characterized by its high efficiency due to the use of SWM: Square Wave Modulation. The main advantage of this mode is the quasi absence of switching losses. A control method is also proposed to resolve some problems incurred by using square wave modulation, in particular to reduce the harmonics distortion of the output inverter voltage and current. Simulation examples as well as experimental results are included.

Keywords: Angle shift, high efficiency, indirect converter, gas turbine, NPC three level converter, square wave modulation SWM, switching angle.

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Authors: Takashi Mitsuishi, Koji Saigusa

Abstract:

This paper presents circular polar coordinates transformation of periodic fuzzy membership function. The purpose is identification of domain of periodic membership functions in consequent part of IF-THEN rules. Proposed methods in this paper remove complicatedness concerning domain of periodic membership function from defuzzification in fuzzy approximate reasoning. Defuzzification on circular polar coordinates is also proposed.

Keywords: Defuzzification, periodic membership function, polar coordinates transformation.

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Authors: Ethar H. Khalil, Bahaa I. Kazem

Abstract:

In this work a software simulation model has been proposed for two driven wheels mobile robot path planning; that can navigate in dynamic environment with static distributed obstacles. The work involves utilizing Bezier curve method in a proposed N order matrix form; for engineering the mobile robot path. The Bezier curve drawbacks in this field have been diagnosed. Two directions: Up and Right function has been proposed; Probability Recursive Function (PRF) to overcome those drawbacks. PRF functionality has been developed through a proposed; obstacle detection function, optimization function which has the capability of prediction the optimum path without comparison between all feasible paths, and N order Bezier curve function that ensures the drawing of the obtained path. The simulation results that have been taken showed; the mobile robot travels successfully from starting point and reaching its goal point. All obstacles that are located in its way have been avoided. This navigation is being done successfully using the proposed PRF techniques.

Keywords: Mobile robot, path planning, Bezier curve.

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