Search results for: fractional (k

Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

Abstract:

In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: Meng Hu, Lili Wang

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In this paper, applying He-s energy balance method to determine frequency formulation relations of nonlinear oscillators with discontinuous term or fractional potential. By calculation and computer simulations, compared with the exact solutions show that the results obtained are of high accuracy.

Keywords: He's energy balance method, periodic solution, nonlinear oscillator, discontinuous, fractional potential.

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Authors: Abdellatif Kasbi, Abderrafii Rahali

Abstract:

During the recent years, much interest has been devoted to fractional order control that has appeared as a very eligible control approach for the systems experiencing parametric uncertainty and outer disturbances. The main purpose of this paper is to design and evaluate the performance of a fractional order proportional integral (FOPI) controller applied to control prototype variable speed wind generation system (WGS) that uses a doubly fed induction generator (DFIG). In this paper, the DFIG-machine is controlled according to the stator field-oriented control (FOC) strategy, which makes it possible to regulate separately the reactive and active powers exchanged between the WGS and the grid. The considered system is modeled and simulated using MATLAB-Simulink, and the performance of FOPI controller applied to the back-to-back power converter control of DFIG based grid connected variable speed wind turbine are evaluated and compared to the ones obtained with a conventional PI controller.

Keywords: Design, fractional order PI controller, wind generation system, doubly fed induction generator, wind turbine, field-oriented control.

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Authors: Nisa Özge Önal, Kamil Karaçuha, Göksu Hazar Erdinç, Banu Bahar Karaçuha, Ertuğrul Karaçuha

Abstract:

The study aims to use a mathematical approach with the fractional calculus which is developed to have the ability to continuously analyze the factors related to the children’s height development. Until now, tracking the development of the child is getting more important and meaningful. Knowing and determining the factors related to the physical development of the child any desired time would provide better, reliable and accurate results for childcare. In this frame, 7 groups for height percentile curve (3th, 10th, 25th, 50th, 75th, 90th, and 97th) of Turkey are used. By using discrete height data of 0-18 years old children and the least squares method, a continuous curve is developed valid for any time interval. By doing so, in any desired instant, it is possible to find the percentage and location of the child in Percentage Chart. Here, with the help of the fractional calculus theory, a mathematical model is developed. The outcomes of the proposed approach are quite promising compared to the linear and the polynomial method. The approach also yields to predict the expected values of children in the sense of height.

Keywords: Children growth percentile, children physical development, fractional calculus, linear and polynomial model.

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Authors: Ryosuke Ito, Goro Obinata, Chikara Nagai, Youngwoo Kim

Abstract:

This paper proposes a new parameter identification method based on Linear Fractional Transformation (LFT). It is assumed that the target linear system includes unknown parameters. The parameter deviations are separated from a nominal system via LFT, and identified by organizing I/O signals around the separated deviations of the real system. The purpose of this paper is to apply LFT to simultaneously identify the parameter deviations in systems with fewer outputs than unknown parameters. As a fundamental example, this method is implemented to one degree of freedom vibratory system. Via LFT, all physical parameters were simultaneously identified in this system. Then, numerical simulations were conducted for this system to verify the results. This study shows that all the physical parameters of a system with fewer outputs than unknown parameters can be effectively identified simultaneously using LFT.

Keywords: Identification, Linear Fractional Transformation, Right inverse system

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Authors: Pei. P. Tan, Don. U.A. Galagedera, Elizabeth A.Maharaj

Abstract:

This paper examines predictability in stock return in developed and emergingmarkets by testing long memory in stock returns using wavelet approach. Wavelet-based maximum likelihood estimator of the fractional integration estimator is superior to the conventional Hurst exponent and Geweke and Porter-Hudak estimator in terms of asymptotic properties and mean squared error. We use 4-year moving windows to estimate the fractional integration parameter. Evidence suggests that stock return may not be predictable indeveloped countries of the Asia-Pacificregion. However, predictability of stock return insome developing countries in this region such as Indonesia, Malaysia and Philippines may not be ruled out. Stock return in the Thailand stock market appears to be not predictable after the political crisis in 2008.

Keywords: Asia-Pacific stock market, long-memory, return predictability, wavelet

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Authors: Raja Muhammad Asif Zahoor, Junaid Ali Khan, I. M. Qureshi

Abstract:

In this article an evolutionary technique has been used for the solution of nonlinear Riccati differential equations of fractional order. In this method, genetic algorithm is used as a tool for the competent global search method hybridized with active-set algorithm for efficient local search. The proposed method has been successfully applied to solve the different forms of Riccati differential equations. The strength of proposed method has in its equal applicability for the integer order case, as well as, fractional order case. Comparison of the method has been made with standard numerical techniques as well as the analytic solutions. It is found that the designed method can provide the solution to the equation with better accuracy than its counterpart deterministic approaches. Another advantage of the given approach is to provide results on entire finite continuous domain unlike other numerical methods which provide solutions only on discrete grid of points.

Keywords: Riccati Equation, Non linear ODE, Fractional differential equation, Genetic algorithm.

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Authors: D.Elleuch, T.Damak

Abstract:

In this paper, the performance of two adaptive observers applied to interconnected systems is studied. The nonlinearity of systems can be written in a fractional form. The first adaptive observer is an adaptive sliding mode observer for a Lipchitz nonlinear system and the second one is an adaptive sliding mode observer having a filtered error as a sliding surface. After comparing their performances throughout the inverted pendulum mounted on a car system, it was shown that the second one is more robust to estimate the state.

Keywords: Adaptive observer, Lipchitz system, Interconnected fractional nonlinear system, sliding mode.

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Authors: H. B. Kekre, Tanuja K. Sarode

Abstract:

This paper presents a very simple and efficient algorithm for codebook search, which reduces a great deal of computation as compared to the full codebook search. The algorithm is based on sorting and centroid technique for search. The results table shows the effectiveness of the proposed algorithm in terms of computational complexity. In this paper we also introduce a new performance parameter named as Average fractional change in pixel value as we feel that it gives better understanding of the closeness of the image since it is related to the perception. This new performance parameter takes into consideration the average fractional change in each pixel value.

Keywords: Vector Quantization, Data Compression, Encoding, Searching.

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Authors: Koushlendra Kumar Singh, Manish Kumar Bajpai, Rajesh K. Pandey

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The edges of low contrast images are not clearly distinguishable to human eye. It is difficult to find the edges and boundaries in it. The present work encompasses a new approach for low contrast images. The Chebyshev polynomial based fractional order filter has been used for filtering operation on an image. The preprocessing has been performed by this filter on the input image. Laplacian of Gaussian method has been applied on preprocessed image for edge detection. The algorithm has been tested on two test images.

Keywords: Chebyshev polynomials, Fractional order differentiator, Laplacian of Gaussian (LoG) method, Low contrast image.

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Authors: Anwar H. Jarndal, Ahmed S. Elwakil

Abstract:

In this paper, a fraction-order model for pad parasitic effect of GaN HEMT on Si substrate is developed and validated. Open de-embedding structure is used to characterize and de-embed substrate loading parasitic effects. Unbiased device measurements are implemented to extract parasitic inductances and resistances. The model shows very good simulation for S-parameter measurements under different bias conditions. It has been found that this approach can improve the simulation of intrinsic part of the transistor, which is very important for small- and large-signal modeling process.

Keywords: Fractional-order modeling, GaN HEMT, Si-substrate, open de-embedding structure.

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Authors: P. Chaipanya, P. Uthansakul, M. Uthansakul

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This paper proposes a vertical beamforming concept to a cellular network employing Fractional Frequency Reuse technique including with cell sectorization. Two different beams are utilized in cell-center and cell-edge, separately. The proposed concept is validated through computer simulation in term of SINR and channel capacity. Also, comparison when utilizing horizontal and vertical beam formation is in focus. The obtained results indicate that the proposed concept can improve the performance of the cellular networks comparing with the one using horizontal beamforming.

Keywords: Beamforming, Fractional Frequency Reuse, Inter- Cell Interference, cell sectorization.

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Authors: Yusuke Uchiyama, Hidetoshi Konno

Abstract:

We have investigated statistical properties of the defect turbulence in 1D CGLE wherein many body interaction is involved between local depressing wave (LDW) and local standing wave (LSW). It is shown that the counting number fluctuation of LDW is subject to the sub-Poisson statistics (SUBP). The physical origin of the SUBP can be ascribed to pair extinction of LDWs based on the master equation approach. It is also shown that the probability density function (pdf) of inter-LDW distance can be identified by the hyper gamma distribution. Assuming a superstatistics of the exponential distribution (Poisson configuration), a plausible explanation is given. It is shown further that the pdf of amplitude of LDW has a fattail. The underlying mechanism of its fluctuation is examined by introducing a generalized fractional Poisson configuration.

Keywords: sub-Poisson statistics, hyper gamma distribution, fractional Poisson configuration.

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Authors: N. Ghatwary, A. Ahmed, H. Jalab

Abstract:

In this paper, an approach for the liver tumor detection in computed tomography (CT) images is represented. The detection process is based on classifying the features of target liver cell to either tumor or non-tumor. Fractional differential (FD) is applied for enhancement of Liver CT images, with the aim of enhancing texture and edge features. Later on, a fusion method is applied to merge between the various enhanced images and produce a variety of feature improvement, which will increase the accuracy of classification. Each image is divided into NxN non-overlapping blocks, to extract the desired features. Support vector machines (SVM) classifier is trained later on a supplied dataset different from the tested one. Finally, the block cells are identified whether they are classified as tumor or not. Our approach is validated on a group of patients’ CT liver tumor datasets. The experiment results demonstrated the efficiency of detection in the proposed technique.

Keywords: Fractional differential (FD), Computed Tomography (CT), fusion.

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Authors: Chatchai Pesee

Abstract:

This paper examines long-range dependence or longmemory of financial time series on the exchange rate data by the fractional Brownian motion (fBm). The principle of spectral density function in Section 2 is used to find the range of Hurst parameter (H) of the fBm. If 0< H <1/2, then it has a short-range dependence (SRD). It simulates long-memory or long-range dependence (LRD) if 1/2< H <1. The curve of exchange rate data is fBm because of the specific appearance of the Hurst parameter (H). Furthermore, some of the definitions of the fBm, long-range dependence and selfsimilarity are reviewed in Section II as well. Our results indicate that there exists a long-memory or a long-range dependence (LRD) for the exchange rate data in section III. Long-range dependence of the exchange rate data and estimation of the Hurst parameter (H) are discussed in Section IV, while a conclusion is discussed in Section V.

Keywords: Fractional Brownian motion, long-rangedependence, memory, short-range dependence.

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Authors: Reza Cheraghi Kootiani, Ariffin Bin Samsuri

Abstract:

To derive the fractional flow equation oil displacement will be assumed to take place under the so-called diffusive flow condition. The constraints are that fluid saturations at any point in the linear displacement path are uniformly distributed with respect to thickness; this allows the displacement to be described mathematically in one dimension. The simultaneous flow of oil and water can be modeled using thickness averaged relative permeability, along the centerline of the reservoir. The condition for fluid potential equilibrium is simply that of hydrostatic equilibrium for which the saturation distribution can be determined as a function of capillary pressure and therefore, height. That is the fluids are distributed in accordance with capillary-gravity equilibrium. This paper focused on the fraction flow of water versus cumulative oil recoveries using Buckley Leverett method. Several field cases have been developed to aid in analysis. Producing watercut (at surface conditions) will be compared with the cumulative oil recovery at breakthrough for the flowing fluid.

Keywords: Fractional Flow, Fluid Saturations, Permeability, Cumulative Oil Recoveries, Buckley Leverett Method.

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Authors: Elysia Barker, Jian Guo Zhou, Ling Qian, Steve Decent

Abstract:

A method of modelling topography used in the simulation of riverbeds is proposed in this paper which removes the need for datapoints and measurements of a physical terrain. While complex scans of the contours of a surface can be achieved with other methods, this requires specialised tools which the proposed method overcomes by using fractional Brownian motion (FBM) as a basis to estimate the real surface within a 15% margin of error while attempting to optimise algorithmic efficiency. This removes the need for complex, expensive equipment and reduces resources spent modelling bed topography. This method also accounts for the change in topography over time due to erosion, sediment transport, and other external factors which could affect the topography of the ground by updating its parameters and generating a new bed. The lattice Boltzmann method (LBM) is used to simulate both stationary and steady flow cases in a side-by-side comparison over the generated bed topography using the proposed method, and a test case taken from an external source. The method, if successful, will be incorporated into the current LBM program used in the testing phase, which will allow an automatic generation of topography for the given situation in future research, removing the need for bed data to be specified.

Keywords: Bed topography, FBM, LBM, shallow water, simulations.

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Authors: Yih-Ferng Peng

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In this paper, the local grid refinement is focused by using a nested grid technique. The Cartesian grid numerical method is developed for simulating unsteady, viscous, incompressible flows with complex immersed boundaries. A finite volume method is used in conjunction with a two-step fractional-step procedure. The key aspects that need to be considered in developing such a nested grid solver are imposition of interface conditions on the inter-block and accurate discretization of the governing equation in cells that are with the inter-block as a control surface. A new interpolation procedure is presented which allows systematic development of a spatial discretization scheme that preserves the spatial accuracy of the underlying solver. The present nested grid method has been tested by two numerical examples to examine its performance in the two dimensional problems. The numerical examples include flow past a circular cylinder symmetrically installed in a Channel and flow past two circular cylinders with different diameters. From the numerical experiments, the ability of the solver to simulate flows with complicated immersed boundaries is demonstrated and the nested grid approach can efficiently speed up the numerical solutions.

Keywords: local grid refinement, Cartesian grid, nested grid, fractional-step method.

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Authors: Yung-Tan Lee, Ren-Yi Huang, Ju-Chin Chen, Jyh-Yi Shih, Meng-Lung Lin, Hsiao-Ling Yu, Yen-Tsui Hu, Chih-Cheng Chen

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Cenozoic basalts found in Jiangsu province of eastern China include tholeiites and alkali basalts. The present paper analyzed the major, trace elements, rare earth elements of these Cenozoic basalts and combined with Sr-Nd isotopic compositions proposed by Chen et al. (1990)[1] in the literatures to discuss the petrogenesis of these basalts and the geochemical characteristics of the source mantle. Based on major, trace elements and fractional crystallization model established by Brooks and Nielsen (1982)[2] we suggest that the basaltic magma has experienced olivine + clinopyroxene fractionation during its evolution. The chemical compositions of basaltic rocks from Jiangsu province indicate that these basalts may belong to the same magmatic system. Spidergrams reveal that Cenozoic basalts from Jiangsu province have geochemical characteristics similar to those of ocean island basalts(OIB). The slight positive Nb and Ti anomalies found in basaltic rocks of this study suggest the presence of Ti-bearing minerals in the mantle source and these Ti-bearing minerals had contributed to basaltic magma during partial melting, indicating a metasomatic event might have occurred before the partial melting. Based on the Sr vs. Nd isotopic ratio plots, we suggest that Jiangsu basalts may be derived from partial melting of mantle source which may represent two-end members mixing of DMM and EM-I. Some Jiangsu basaltic magma may be derived from partial melting of EM-I heated by the upwelling asthenospheric mantle or asthenospheric diapirism.

Keywords: Geochemistry, Jiangsu Province, Cenozoic basalts, Fractional crystallization.

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Authors: Mahdi Masoumi, Mehrdad Ardebilipoor, Seyed Aidin Bassam

Abstract:

This paper proposes a novel frequency offset (FO) estimator for orthogonal frequency division multiplexing. Simplicity is most significant feature of this algorithm and can be repeated to achieve acceptable accuracy. Also fractional and integer part of FO is estimated jointly with use of the same algorithm. To do so, instead of using conventional algorithms that usually use correlation function, we use DFT of received signal. Therefore, complexity will be reduced and we can do synchronization procedure by the same hardware that is used to demodulate OFDM symbol. Finally, computer simulation shows that the accuracy of this method is better than other conventional methods.

Keywords: DFT, Estimator, Frequency Offset, IEEE802.11a, OFDM.

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Authors: G. Kalpanadevi, S. Ravimaran, M. Shanmugapriya

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A Reconfigurable Wilkinson power divider is proposed in this paper. In existing system only a limited number of bandwidth is used at the output ports, in the proposed Wilkinson power divider different band of frequencies are obtained by using PIN diode. By tuning the PIN diode, different frequencies are achieved. The size of the power divider is reduced for the operating frequency and increases the fractional bandwidth.

Keywords: Isolation loss, PIN diode, Reconfigurable Wilkinson power divider and WLAN applications.

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Authors: Sachin Bhalekar, Varsha Daftardar-Gejji

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In the present paper, we present a modification of the New Iterative Method (NIM) proposed by Daftardar-Gejji and Jafari [J. Math. Anal. Appl. 2006;316:753–763] and use it for solving systems of nonlinear functional equations. This modification yields a series with faster convergence. Illustrative examples are presented to demonstrate the method.

Keywords: Caputo fractional derivative, System of nonlinear functional equations, Revised new iterative method.

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Authors: V. Golubev, A. Dosmakanbetova, A. Brener

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The purpose of this work is to establish the theoretical foundations for calculating and designing the sublimationcondensation processes in chemical apparatuses which are intended for production of ultrafine powders of crystalline and amorphous materials with controlled fractional composition. Theoretic analysis of the primary processes of nucleation and growth kinetics of the clusters according to the degree of super-saturation and the homogeneous or heterogeneous nature of nucleation has been carried out. The engineering design procedures of desublimation processes have been offered and tested for modification of the Claus process.

Keywords: Desublimation, controlled fraction composition, nucleation, ultrafine powders.

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Authors: Henri El Zakhem, Christina Romanos, Charlie Bakhos, Hassan Chahal, Jessica Koura

Abstract:

Squalene is a valuable component of the oil composed of 30 carbon atoms and is mainly used for cosmetic materials. The main concern of this article is to study the Squalene composition in the Lebanese olive oil and to compare it with foreign oil results. To our knowledge, extraction of Squalene from the Lebanese olive oil has not been conducted before. Three different techniques were studied and experiments were performed on three brands of olive oil, Al Wadi Al Akhdar, Virgo Bio and Boulos. The techniques performed are the Fractional Crystallization, the Soxhlet and the Esterification. By comparing the results, it is found that the Lebanese oil contains squalene and Soxhlet method is the most effective between the three methods extracting about 6.5E-04 grams of Squalene per grams of olive oil.

Keywords: Squalene, extraction, crystallization, Soxhlet.‎

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Authors: H. B. Kekre, Tanuja K. Sarode

Abstract:

Mostly transforms are used for speech data compressions which are lossy algorithms. Such algorithms are tolerable for speech data compression since the loss in quality is not perceived by the human ear. However the vector quantization (VQ) has a potential to give more data compression maintaining the same quality. In this paper we propose speech data compression algorithm using vector quantization technique. We have used VQ algorithms LBG, KPE and FCG. The results table shows computational complexity of these three algorithms. Here we have introduced a new performance parameter Average Fractional Change in Speech Sample (AFCSS). Our FCG algorithm gives far better performance considering mean absolute error, AFCSS and complexity as compared to others.

Keywords: Vector Quantization, Data Compression, Encoding, , Speech coding.

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Authors: Taro Matsuno, Yuta Otani, Ryo Tanaka, Kaori Ikezaki, Hitoshi Yamamoto, Masaru Fujieda, Yoshihisa Ishida

Abstract:

This paper presents an improvement method of the multiple pitch estimation algorithm using comb filters. Conventionally the pitch was estimated by using parallel -connected comb filters method (PCF). However, PCF has problems which often fail in the pitch estimation when there is the fundamental frequency of higher tone near harmonics of lower tone. Therefore the estimation is assigned to a wrong note when shared frequencies happen. This issue often occurs in estimating octave 3 or more. Proposed method, for solving the problem, estimates the pitch with every harmonic instead of every octave. As a result, our method reaches the accuracy of more than 80%.

Keywords: music transcription, pitch estimation, comb filter, fractional delay

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Authors: Yasunori Sugita, Toshinori Yoshikawa, Naoyuki Aikawa

Abstract:

Variable digital filters are useful for various signal processing and communication applications where the frequency characteristics, such as fractional delays and cutoff frequencies, can be varied. In this paper, we propose a design method of variable FIR digital filters with an approximate linear phase characteristic in the passband. The proposed variable FIR filters have some large attenuation in stopband and their large attenuation can be varied by spectrum parameters. In the proposed design method, a quasi-equiripple characteristic can be obtained by using an iterative weighted least square method. The usefulness of the proposed design method is verified through some examples.

Keywords: Weighted Least Squares Approximation, Variable FIR Filters, Low-Delay, Quasi-Equiripple

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Authors: Seok Hong Min, Tae Kwon Ha

Abstract:

With the increasing interest on Ti alloys, the extraction process of Ti from its typical ore, TiO₂, has long been and will be important issue. As an intermediate product for the production of pigment or titanium metal sponge, tetrachloride (TiCl₄) is produced by fluidized bed using high TiO₂ feedstock. The purity of TiCl₄ after chlorination is subjected to the quality of the titanium feedstock. Since the impurities in the TiCl₄ product are reported to final products, the purification process of the crude TiCl₄ is required. The purification process includes fractional distillation and chemical treatment, which depends on the nature of the impurities present and the required quality of the final product. In this study, thermodynamic analysis on the impurity effect in the chlorination process, which is the first step of extraction of Ti from TiO₂, has been conducted. All thermodynamic calculations were performed using the FactSage thermodynamical software.

Keywords: Rutile, titanium, chlorination process, impurities, thermodynamic calculation, FactSage.

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Authors: Taeung Yoon, Youngpo Lee, Chonghan Song, Na Young Ha, Seokho Yoon

Abstract:

Ren et al. presented an efficient carrier frequency offset (CFO) estimation method for orthogonal frequency division multiplexing (OFDM), which has an estimation range as large as the bandwidth of the OFDM signal and achieves high accuracy without any constraint on the structure of the training sequence. However, its detection probability of the integer frequency offset (IFO) rapidly varies according to the fractional frequency offset (FFO) change. In this paper, we first analyze the Ren-s method and define two criteria suitable for detection of IFO. Then, we propose a novel method for the IFO estimation based on the maximum-likelihood (ML) principle and the detection criteria defined in this paper. The simulation results demonstrate that the proposed method outperforms the Ren-s method in terms of the IFO detection probability irrespective of a value of the FFO.

Keywords: Orthogonal frequency division multiplexing, integer frequency offset, estimation, training symbol

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Authors: Padmakumar S., Vivek Agarwal, Kallol Roy

Abstract:

With the advent of inexpensive 32 bit floating point digital signal processor-s availability in market, many computationally intensive algorithms such as Kalman filter becomes feasible to implement in real time. Dynamic simulation of a self excited DC motor using second order state variable model and implementation of Kalman Filter in a floating point DSP TMS320C6713 is presented in this paper with an objective to introduce and implement such an algorithm, for beginners. A fractional hp DC motor is simulated in both Matlab® and DSP and the results are included. A step by step approach for simulation of DC motor in Matlab® and “C" routines in CC Studio® is also given. CC studio® project file details and environmental setting requirements are addressed. This tutorial can be used with 6713 DSK, which is based on floating point DSP and CC Studio either in hardware mode or in simulation mode.

Keywords: DC motor, DSP, Dynamic simulation, Kalman Filter

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