Search results for: Dynamic Clusters algorithm

Authors: Hongkui Li, Tongli Lu , Jianwu Zhang

Abstract:

This paper focuses on developing an estimation method of clutch drag torque in wet DCT. The modelling of clutch drag torque is investigated. As the main factor affecting the clutch drag torque, dynamic viscosity of oil is discussed. The paper proposes an estimation method of clutch drag torque based on recursive least squares by utilizing the dynamic equations of gear shifting synchronization process. The results demonstrate that the estimation method has good accuracy and efficiency.

Keywords: Clutch drag torque, wet DCT, dynamic viscosity, recursive least squares.

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Authors: Ahmed Helal, Sherif Zain Elabideen, Ahmed Lotfy

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In this paper the modeling and analysis of Space Vector Pulse Width Modulation (SVPWM) based Dynamic Voltage Restorer (DVR) using PSCAD/EMTDC software will be presented in details. The simulation includes full modeling of the SVPWM technique used to control the DVR inverter. A test power system composed of three phase voltage source, sag generator, DVR and three phase resistive load is used to demonstrate restoration capability of the DVR. The simulation results of the presented DVR proved excellent voltage sag mitigation to protect sensitive loads.

Keywords: Dynamic voltage restorer, power quality, simulationand modeling, voltage sag.

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Authors: A. B.Bhattacharyya, B. S.K.Goswami

Abstract:

This paper presents Genetic Algorithm (GA) based approach for the allocation of FACTS (Flexible AC Transmission System) devices for the improvement of Power transfer capacity in an interconnected Power System. The GA based approach is applied on IEEE 30 BUS System. The system is reactively loaded starting from base to 200% of base load. FACTS devices are installed in the different locations of the power system and system performance is noticed with and without FACTS devices. First, the locations, where the FACTS devices to be placed is determined by calculating active and reactive power flows in the lines. Genetic Algorithm is then applied to find the amount of magnitudes of the FACTS devices. This approach of GA based placement of FACTS devices is tremendous beneficial both in terms of performance and economy is clearly observed from the result obtained.

Keywords: FACTS Devices, Line Power Flow, OptimalLocation of FACTS Devices, Genetic Algorithm.

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Authors: Masoud Sadeghian, Alireza Fatehi

Abstract:

One of the most important parts of a cement factory is the cement rotary kiln which plays a key role in quality and quantity of produced cement. In this part, the physical exertion and bilateral movement of air and materials, together with chemical reactions take place. Thus, this system has immensely complex and nonlinear dynamic equations. These equations have not worked out yet. Only in exceptional case; however, a large number of the involved parameter were crossed out and an approximation model was presented instead. This issue caused many problems for designing a cement rotary kiln controller. In this paper, we presented nonlinear predictor and simulator models for a real cement rotary kiln by using nonlinear identification technique on the Locally Linear Neuro- Fuzzy (LLNF) model. For the first time, a simulator model as well as a predictor one with a precise fifteen minute prediction horizon for a cement rotary kiln is presented. These models are trained by LOLIMOT algorithm which is an incremental tree-structure algorithm. At the end, the characteristics of these models are expressed. Furthermore, we presented the pros and cons of these models. The data collected from White Saveh Cement Company is used for modeling.

Keywords: Cement rotary kiln, nonlinear identification, Locally Linear Neuro-Fuzzy model.

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Authors: Said Elkassimi, Said Safi, B. Manaut

Abstract:

This paper presented a study of three algorithms, the equalization algorithm to equalize the transmission channel with ZF and MMSE criteria, application of channel Bran A, and adaptive filtering algorithms LMS and RLS to estimate the parameters of the equalizer filter, i.e. move to the channel estimation and therefore reflect the temporal variations of the channel, and reduce the error in the transmitted signal. So far the performance of the algorithm equalizer with ZF and MMSE criteria both in the case without noise, a comparison of performance of the LMS and RLS algorithm.

Keywords: Adaptive filtering second equalizer, LMS, RLS Bran A, Proakis (B) MMSE, ZF.

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Authors: Boualem Chetti

Abstract:

In this paper, the dynamic characteristics of a threelobe journal bearing lubricated with micropolar fluids are determined by the linear stability theory. Lubricating oil containing additives and contaminants is modelled as micropolar fluid. The modified Reynolds equation is obtained using the micropolar lubrication theory .The finite difference technique has been used to determine the solution of the modified Reynolds equation. The dynamic characteristics in terms of stiffness, damping coefficients, the critical mass and whirl ratio are determined for various values of size of material characteristic length and the coupling number. The computed results show that the three-lobe bearing lubricated with micropolar fluid exhibits better stability compared with that lubricated with Newtonian fluid. According to the results obtained, the effect of the parameter micropolar fluid is remarkable on the dynamic characteristics and stability of the three-lobe bearing.

Keywords: Three-lobe bearings, Micropolar fluid, Dynamic characteristics, Stability analysis.

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Authors: Hassan Haghighi, Seyedeh Zahra Hosseini, Seyedeh Elahe Jalambadani

Abstract:

One of the most important aspects expected from an ERP system is to mange user\administrator manual documents dynamically. Since an ERP package is frequently changed during its implementation in customer sites, it is often needed to add new documents and/or apply required changes to existing documents in order to cover new or changed capabilities. The worse is that since these changes occur continuously, the corresponding documents should be updated dynamically; otherwise, implementing the ERP package in the organization encounters serious risks. In this paper, we propose a new architecture which is based on the agent oriented vision and supplies the dynamic document generation expected from ERP systems using several independent but cooperative agents. Beside the dynamic document generation which is the main issue of this paper, the presented architecture will address some aspects of intelligence and learning capabilities existing in ERP.

Keywords: enterprise resource planning, dynamic documentgeneration, software architecture, agent oriented architecture, learning, intelligence

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Authors: Konstanca Nikolajevic, Nicolas Belanger, David Duvivier, Rabie Ben Atitallah, Abdelhakim Artiba

Abstract:

Finding the optimal 3D path of an aerial vehicle under flight mechanics constraints is a major challenge, especially when the algorithm has to produce real time results in flight. Kinematics models and Pythagorian Hodograph curves have been widely used in mobile robotics to solve this problematic. The level of difficulty is mainly driven by the number of constraints to be saturated at the same time while minimizing the total length of the path. In this paper, we suggest a pragmatic algorithm capable of saturating at the same time most of dimensioning helicopter 3D trajectories’ constraints like: curvature, curvature derivative, torsion, torsion derivative, climb angle, climb angle derivative, positions. The trajectories generation algorithm is able to generate versatile complex 3D motion primitives feasible by a helicopter with parameterization of the curvature and the climb angle. An upper ”motion primitives’ concatenation” algorithm is presented based. In this article we introduce a new way of designing three-dimensional trajectories based on what we call the ”Dubins gliding symmetry conjecture”. This extremely performing algorithm will be soon integrated to a real-time decisional system dealing with inflight safety issues.

Keywords: Aerial robots, Motion primitives, Robotics.

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Authors: Nikolaos Kroupis, Minas Dasygenis, Dimitrios Soudris, Antonios Thanailakis

Abstract:

One of the most growing areas in the embedded community is multimedia devices. Multimedia devices incorporate a number of complicated functions for their operation, like motion estimation. A multitude of different implementations have been proposed to reduce motion estimation complexity, such as spiral search. We have studied the implementations of spiral search and identified areas of improvement. We propose a modified spiral search algorithm, with lower computational complexity compared to the original spiral search. We have implemented our algorithm on an embedded ARM based architecture, with custom memory hierarchy. The resulting system yields energy consumption reduction up to 64% and performance increase up to 77%, with a small penalty of 2.3 dB, in average, of video quality compared with the original spiral search algorithm.

Keywords: Spiral Search, Motion Estimation, Embedded Systems, Low Power

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Authors: Bing Yu , Xingshi He

Abstract:

In this paper, Differential Evolution (DE) algorithm, a new promising evolutionary algorithm, is proposed to train Radial Basis Function (RBF) network related to automatic configuration of network architecture. Classification tasks on data sets: Iris, Wine, New-thyroid, and Glass are conducted to measure the performance of neural networks. Compared with a standard RBF training algorithm in Matlab neural network toolbox, DE achieves more rational architecture for RBF networks. The resulting networks hence obtain strong generalization abilities.

Keywords: differential evolution, neural network, Rbf function

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Authors: J. S. Nah, A. Y. Jeon, J. H. Ro, G. R. Jeon

Abstract:

ECG analysis method was developed using ROC analysis of PVC detecting algorithm. ECG signal of MIT-BIH arrhythmia database was analyzed by MATLAB. First of all, the baseline was removed by median filter to preprocess the ECG signal. R peaks were detected for ECG analysis method, and normal VCG was extracted for VCG analysis method. Four PVC detecting algorithm was analyzed by ROC curve, which parameters are maximum amplitude of QRS complex, width of QRS complex, r-r interval and geometric mean of VCG. To set cut-off value of parameters, ROC curve was estimated by true-positive rate (sensitivity) and false-positive rate. sensitivity and false negative rate (specificity) of ROC curve calculated, and ECG was analyzed using cut-off value which was estimated from ROC curve. As a result, PVC detecting algorithm of VCG geometric mean have high availability, and PVC could be detected more accurately with amplitude and width of QRS complex.

Keywords: Vectorcardiogram (VCG), Premature Ventricular contraction (PVC), ROC (receiver operating characteristic) curve, ECG

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Authors: Abhijit Chandra, Sudipta Chattopadhyay

Abstract:

In this communication, we have made an attempt to design multiplier-less low-pass finite impulse response (FIR) filter with the aid of various mutation strategies of Differential Evolution (DE) algorithm. Impulse response coefficient of the designed FIR filter has been represented as sums or differences of powers of two. Performance of the proposed filter has been evaluated in terms of its frequency response and associated hardware cost. Supremacy of our approach has been substantiated by comparing our result with many of the existing multiplier-less filter design algorithms of recent interest. It has also been demonstrated that DE-optimized filter outperforms Genetic Algorithm (GA) based design by a large margin.  Hardware efficiency of our algorithm has further been validated by implementing those filters on a Field Programmable Gate Array (FPGA) chip.

Keywords: Convergence speed, Differential Evolution (DE), error histogram, finite impulse response (FIR) filter, total power of two (TPT), zero-valued filter coefficient (ZFC).

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Authors: P. Asadee

Abstract:

Multiplication algorithms have considerable effect on processors performance. A new high-speed, low-power multiplication algorithm has been presented using modified Dadda tree structure. Three important modifications have been implemented in inner product generation step, inner product reduction step and final addition step. Optimized algorithms have to be used into basic computation components, such as multiplication algorithms. In this paper, we proposed a new algorithm to reduce power, delay, and transistor count of a multiplication algorithm implemented using low power modified counter. This work presents a novel design for Dadda multiplication algorithms. The proposed multiplication algorithm includes structured parts, which have important effect on inner product reduction tree. In this paper, a 1.3V, 64-bit carry hybrid adder is presented for fast, low voltage applications. The new 64-bit adder uses a new circuit to implement the proposed carry hybrid adder. The new adder using 80 nm CMOS technology has been implemented on 700 MHz clock frequency. The proposed multiplication algorithm has achieved 14 percent improvement in transistor count, 13 percent reduction in delay and 12 percent modification in power consumption in compared with conventional designs.

Keywords: adder, CMOS, counter, Dadda tree, encoder.

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Authors: H. Mehdi, Kh. S. Karimov, A. A. Kavokin

Abstract:

Methods of clustering which were developed in the data mining theory can be successfully applied to the investigation of different kinds of dependencies between the conditions of environment and human activities. It is known, that environmental parameters such as temperature, relative humidity, atmospheric pressure and illumination have significant effects on the human mental performance. To investigate these parameters effect, data mining technique of clustering using entropy and Information Gain Ratio (IGR) K(Y/X) = (H(X)–H(Y/X))/H(Y) is used, where H(Y)=-ΣPi ln(Pi). This technique allows adjusting the boundaries of clusters. It is shown that the information gain ratio (IGR) grows monotonically and simultaneously with degree of connectivity between two variables. This approach has some preferences if compared, for example, with correlation analysis due to relatively smaller sensitivity to shape of functional dependencies. Variant of an algorithm to implement the proposed method with some analysis of above problem of environmental effects is also presented. It was shown that proposed method converges with finite number of steps.

Keywords: Clustering, Correlation analysis, EnvironmentalParameters, Information Gain Ratio, Mental Performance.

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Authors: Banaja Mohanty, Prakash Kumar Hota

Abstract:

This paper presents a differential evolution algorithm to design a robust PI and PID controllers for Load Frequency Control (LFC) of nonlinear interconnected power systems considering the boiler dynamics, Governor Dead Band (GDB), Generation Rate Constraint (GRC). Differential evolution algorithm is employed to search for the optimal controller parameters. The proposed method easily copes of with nonlinear constraints. Further the proposed controller is simple, effective and can ensure the desirable overall system performance. The superiority of the proposed approach has been shown by comparing the results with published fuzzy logic controller for the same power systems. The comparison is done using various performance measures like overshoot, settling time and standard error criteria of frequency and tie-line power deviation following a 1% step load perturbation in hydro area. It is noticed that, the dynamic performance of proposed controller is better than fuzzy logic controller. Furthermore, it is also seen that the proposed system is robust and is not affected by change in the system parameters.

Keywords: Automatic Generation control (AGC), Generation Rate Constraint (GRC), Governor Dead Band (GDB), Differential Evolution (DE)

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Authors: F. Rarbi, D. Dzahini, W. Uhring

Abstract:

In this paper, a dynamic and power efficient 8-bit and 100-MSPS Successive Approximation Register (SAR) Analog-to-Digital Converter (ADC) is presented. The circuit uses a non-differential capacitive Digital-to-Analog (DAC) architecture segmented by 2. The prototype is produced in a commercial 65-nm 1P7M CMOS technology with 1.2-V supply voltage. The size of the core ADC is 208.6 x 103.6 µm². The post-layout noise simulation results feature a SNR of 46.9 dB at Nyquist frequency, which means an effective number of bit (ENOB) of 7.5-b. The total power consumption of this SAR ADC is only 1.55 mW at 100-MSPS. It achieves then a figure of merit of 85.6 fJ/step.

Keywords: CMOS analog to digital converter, dynamic comparator, image sensor application, successive approximation register.

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Authors: Alireza Keshmiri, Shahriar Bagheri, Nan Wu

Abstract:

This research presents an analytical model for the development of an energy harvester with piezoelectric rings stacked at the boundary of the structure based on the Adomian decomposition method. The model is applied to geometrically non-uniform beams to derive the steady-state dynamic response of the structure subjected to base motion excitation and efficiently harvest the subsequent vibrational energy. The in-plane polarization of the piezoelectric rings is employed to enhance the electrical power output. A parametric study for the proposed energy harvester with various design parameters is done to prepare the dataset required for optimization. Finally, simulation-based optimization technique helps to find the optimum structural design with maximum efficiency. To solve the optimization problem, an artificial neural network is first trained to replace the simulation model, and then, a genetic algorithm is employed to find the optimized design variables. Higher geometrical non-uniformity and length of the beam lowers the structure natural frequency and generates a larger power output.

Keywords: Piezoelectricity, energy harvesting, simulation-based optimization, artificial neural network, genetic algorithm.

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Authors: Banaja Mohanty, Prakash Kumar Hota

Abstract:

This paper represents performance of particle swarm optimisation (PSO) algorithm based integral (I) controller and proportional-integral controller (PI) for interconnected hydro-thermal automatic generation control (AGC) with generation rate constraint (GRC) and Thyristor controlled phase shifter (TCPS) in series with tie line. The control strategy of TCPS provides active control of system frequency. Conventional objective function integral square error (ISE) and another objective function considering square of derivative of change in frequencies of both areas and change in tie line power are considered. The aim of designing the objective function is to suppress oscillation in frequency deviations and change in tie line power oscillation. The controller parameters are searched by PSO algorithm by minimising the objective functions. The dynamic performance of the controllers I and PI, for both the objective functions, are compared with conventionally optimized I controller.

Keywords: Automatic generation control (AGC), Generation rate constraint (GRC), Thyristor control phase shifter (TCPS), Particle swarm optimization (PSO).

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Authors: G. B. M. Carvalho, V. A. C. Vale, E. T. L. Cöuras Ford

Abstract:

With the aim of increasing the levels of comfort and security structures, the study of dynamic loads on buildings has been one of the focuses in the area of control engineering, civil engineering and architecture. Thus, this work presents a study based on simulation of the dynamics of buildings in the form of portico subjected to wind action, besides presenting an action of passive control, using for this the dynamics of the structure, consequently representing a system appropriated on environmental issues. These control systems are named the dynamic vibration absorbers.

Keywords: Dynamic vibration absorber, structure, comfort, safety, wind behavior, structure.

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Authors: Jiadong Liang

Abstract:

This paper presented a video watermarking algorithm based on wavelet chaotic neural network. First, to enhance binary image’s security, the algorithm encrypted it with double chaotic based on Arnold and Logistic map, Then, the host video was divided into some equal frames and distilled the key frame through chaotic sequence which generated by Logistic. Meanwhile, we distilled the low frequency coefficients of luminance component and self-adaptively embedded the processed image watermark into the low frequency coefficients of the wavelet transformed luminance component with the wavelet neural network. The experimental result suggested that the presented algorithm has better invisibility and robustness against noise, Gaussian filter, rotation, frame loss and other attacks.

Keywords: Video watermark, double chaotic encryption, wavelet neural network.

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Authors: Da-Xue Chen, Guang-Hui Liu

Abstract:

In this paper, we establish several oscillation criteria for the nonlinear second-order damped delay dynamic equation r(t)|xΔ(t)|β-1xΔ(t)Δ + p(t)|xΔσ(t)|β-1xΔσ(t) + q(t)f(x(τ (t))) = 0 on an arbitrary time scale T, where β > 0 is a constant. Our results generalize and improve some known results in which β > 0 is a quotient of odd positive integers. Some examples are given to illustrate our main results.

Keywords: Oscillation, damped delay dynamic equation, time scale.

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Authors: S. Khamsawang, S. Jiriwibhakorn

Abstract:

This paper proposes an application of the differential evolution (DE) algorithm for solving the economic dispatch problem (ED). Furthermore, the regenerating population procedure added to the conventional DE in order to improve escaping the local minimum solution. To test performance of DE algorithm, three thermal generating units with valve-point loading effects is used for testing. Moreover, investigating the DE parameters is presented. The simulation results show that the DE algorithm, which had been adjusted parameters, is better convergent time than other optimization methods.

Keywords: Differential evolution, Economic dispatch problem, Valve-point loading effect, Optimization method.

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Authors: Dongsu Wu, Hongbin Gu, Peng Li

Abstract:

A novel adaptive fuzzy trajectory tracking algorithm of Stewart platform based motion platform is proposed to compensate path deviation and degradation of controller-s performance due to actuator torque limit. The algorithm can be divided into two parts: the real-time trajectory shaping part and the joint space adaptive fuzzy controller part. For a reference trajectory in task space whenever any of the actuators is saturated, the desired acceleration of the reference trajectory is modified on-line by using dynamic model of motion platform. Meanwhile an additional action with respect to the difference between the nominal and modified trajectories is utilized in the non-saturated region of actuators to reduce the path error. Using modified trajectory as input, the joint space controller incorporates compute torque controller, leg velocity observer and fuzzy disturbance observer with saturation compensation. It can ensure stability and tracking performance of controller in present of external disturbance and position only measurement. Simulation results verify the effectiveness of proposed control scheme.

Keywords: Actuator saturation, adaptive fuzzy control, Stewartplatform, trajectory shaping, flight simulator

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Authors: M. Zahid Hossain, M. Ashraful Amin

Abstract:

The algorithms of convex hull have been extensively studied in literature, principally because of their wide range of applications in different areas. This article presents an efficient algorithm to construct approximate convex hull from a set of n points in the plane in O(n + k) time, where k is the approximation error control parameter. The proposed algorithm is suitable for applications preferred to reduce the computation time in exchange of accuracy level such as animation and interaction in computer graphics where rapid and real-time graphics rendering is indispensable.

Keywords: Convex hull, Approximation algorithm, Computational geometry, Linear time.

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Authors: Wanhyun Cho, Soonja Kang, Sangkyoon Kim, Soonyoung Park

Abstract:

In this paper, we propose the variational EM inference algorithm for the multi-class Gaussian process classification model that can be used in the field of human behavior recognition. This algorithm can drive simultaneously both a posterior distribution of a latent function and estimators of hyper-parameters in a Gaussian process classification model with multiclass. Our algorithm is based on the Laplace approximation (LA) technique and variational EM framework. This is performed in two steps: called expectation and maximization steps. First, in the expectation step, using the Bayesian formula and LA technique, we derive approximately the posterior distribution of the latent function indicating the possibility that each observation belongs to a certain class in the Gaussian process classification model. Second, in the maximization step, using a derived posterior distribution of latent function, we compute the maximum likelihood estimator for hyper-parameters of a covariance matrix necessary to define prior distribution for latent function. These two steps iteratively repeat until a convergence condition satisfies. Moreover, we apply the proposed algorithm with human action classification problem using a public database, namely, the KTH human action data set. Experimental results reveal that the proposed algorithm shows good performance on this data set.

Keywords: Bayesian rule, Gaussian process classification model with multiclass, Gaussian process prior, human action classification, laplace approximation, variational EM algorithm.

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Authors: B. Moaveni, S. Morovati

Abstract:

In recent years, increasing the usage of railway transportations especially in developing countries caused more attention to control systems railway vehicles. Consequently, designing and implementing the modern control systems to improve the operating performance of trains and locomotives become one of the main concerns of researches. Dynamic braking systems is an important safety system which controls the amount of braking torque generated by traction motors, to keep the adhesion coefficient between the wheel-sets and rail road in optimum bound. Adhesion force has an important role to control the braking distance and prevent the wheels from slipping during the braking process. Cascade control structure is one of the best control methods for the wide range of industrial plants in the presence of disturbances and errors. This paper presents cascade control structure based on two forward simple controllers with two feedback loops to control the slip ratio and braking torque. In this structure, the inner loop controls the angular velocity and the outer loop control the longitudinal velocity of the locomotive that its dynamic is slower than the dynamic of angular velocity. This control structure by controlling the torque of DC traction motors, tries to track the desired velocity profile to access the predefined braking distance and to control the slip ratio. Simulation results are employed to show the effectiveness of the introduced methodology in dynamic braking system.

Keywords: Cascade control, dynamic braking system, DC traction motors, slip control.

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Authors: Ram Kumar Soni, Alok Jain, Rajiv Saxena

Abstract:

This paper proposes an efficient method for the design of two channel quadrature mirror filter (QMF) bank. To achieve minimum value of reconstruction error near to perfect reconstruction, a linear optimization process has been proposed. Prototype low pass filter has been designed using Kaiser window function. The modified algorithm has been developed to optimize the reconstruction error using linear objective function through iteration method. The result obtained, show that the performance of the proposed algorithm is better than that of the already exists methods.

Keywords: Filterbank, near perfect reconstruction, Kaiserwindow, QMF.

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Authors: Suhas K, Sripadaraja K

Abstract:

This paper details few mechanical modeling and design issues of RF MEMS switches. We concentrate on an electrostatically actuated broad side series switch; surface micromachined with a crab leg membrane. The same results are extended to any complex structure. With available experimental data and fabrication results, we present the variation in dynamic performance and compliance of the switch with reference to few design issues, which we find are critical in deciding the dynamic behavior of the switch, without compromise on the RF characteristics. The optimization of pull in voltage, transient time and resonant frequency with regard to these critical design parameters are also presented.

Keywords: Microelectromechanical Systems (MEMS), RadioFrequency MEMS, Modeling, Actuators

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Authors: Raghvendra Kumar, Lillie Dewan

Abstract:

Exchange algorithm with constraints on magnitude and phase error separately in new way is presented in this paper. An important feature of the algorithms presented in this paper is that they allow for design constraints which often arise in practical filter design problems. Meeting required minimum stopband attenuation or a maximum deviation from the desired magnitude and phase responses in the passbands are common design constraints that can be handled by the methods proposed here. This new algorithm may have important advantages over existing technique, with respect to the speed and stability of convergence, memory requirement and low ripples.

Keywords: Least square estimation, Constraints, Exchange algorithm.

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Authors: Abdelali Joumad, Abdelaziz Nasroallah

Abstract:

In unsupervised segmentation context, we propose a bi-dimensional hidden Markov chain model (X,Y) that we adapt to the image segmentation problem. The bi-dimensional observed process Y = (Y 1, Y 2) is such that Y 1 represents the noisy image and Y 2 represents a noisy supplementary information on the image, for example a noisy proportion of pixels of the same type in a neighborhood of the current pixel. The proposed model can be seen as a competitive alternative to the Hilbert-Peano scan. We propose a bayesian algorithm to estimate parameters of the considered model. The performance of this algorithm is globally favorable, compared to the bi-dimensional EM algorithm through numerical and visual data.

Keywords: Image segmentation, Hidden Markov chain with a bi-dimensional observed process, Peano-Hilbert scan, Bayesian approach, MCMC methods, Bi-dimensional EM algorithm.

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