Search results for: Periodic output feedback control
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 5064

Search results for: Periodic output feedback control

4974 Analysis of Periodic Solution of Delay Fuzzy BAM Neural Networks

Authors: Qianhong Zhang, Lihui Yang, Daixi Liao

Abstract:

In this paper, by employing a new Lyapunov functional and an elementary inequality analysis technique, some sufficient conditions are derived to ensure the existence and uniqueness of periodic oscillatory solution for fuzzy bi-directional memory (BAM) neural networks with time-varying delays, and all other solutions of the fuzzy BAM neural networks converge the uniqueness periodic solution. These criteria are presented in terms of system parameters and have important leading significance in the design and applications of neural networks. Moreover an example is given to illustrate the effectiveness and feasible of results obtained.

Keywords: Fuzzy BAM neural networks, Periodic solution, Global exponential stability, Time-varying delays

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4973 Harmonic Analysis and Performance Improvement of a Wind Energy Conversions System with Double Output Induction Generator

Authors: M. Sedighizadeh, A. Rezazadeh

Abstract:

Wind turbines with double output induction generators can operate at variable speed permitting conversion efficiency maximization over a wide range of wind velocities. This paper presents the performance analysis of a wind driven double output induction generator (DOIG) operating at varying shafts speed. A periodic transient state analysis of DOIG equipped with two converters is carried out using a hybrid induction machine model. This paper simulates the harmonic content of waveforms in various points of drive at different speeds, based on the hybrid model (dqabc). Then the sinusoidal and trapezoidal pulse-width–modulation control techniques are used in order to improve the power factor of the machine and to weaken the injected low order harmonics to the supply. Based on the frequency spectrum, total harmonics distortion, distortion factor and power factor. Finally advantages of sinusoidal and trapezoidal pulse width modulation techniques are compared.

Keywords: DOIG, Harmonic Analysis, Wind.

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4972 Control and Simulation of FOPDT Food Processes with Constraints using PI Controller

Authors: M.Y. Pua, M.C. Tan, L.W. Tan, N. Ab.Aziz, F.S. Taip

Abstract:

The most common type of controller being used in the industry is PI(D) controller which has been used since 1945 and is still being widely used due to its efficiency and simplicity. In most cases, the PI(D) controller was tuned without taking into consideration of the effect of actuator saturation. In real processes, the most common actuator which is valve will act as constraint and restrict the controller output. Since the controller is not designed to encounter saturation, the process may windup and consequently resulted in large oscillation or may become unstable. Usually, an antiwindup compensator is added to the feedback control loop to reduce the deterioration effect of integral windup. This research aims to specifically control processes with constraints. The proposed method was applied to two different types of food processes, which are blending and spray drying. Simulations were done using MATLAB and the performances of the proposed method were compared with other conventional methods. The proposed technique was able to control the processes and avoid saturation such that no anti windup compensator is needed.

Keywords: constraints, food process control, first order plusdead time process, PI

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4971 The Electronic and Computer-Aided Periodic Table Prepared for the Visually Impaired Individuals

Authors: Ayşe Eldem, Fatih Başçiftçi

Abstract:

Visually impaired individuals cannot lead their lives as comfortable as others. Therefore, new applications are being developed every passing day in order to make their lives easier. In this study, an electronic and computer-aided audio device was developed with the aim of making the learning of the periodic table easier for the visually impaired. In this device, a board includes buttons for each element of the periodic table. After pressing a button, the visually impaired individual not only hears the name of the element but also feels with his/her hands where that specific element is located.

Keywords: Periodic Table, PIC16F877, Serial port, Visually Impaired Individual.

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4970 Adaptive Control Strategy of Robot Polishing Force Based on Position Impedance

Authors: Wang Zhan-Xi, Zhang Yi-Ming, Chen Hang, Wang Gang

Abstract:

Manual polishing has problems such as high labor intensity, low production efficiency and difficulty in guaranteeing the consistency of polishing quality. The use of robot polishing instead of manual polishing can effectively avoid these problems. Polishing force directly affects the quality of polishing, so accurate tracking and control of polishing force is one of the most important conditions for improving the accuracy of robot polishing. The traditional force control strategy is difficult to adapt to the strong coupling of force control and position control during the robot polishing process. Therefore, based on the analysis of force-based impedance control and position-based impedance control, this paper proposed a type of adaptive controller. Based on force feedback control of active compliance control, the controller can adaptively estimate the stiffness and position of the external environment and eliminate the steady-state force error produced by traditional impedance control. The simulation results of the model show that the adaptive controller has good adaptability to changing environmental positions and environmental stiffness, and can accurately track and control polishing force.

Keywords: robot polishing, force feedback, impedance control, adaptive control

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4969 Design of Speed and Power Control System for Wind Turbine with Reference Tracking Method

Authors: H. Ghanbari, H. Nikbakht, A. Zahedi, M. Ghanbari

Abstract:

This paper is focusing on designing a control system for wind turbine which can control the speed and output power according to arbitrary algorithm. Reference Tracking Method is used to control the turbine spinning speed in order to increase its output energy.

Keywords: Wind Turbine, Simulink, Reference Tracking Method.

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4968 Design of Permanent Sensor Fault Tolerance Algorithms by Sliding Mode Observer for Smart Hybrid Powerpack

Authors: Sungsik Jo, Hyeonwoo Kim, Iksu Choi, Hunmo Kim

Abstract:

In the SHP, LVDT sensor is for detecting the length changes of the EHA output, and the thrust of the EHA is controlled by the pressure sensor. Sensor is possible to cause hardware fault by internal problem or external disturbance. The EHA of SHP is able to be uncontrollable due to control by feedback from uncertain information, on this paper; the sliding mode observer algorithm estimates the original sensor output information in permanent sensor fault. The proposed algorithm shows performance to recovery fault of disconnection and short circuit basically, also the algorithm detect various of sensor fault mode.

Keywords: Smart Hybrid Powerpack (SHP), Electro Hydraulic Actuator (EHA), Permanent Sensor fault tolerance, Sliding mode observer (SMO), Graphic User Interface (GUI).

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4967 Limit Cycle Behaviour of a Neural Controller with Delayed Bang-Bang Feedback

Authors: Travis Wiens, Greg Schoenau, Rich Burton

Abstract:

It is well known that a linear dynamic system including a delay will exhibit limit cycle oscillations when a bang-bang sensor is used in the feedback loop of a PID controller. A similar behaviour occurs when a delayed feedback signal is used to train a neural network. This paper develops a method of predicting this behaviour by linearizing the system, which can be shown to behave in a manner similar to an integral controller. Using this procedure, it is possible to predict the characteristics of the neural network driven limit cycle to varying degrees of accuracy, depending on the information known about the system. An application is also presented: the intelligent control of a spark ignition engine.

Keywords: Control and automation, artificial neural networks, limit cycle

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4966 State Estimation Based on Unscented Kalman Filter for Burgers’ Equation

Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

Controlling the flow of fluids is a challenging problem that arises in many fields. Burgers’ equation is a fundamental equation for several flow phenomena such as traffic, shock waves, and turbulence. The optimal feedback control method, so-called model predictive control, has been proposed for Burgers’ equation. However, the model predictive control method is inapplicable to systems whose all state variables are not exactly known. In practical point of view, it is unusual that all the state variables of systems are exactly known, because the state variables of systems are measured through output sensors and limited parts of them can be only available. In fact, it is usual that flow velocities of fluid systems cannot be measured for all spatial domains. Hence, any practical feedback controller for fluid systems must incorporate some type of state estimator. To apply the model predictive control to the fluid systems described by Burgers’ equation, it is needed to establish a state estimation method for Burgers’ equation with limited measurable state variables. To this purpose, we apply unscented Kalman filter for estimating the state variables of fluid systems described by Burgers’ equation. The objective of this study is to establish a state estimation method based on unscented Kalman filter for Burgers’ equation. The effectiveness of the proposed method is verified by numerical simulations.

Keywords: State estimation, fluid systems, observer systems, unscented Kalman filter.

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4965 Almost Periodic Solution for an Impulsive Neural Networks with Distributed Delays

Authors: Lili Wang

Abstract:

By using the estimation of the Cauchy matrix of linear impulsive differential equations and Banach fixed point theorem as well as Gronwall-Bellman’s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for an impulsive neural networks with distributed delays. An example is presented to illustrate the feasibility and  effectiveness of the results.

Keywords: Almost periodic solution, Exponential stability, Neural networks, Impulses.

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4964 Three-Level Converters Back-to-Back DC Bus Control for Torque Ripple Reduction of Induction Motor

Authors: T. Abdelkrim, K. Benamrane, B. Bezza, Aeh Benkhelifa, A. Borni

Abstract:

This paper proposes a regulation method of back-to-back connected three-level converters in order to reduce the torque ripple in induction motor. First part is dedicated to the presentation of the feedback control of three-level PWM rectifier. In the second part, three-level NPC voltage source inverter balancing DC bus algorithm is presented. A theoretical analysis with a complete simulation of the system is presented to prove the excellent performance of the proposed technique.

Keywords: Back-to-back connection, Feedback control, Neutral-point balance, Three-level converter, Torque ripple.

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4963 Design of a Three Phase Active Power Filter with Sliding Mode Control and Energy Feedback

Authors: M. Nayeripour, T. Niknam

Abstract:

Nonlinear and unbalance loads in three phase networks create harmonics and losses. Active and passive filters are used for elimination or reduction of these effects. Passive filters have some limitations. For example, they are designed only for a specific frequency and they may cause to resonance in the network at the point of common coupling. The other drawback of a passive filter is that the sizes of required elements are normally large. The active filter can improve some of limitations of passive filter for example; they can eliminate more than one harmonic and don't cause resonance in the network. In this paper inverter analysis have been done simultaneously in three phase and the RL impedance of the line have been considered. A sliding mode control based on energy feedback of capacitors is employed in the design with this method, the dynamic speed of the filter is improved effectively and harmonics and load unbalance is compensating quickly.

Keywords: Shunt active filter, harmonic, inverter, sliding mode control, energy feedback.

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4962 Periodic Solutions for a Third-order p-Laplacian Functional Differential Equation

Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: p–Laplacian, distributed delay, periodic solution, Mawhin's continuation theorem.

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4961 A New Stability Analysis and Stabilization of Discrete-Time Switched Linear Systems Using Vector Norms Approach

Authors: Marwen Kermani, Anis Sakly, Faouzi M'sahli

Abstract:

In this paper, we aim to investigate a new stability analysis for discrete-time switched linear systems based on the comparison, the overvaluing principle, the application of Borne-Gentina criterion and the Kotelyanski conditions. This stability conditions issued from vector norms correspond to a vector Lyapunov function. In fact, the switched system to be controlled will be represented in the Companion form. A comparison system relative to a regular vector norm is used in order to get the simple arrow form of the state matrix that yields to a suitable use of Borne-Gentina criterion for the establishment of sufficient conditions for global asymptotic stability. This proposed approach could be a constructive solution to the state and static output feedback stabilization problems.

Keywords: Discrete-time switched linear systems, Global asymptotic stability, Vector norms, Borne-Gentina criterion, Arrow form state matrix, Arbitrary switching, State feedback controller, Static output feedback controller.

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4960 Model and Control of Renewable Energy Systems

Authors: Yelena Chaiko

Abstract:

This paper presents a developed method for controlling multi-renewable energy generators. The control system depends basically on three sensors (wind anemometer, solar sensor, and voltage sensor). These sensors represent PLC-s analogue inputs. Controlling the output voltage supply can be achieved by an enhanced method of interlocking between the renewable energy generators, depending on those sensors and output contactors.

Keywords: Renewable, energy, control, model, generator.

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4959 Stochastic Control of Decentralized Singularly Perturbed Systems

Authors: Walid S. Alfuhaid, Saud A. Alghamdi, John M. Watkins, M. Edwin Sawan

Abstract:

Designing a controller for stochastic decentralized interconnected large scale systems usually involves a high degree of complexity and computation ability. Noise, observability, and controllability of all system states, connectivity, and channel bandwidth are other constraints to design procedures for distributed large scale systems. The quasi-steady state model investigated in this paper is a reduced order model of the original system using singular perturbation techniques. This paper results in an optimal control synthesis to design an observer based feedback controller by standard stochastic control theory techniques using Linear Quadratic Gaussian (LQG) approach and Kalman filter design with less complexity and computation requirements. Numerical example is given at the end to demonstrate the efficiency of the proposed method.

Keywords: Decentralized, optimal control, output, singular perturb.

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4958 Positive Periodic Solutions for a Neutral Impulsive Delay Competition System

Authors: Daiming Wang

Abstract:

In this paper, a neutral impulsive competition system with distributed delays is studied by using Mawhin-s coincidence degree theory and the mean value theorem of differential calculus. Sufficient conditions on the existence of positive periodic solution of the system are obtained.

Keywords: Neutral impulsive delay system, competitive system, coincidence degree, periodic solution, existence.

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4957 Fractional Order Feedback Control of a Ball and Beam System

Authors: Santosh Kr. Choudhary

Abstract:

In this paper, fractional order feedback control of a ball beam model is investigated. The ball beam model is a particular example of the double Integrator system having strongly nonlinear characteristics and unstable dynamics which make the control of such system a challenging task. Most of the work in fractional order control systems are in theoretical nature and controller design and its implementation in practice is very small. In this work, a successful attempt has been made to design a fractional order PIλDμcontroller for a benchmark laboratory ball and beam model. Better performance can be achieved using a fractional order PID controller and it is demonstrated through simulations results with a comparison to the classic PID controller.

Keywords: Fractional order calculus, fractional order controller, fractional order system, ball and beam system, PIλDμ controller, modelling, simulation.

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4956 Broadcasting Stabilization for Dynamical Multi-Agent Systems

Authors: Myung-Gon Yoon, Jung-Ho Moon, Tae Kwon Ha

Abstract:

This paper deals with a stabilization problem for multi-agent systems, when all agents in a multi-agent system receive the same broadcasting control signal and the controller can measure not each agent output but the sum of all agent outputs. It is analytically shown that when the sum of all agent outputs is bounded with a certain broadcasting controller for a given reference, each agent output is separately bounded: stabilization of the sum of agent outputs always results in the stability of every agent output. A numerical example is presented to illustrate our theoretic findings in this paper.

Keywords: Broadcasting Control, Multi-agent System, Transfer Function

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4955 Model Predictive Control with Unscented Kalman Filter for Nonlinear Implicit Systems

Authors: Takashi Shimizu, Tomoaki Hashimoto

Abstract:

A class of implicit systems is known as a more generalized class of systems than a class of explicit systems. To establish a control method for such a generalized class of systems, we adopt model predictive control method which is a kind of optimal feedback control with a performance index that has a moving initial time and terminal time. However, model predictive control method is inapplicable to systems whose all state variables are not exactly known. In other words, model predictive control method is inapplicable to systems with limited measurable states. In fact, it is usual that the state variables of systems are measured through outputs, hence, only limited parts of them can be used directly. It is also usual that output signals are disturbed by process and sensor noises. Hence, it is important to establish a state estimation method for nonlinear implicit systems with taking the process noise and sensor noise into consideration. To this purpose, we apply the model predictive control method and unscented Kalman filter for solving the optimization and estimation problems of nonlinear implicit systems, respectively. The objective of this study is to establish a model predictive control with unscented Kalman filter for nonlinear implicit systems.

Keywords: Model predictive control, unscented Kalman filter, nonlinear systems, implicit systems.

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4954 Quantitative Estimation of Periodicities in Lyari River Flow Routing

Authors: Rana Khalid Naeem, Asif Mansoor

Abstract:

The hydrologic time series data display periodic structure and periodic autoregressive process receives considerable attention in modeling of such series. In this communication long term record of monthly waste flow of Lyari river is utilized to quantify by using PAR modeling technique. The parameters of model are estimated by using Frances & Paap methodology. This study shows that periodic autoregressive model of order 2 is the most parsimonious model for assessing periodicity in waste flow of the river. A careful statistical analysis of residuals of PAR (2) model is used for establishing goodness of fit. The forecast by using proposed model confirms significance and effectiveness of the model.

Keywords: Diagnostic checks, Lyari river, Model selection, Monthly waste flow, Periodicity, Periodic autoregressive model.

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4953 Response Time Behavior Trends of Proptional, Propotional Integral and Proportional Integral Derivative Mode on Lab Scale

Authors: Syed Zohaib Javaid Zaidi, W. Iqbal

Abstract:

The industrial automation is dependent upon pneumatic control systems. The industrial units are now controlled with digital control systems to tackle the process variables like Temperature, Pressure, Flow rates and Composition.

This research work produces an evaluation of the response time fluctuations for proportional mode, proportional integral and proportional integral derivative modes of automated chemical process control. The controller output is measured for different values of gain with respect to time in three modes (P, PI and PID). In case of P-mode for different values of gain the controller output has negligible change. When the controller output of PI-mode is checked for constant gain, it can be seen that by decreasing the integral time the controller output has showed more fluctuations. The PID mode results have found to be more interesting in a way that when rate minute has changed, the controller output has also showed fluctuations with respect to time.  The controller output for integral mode and derivative mode are observed with lesser steady state error, minimum offset and larger response time to control the process variable.   The tuning parameters in case of P-mode are only steady state gain with greater errors with respect to controller output. The integral mode showed controller outputs with intermediate responses during integral gain (ki).  By increasing the rate minute the derivative gain (kd) also increased which showed the controlled oscillations in case of PID mode and lesser overshoot.

Keywords: Controller Output, P, PI &PID modes, Steady state gain.

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4952 Stability of Discrete Linear Systems with Periodic Coefficients under Parametric Perturbations

Authors: Adam Czornik, Aleksander Nawrat

Abstract:

This paper studies the problem of exponential stability of perturbed discrete linear systems with periodic coefficients. Assuming that the unperturbed system is exponentially stable we obtain conditions on the perturbations under which the perturbed system is exponentially stable.

Keywords: Exponential stability, time-varying linear systems, periodic systems.

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4951 Application of Fractional Model Predictive Control to Thermal System

Authors: Aymen Rhouma, Khaled Hcheichi, Sami Hafsi

Abstract:

The article presents an application of Fractional Model Predictive Control (FMPC) to a fractional order thermal system using Controlled Auto Regressive Integrated Moving Average (CARIMA) model obtained by discretization of a continuous fractional differential equation. Moreover, the output deviation approach is exploited to design the K -step ahead output predictor, and the corresponding control law is obtained by solving a quadratic cost function. Experiment results onto a thermal system are presented to emphasize the performances and the effectiveness of the proposed predictive controller.

Keywords: Fractional model predictive control, fractional order systems, thermal system.

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4950 Parametric Vibrations of Periodic Shells

Authors: B. Tomczyk, R. Mania

Abstract:

Thin linear-elastic cylindrical circular shells having a micro-periodic structure along two directions tangent to the shell midsurface (biperiodic shells) are object of considerations. The aim of this paper is twofold. First, we formulate an averaged nonasymptotic model for the analysis of parametric vibrations or dynamical stability of periodic shells under consideration, which has constant coefficients and takes into account the effect of a cell size on the overall shell behavior (a length-scale effect). This model is derived employing the tolerance modeling procedure. Second we apply the obtained model to derivation of frequency equation being a starting point in the analysis of parametric vibrations. The effect of the microstructure length oh this frequency equation is discussed.

Keywords: Micro-periodic shells, mathematical modeling, length-scale effect, parametric vibrations

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4949 A New Approach to Feedback Shift Registers

Authors: Myat Su Mon Win

Abstract:

The pseudorandom number generators based on linear feedback shift registers (LFSRs), are very quick, easy and secure in the implementation of hardware and software. Thus they are very popular and widely used. But LFSRs lead to fairly easy cryptanalysis due to their completely linearity properties. In this paper, we propose a stochastic generator, which is called Random Feedback Shift Register (RFSR), using stochastic transformation (Random block) with one-way and non-linearity properties.

Keywords: Linear Feedback Shift Register, Non Linearity, R_Block, Random Feedback Shift Register

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4948 Optimal Speed Controller Design of the Two-Inertia Stabilization System

Authors: Byoung-Uk Nam, Hag-Seong Kim, Ho-Jung Lee, Dong-Hyun Kim

Abstract:

This paper focuses on systematic analysis and controller design of the two-inertia STABILIZATION system, considering the angular motion on a base body. This approach is essential to the stabilization system to aim at a target under three or six degrees of freedom base motion. Four controllers, such as conventional PDF(Pseudo-Derivative Feedback) controller with motor speed feedback, PDF controller with load speed feedback, modified PDF controller with motor-load speed feedback and feedforward controller added to modified PDF controller, are suggested to improve reference tracking and disturbance rejection performance. Characteristics and performance of each controller are analyzed and validated by simulation in the case of the modified PDF controller with and without a feedforward controller.

Keywords: Two-Inertia stabilization System, ITAE criterion, Speed Control.

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4947 Peer Corrective Feedback on Written Errors in Computer-Mediated Communication

Authors: S. H. J. Liu

Abstract:

This paper aims to explore the role of peer Corrective Feedback (CF) in improving written productions by English-as-a- foreign-language (EFL) learners who work together via Wikispaces. It attempted to determine the effect of peer CF on form accuracy in English, such as grammar and lexis. Thirty-four EFL learners at the tertiary level were randomly assigned into the experimental (with peer feedback) or the control (without peer feedback) group; each group was subdivided into small groups of two or three. This resulted in six and seven small groups in the experimental and control groups, respectively. In the experimental group, each learner played a role as an assessor (providing feedback to others), as well as an assessee (receiving feedback from others). Each participant was asked to compose his/her written work and revise it based on the feedback. In the control group, on the other hand, learners neither provided nor received feedback but composed and revised their written work on their own. Data collected from learners’ compositions and post-task interviews were analyzed and reported in this study. Following the completeness of three writing tasks, 10 participants were selected and interviewed individually regarding their perception of collaborative learning in the Computer-Mediated Communication (CMC) environment. Language aspects to be analyzed included lexis (e.g., appropriate use of words), verb tenses (e.g., present and past simple), prepositions (e.g., in, on, and between), nouns, and articles (e.g., a/an). Feedback types consisted of CF, affective, suggestive, and didactic. Frequencies of feedback types and the accuracy of the language aspects were calculated. The results first suggested that accurate items were found more in the experimental group than in the control group. Such results entail that those who worked collaboratively outperformed those who worked non-collaboratively on the accuracy of linguistic aspects. Furthermore, the first type of CF (e.g., corrections directly related to linguistic errors) was found to be the most frequently employed type, whereas affective and didactic were the least used by the experimental group. The results further indicated that most participants perceived that peer CF was helpful in improving the language accuracy, and they demonstrated a favorable attitude toward working with others in the CMC environment. Moreover, some participants stated that when they provided feedback to their peers, they tended to pay attention to linguistic errors in their peers’ work but overlook their own errors (e.g., past simple tense) when writing. Finally, L2 or FL teachers or practitioners are encouraged to employ CMC technologies to train their students to give each other feedback in writing to improve the accuracy of the language and to motivate them to attend to the language system.

Keywords: Peer corrective feedback, computer-mediated communication, second or foreign language learning, Wikispaces.

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4946 Novel Sinusoidal Pulse Width Modulation with Least Correlated Noise

Authors: Shiang-Hwua Yu, Han-Sheng Tseng

Abstract:

This paper presents a novel sinusoidal modulation scheme that features least correlated noise and high linearity. The modulation circuit, which is composed of a quantizer, a resonator, and a comparator, is capable of eliminating correlated modulation noise while doing modulation. The proposed modulation scheme combined with the linear quadratic optimal control is applied to a single-phase voltage source inverter and validated with the experiment results. The experiments show that the inverter supplies stable 60Hz 110V AC power with a total harmonic distortion of less than 1%, under the DC input variation from 190 V to 300 V and the output power variation from 0 to 600 W.

Keywords: Pulse width modulation, feedback dithering, linear quadratic control, inverter.

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4945 Existence and Exponential Stability of Almost Periodic Solution for Cohen-Grossberg SICNNs with Impulses

Authors: Meng Hu, Lili Wang

Abstract:

In this paper, based on the estimation of the Cauchy matrix of linear impulsive differential equations, by using Banach fixed point theorem and Gronwall-Bellman-s inequality, some sufficient conditions are obtained for the existence and exponential stability of almost periodic solution for Cohen-Grossberg shunting inhibitory cellular neural networks (SICNNs) with continuously distributed delays and impulses. An example is given to illustrate the main results.

Keywords: Almost periodic solution, exponential stability, neural networks, impulses.

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