Search results for: feedback training.
Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 1406

Search results for: feedback training.

1406 Primary School Principles- Views about In-service Training Activities

Authors: Sadık Kartal

Abstract:

This study was carried out to determine the feedback from the primary school headmasters on in-service training activities. 384 primary school headmasters were asked to give feedback on the in-service training facilities organized by the Ministry of Education through an open –ended question. The study group was formed by 359 primary school headmasters who attended “Management Skills" seminars which were organized in March, April and May in the extent of 2006 In-service Training Facilities Plan by the Ministry of Education and were also volunteers to give feedback on the inservice training activities. The qualitative research method was used in the analysis of the data since the primary school headmasters gave written feedback on the in-service training activities. Having analyzed the feedback, certain categories were formed by coding it. Certain frequencies and percentages were determined according to the codes. It was made obvious that the primary school headmasters benefitted from those facilities by sharing their experiences, problems and their possible solutions mutually

Keywords: In-service training, primary school principles, educates.

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1405 A Comparative Study of the Effectiveness of Trained Inspectors in Different Workloads between Feed Forward and Feedback Training

Authors: Sittichai K., Anucha W., Phonsak L.

Abstract:

Objective of this study was to study and compare the effectiveness of inspectors who had different workloads for feed forward and feedback training. The visual search task was simulated to search for specified alphabets called defects. These defects were included of four alphabets in Thai and English such as s ภ, ถ, X, and V with different background. These defects were combined in the specified alphabets and were given the different three backgrounds i.e., Thai, English, and mixed English and Thai alphabets. Sixty students were chosen as a sample in this study and test for final selection subject. Finally, five subjects were taken into testing process. They were asked to search for defects after they were provided basic information. Experiment design was used factorial design and subjects were trained for feed forward and the feedback training. The results show that both trainings were affected on mean search time. It was also found that the feedback training can increase the effectiveness of visual inspectors rather than the feed forward training significantly different at the level of .05

Keywords: visual search, feed forward, feedback training.

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1404 Role of Feedbacks in Simulation-Based Learning

Authors: Usman Ghani

Abstract:

Feedback is a vital element for improving student learning in a simulation-based training as it guides and refines learning through scaffolding. A number of studies in literature have shown that students’ learning is enhanced when feedback is provided with personalized tutoring that offers specific guidance and adapts feedback to the learner in a one-to-one environment. Thus, emulating these adaptive aspects of human tutoring in simulation provides an effective methodology to train individuals. This paper presents the results of a study that investigated the effectiveness of automating different types of feedback techniques such as Knowledge-of-Correct-Response (KCR) and Answer-Until- Correct (AUC) in software simulation for learning basic information technology concepts. For the purpose of comparison, techniques like simulation with zero or no-feedback (NFB) and traditional hands-on (HON) learning environments are also examined. The paper presents the summary of findings based on quantitative analyses which reveal that the simulation based instructional strategies are at least as effective as hands-on teaching methodologies for the purpose of learning of IT concepts. The paper also compares the results of the study with the earlier studies and recommends strategies for using feedback mechanism to improve students’ learning in designing and simulation-based IT training.

Keywords: Simulation, feedback, training, hands-on, labs.

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1403 A Study of Feedback Strategy to Improve Inspector Performance by Using Computer Based Training

Authors: Santirat Nansaarng, Sittichai Kaewkuekool, Supreeya Siripattanakunkajorn

Abstract:

The purpose of this research was to study the inspector performance by using computer based training (CBT). Visual inspection task was printed circuit board (PCB) simulated on several types of defects. Subjects were 16 undergraduate randomly selected from King Mongkut-s University of Technology Thonburi and test for 20/20. Then, they were equally divided on performance into two groups (control and treatment groups) and were provided information before running the experiment. Only treatment group was provided feedback information after first experiment. Results revealed that treatment group was showed significantly difference at the level of 0.01. The treatment group showed high percentage on defects detected. Moreover, the attitude of inspectors on using the CBT to inspection was showed on good. These results have been showed that CBT could be used for training to improve inspector performance.

Keywords: Training, Feedback, Computer based Training (CBT)

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1402 Dynamics and Feedback Control for a New Hyperchaotic System

Authors: Kejun Zhuang, Hailong Zhu

Abstract:

In this paper, stability and Hopf bifurcation analysis of a novel hyperchaotic system are investigated. Four feedback control strategies, the linear feedback control method, enhancing feedback control method, speed feedback control method and delayed feedback control method, are used to control the hyperchaotic attractor to unstable equilibrium. Moreover numerical simulations are given to verify the theoretical results.

Keywords: Feedback control, Hopf bifurcation, hyperchaotic system, stability.

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1401 Research on the Relevance Feedback-based Image Retrieval in Digital Library

Authors: Rongtao Ding, Xinhao Ji, Linting Zhu

Abstract:

In recent years, the relevance feedback technology is regarded in content-based image retrieval. This paper suggests a neural networks feedback algorithm based on the radial basis function, coming to extract the semantic character of image. The results of experiment indicated that the performance of this relevance feedback is better than the feedback algorithm based on Single-RBF.

Keywords: Image retrieval, relevance feedback, radial basis function.

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1400 On the Fast Convergence of DD-LMS DFE Using a Good Strategy Initialization

Authors: Y.Ben Jemaa, M.Jaidane

Abstract:

In wireless communication system, a Decision Feedback Equalizer (DFE) to cancel the intersymbol interference (ISI) is required. In this paper, an exact convergence analysis of the (DFE) adapted by the Least Mean Square (LMS) algorithm during the training phase is derived by taking into account the finite alphabet context of data transmission. This allows us to determine the shortest training sequence that allows to reach a given Mean Square Error (MSE). With the intention of avoiding the problem of ill-convergence, the paper proposes an initialization strategy for the blind decision directed (DD) algorithm. This then yields a semi-blind DFE with high speed and good convergence.

Keywords: Adaptive Decision Feedback Equalizer, PerformanceAnalysis, Finite Alphabet Case, Ill-Convergence, Convergence speed.

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1399 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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1398 Stabilization and Observation of Attitude Control Systems for Micro Satellites

Authors: A. Elakkary, A. Echchatbi, N. Elalami

Abstract:

In this paper, we are interested in attitude control of a satellite, which using wheels of reaction, by state feedback. First, we develop a method allowing us to put the control and its integral in the state-feedback form. Then, by using the theorem of Gronwall- Bellman, we put the sufficient conditions so that the nonlinear system modeling the satellite is stabilisable and observed by state feedback.

Keywords: Satellite, attitude control, state feedback, attitude stabilization.

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1397 Repetitive Control and Feedback Dithering Modulation of a DC/AC Converter

Authors: Sing-Han Wang, Shiang-Hwua Yu, Chih-Po Yang

Abstract:

Repetitive control and feedback dithering modulation are applied to a single-phase voltage source inverter, with an aim to eliminate harmonics and stabilize the inverter under load variations. The proposed control and modulation scheme comprise multiple loops of feedback, which helps improve inverter performance and robustness. Experimental results show that the designed inverter exhibits very low distortion at its output with THD of about 0.3% under different load variations.

Keywords: Feedback dithering modulation, repetitive control, state feedback, inverter, harmonics elimination.

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1396 Explicit Feedback Linearization of Magnetic Levitation System

Authors: Bhawna Tandon, Shiv Narayan, Jagdish Kumar

Abstract:

This study proposes the transformation of nonlinear Magnetic Levitation System into linear one, via state and feedback transformations using explicit algorithm. This algorithm allows computing explicitly the linearizing state coordinates and feedback for any nonlinear control system, which is feedback linearizable, without solving the Partial Differential Equations. The algorithm is performed using a maximum of N-1 steps where N being the dimension of the system.

Keywords: Explicit Algorithm, Feedback Linearization, Nonlinear control, Magnetic Levitation System.

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1395 A Case Study of Reactive Focus on Form through Negotiation on Spoken Errors: Does It Work for All Learners?

Authors: Vahid Parvaresh, Zohre Kassaian, Saeed Ketabi, Masoud Saeedi

Abstract:

This case study investigates the effects of reactive focus on form through negotiation on the linguistic development of an adult EFL learner in an exclusive private EFL classroom. The findings revealed that in this classroom negotiated feedback occurred significantly more often than non-negotiated feedback. However, it was also found that in the long run the learner was significantly more successful in correcting his own errors when he had received nonnegotiated feedback than negotiated feedback. This study, therefore, argues that although negotiated feedback seems to be effective for some learners in the short run, it is non-negotiated feedback which seems to be more effective in the long run. This long lasting effect might be attributed to the impact of schooling system which is itself indicative of the dominant culture, or to the absence of other interlocutors in the course of interaction.

Keywords: error, feedback, focus on form, interaction, schooling.

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1394 State-Space PD Feedback Control

Authors: John Florescu

Abstract:

A challenged control problem is when the performance is pushed to the limit. The state-derivative feedback control strategy directly uses acceleration information for feedback and state estimation. The derivative part is concerned with the rateof- change of the error with time. If the measured variable approaches the set point rapidly, then the actuator is backed off early to allow it to coast to the required level. Derivative action makes a control system behave much more intelligently. A sensor measures the variable to be controlled and the measured in formation is fed back to the controller to influence the controlled variable. A high gain problem can be also formulated for proportional plus derivative feedback transformation. Using MATLAB Simulink dynamic simulation tool this paper examines a system with a proportional plus derivative feedback and presents an automatic implementation of finding an acceptable controlled system. Using feedback transformations the system is transformed into another system.

Keywords: Feedback, PD, state-space, derivative.

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1393 Pre-Service EFL Teachers' Perceptions of Written Corrective Feedback in a Wiki-Based Environment

Authors: Mabel Ortiz, Claudio Díaz

Abstract:

This paper explores Chilean pre-service teachers' perceptions about the provision of corrective feedback in a wiki environment during the collaborative writing of an argumentative essay. After conducting a semi-structured interview on 22 participants, the data were processed through the content analysis technique. The results show that students have positive perceptions about corrective feedback, provided through a wiki virtual environment, which in turn facilitates feedback provision and impacts language learning effectively. Some of the positive perceptions about virtual feedback refer to permanent access, efficiency, simultaneous revision and immediacy. It would then be advisable to integrate wiki-based feedback as a methodology for the language classroom and collaborative writing tasks.

Keywords: Argumentative essay, focused corrective feedback, perception, wiki environment.

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1392 ILMI Approach for Robust Output Feedback Control of Induction Machine

Authors: Abdelwahed Echchatbi, Adil Rizki, Ali Haddi, Nabil Mrani, Noureddine Elalami

Abstract:

In this note, the robust static output feedback stabilisation of an induction machine is addressed. The machine is described by a non homogenous bilinear model with structural uncertainties, and the feedback gain is computed via an iterative LMI (ILMI) algorithm.

Keywords: Induction machine, Static output feedback, robust stabilisation.

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1391 Helicopter Adaptive Control with Parameter Estimation Based on Feedback Linearization

Authors: A. R. Nemati, M. Haddad Zarif, M. M. Fateh

Abstract:

This paper presents an adaptive feedback linearization approach to derive helicopter. Ideal feedback linearization is defined for the cases when the system model is known. Adaptive feedback linearization is employed to get asymptotically exact cancellation for the inherent uncertainty in the knowledge of the given parameters of system. The control algorithm is implemented using the feedback linearization technique and adaptive method. The controller parameters are unknown where an adaptive control law aims to drive them towards their ideal values for providing perfect model matching between the reference model and the closed-loop plant model. The converged parameters of controller would then provide good estimates for the unknown plant parameters.

Keywords: Adaptive control, helicopter, feedback linearization, nonlinear control.

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1390 Approximation Incremental Training Algorithm Based on a Changeable Training Set

Authors: Yi-Fan Zhu, Wei Zhang, Xuan Zhou, Qun Li, Yong-Lin Lei

Abstract:

The quick training algorithms and accurate solution procedure for incremental learning aim at improving the efficiency of training of SVR, whereas there are some disadvantages for them, i.e. the nonconvergence of the formers for changeable training set and the inefficiency of the latter for a massive dataset. In order to handle the problems, a new training algorithm for a changeable training set, named Approximation Incremental Training Algorithm (AITA), was proposed. This paper explored the reason of nonconvergence theoretically and discussed the realization of AITA, and finally demonstrated the benefits of AITA both on precision and efficiency.

Keywords: support vector regression, incremental learning, changeable training set, quick training algorithm, accurate solutionprocedure

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1389 A VR Cybersecurity Training Knowledge-Based Ontology

Authors: Shaila Rana, Wasim Alhamdani

Abstract:

Effective cybersecurity learning relies on an engaging, interactive, and entertaining activity that fosters positive learning outcomes. VR cybersecurity training may provide a training format that is engaging, interactive, and entertaining. A methodological approach and framework are needed to allow trainers and educators to employ VR cybersecurity training methods to promote positive learning outcomes. Thus, this paper aims to create an approach that cybersecurity trainers can follow to create a VR cybersecurity training module. This methodology utilizes concepts from other cybersecurity training frameworks, such as NICE and CyTrONE. Other cybersecurity training frameworks do not incorporate the use of VR. VR training proposes unique challenges that cannot be addressed in current cybersecurity training frameworks. Subsequently, this ontology utilizes concepts to develop VR training to create a relevant methodology for creating VR cybersecurity training modules.

Keywords: Virtual reality cybersecurity training, VR cybersecurity training, traditional cybersecurity training, ontology.

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1388 Using Collaborative Pictures to Understand Student Experience

Authors: Tessa Berg, Emma Guion Akdag

Abstract:

Summative feedback forms are used in academia for gathering data on course quality and student understanding. Students answer a series of questions based on the course they are soon to finish in these forms. Feedback forms are notorious for being homogenised and limiting and thus the data captured is often neutral and lacking in tacit emotional responses. This paper contrasts student feedback forms with collaborative drawing. We analyse 19 pictures drawn by international students on a pre-sessional course. Through visuals we present an approach to enable a holistic level of student understanding. Visuals communicate irrespective of possible language, cultural and educational barriers. This paper sought to discover if the pictures mirrored the feedback given on a typical feedback form. Findings indicate a considerable difference in the two approaches and thus we highlight the value of collaborative drawing as a complimentary resource to aid the understanding of student experience.

Keywords: Feedback forms, visualisation, student experience, collaborative drawing.

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1387 Changes in Vocational Teacher Training in Hungary: Challenges and Possibilities

Authors: A. Bacsa-Bán

Abstract:

The training of vocational education teachers in Hungary was a special training system before the Bologna system, but under the influence of the Bologna system, the structure and content of the training changed significantly. The training of vocational teachers, including engineering teacher and vocational trainers, is considerably different when compared to the training of public education teachers. This study aims to present these differences and peculiarities, problems, and issues of the training as well as to outline the possibilities of further development. During the study the following methods were implemented: empirical research among students and graduates of vocational teacher training, as well as analysis of the relevant literature. The study summarizes the research and theoretical results related to Vocational Education and Training (VET) teacher training over the past 15 years, with the aim of developing the training and mapping new directions in the field.

Keywords: Bologna system, vocational educators, vocational teachers, vocational teacher training.

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1386 Strategic Management of a Geoscience Education and Training Program

Authors: Lee Ock-Sun

Abstract:

The effective development of a geoscience education and training program takes account of the rapidly changing environment in the geoscience market, includes information about resource-rich countries which have international education demands. In this paper, we introduce the geoscience program run by the International School for Geoscience Resources at the Korea Institute of Geoscience and Mineral Resources (IS-Geo of KIGAM), and show its remarkable performance. To further effective geoscience program planning and operation, we present recommendations for strategic management for customer-oriented operation with a more favorable program format and advanced training aids. Above all, the IS-Geo of KIGAM should continue improve through ‘plan-do-see-feedback’ activities based on the recommendations.

Keywords: Demand survey, geoscience program, program performance, strategic management.

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1385 Constructing a Suitable Model of Distance Training for Community Leader in the Upper Northeastern Region

Authors: Teerawach Khamkorn, Laongtip Mathurasa, Savittree Rochanasmita Arnold, Witthaya Mekhum

Abstract:

The objective of this research intends to create a suitable model of distance training for community leaders in the upper northeastern region of Thailand. The implementation of the research process is divided into four steps: The first step is to analyze relevant documents. The second step deals with an interview in depth with experts. The third step is concerned with constructing a model. And the fourth step takes aim at model validation by expert assessments. The findings reveal the two important components for constructing an appropriate model of distance training for community leaders in the upper northeastern region. The first component consists of the context of technology management, e.g., principle, policy and goals. The second component can be viewed in two ways. Firstly, there are elements comprising input, process, output and feedback. Secondly, the sub-components include steps and process in training. The result of expert assessments informs that the researcher-s constructed model is consistent and suitable and overall the most appropriate.

Keywords: Constructing, Distance Training, Management, Technology.

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1384 Text Retrieval Relevance Feedback Techniques for Bag of Words Model in CBIR

Authors: Nhu Van NGUYEN, Jean-Marc OGIER, Salvatore TABBONE, Alain BOUCHER

Abstract:

The state-of-the-art Bag of Words model in Content- Based Image Retrieval has been used for years but the relevance feedback strategies for this model are not fully investigated. Inspired from text retrieval, the Bag of Words model has the ability to use the wealth of knowledge and practices available in text retrieval. We study and experiment the relevance feedback model in text retrieval for adapting it to image retrieval. The experiments show that the techniques from text retrieval give good results for image retrieval and that further improvements is possible.

Keywords: Relevance feedback, bag of words model, probabilistic model, vector space model, image retrieval

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1383 A Simplified Adaptive Decision Feedback Equalization Technique for π/4-DQPSK Signals

Authors: V. Prapulla, A. Mitra, R. Bhattacharjee, S. Nandi

Abstract:

We present a simplified equalization technique for a π/4 differential quadrature phase shift keying ( π/4 -DQPSK) modulated signal in a multipath fading environment. The proposed equalizer is realized as a fractionally spaced adaptive decision feedback equalizer (FS-ADFE), employing exponential step-size least mean square (LMS) algorithm as the adaptation technique. The main advantage of the scheme stems from the usage of exponential step-size LMS algorithm in the equalizer, which achieves similar convergence behavior as that of a recursive least squares (RLS) algorithm with significantly reduced computational complexity. To investigate the finite-precision performance of the proposed equalizer along with the π/4 -DQPSK modem, the entire system is evaluated on a 16-bit fixed point digital signal processor (DSP) environment. The proposed scheme is found to be attractive even for those cases where equalization is to be performed within a restricted number of training samples.

Keywords: Adaptive decision feedback equalizer, Fractionally spaced equalizer, π/4 DQPSK signal, Digital signal processor.

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1382 Does Training in the Use of a Magnifier Improve Efficiency?

Authors: Norliza Mohamad Fadzil, Kerry Fitzmaurice, Linda Malesic

Abstract:

Provision of optical devices without proper instruction and training may cause frustration resulting in rejection or incorrect use of the magnifiers. However training in the use of magnifiers increases the cost of providing these devices. This study compared the efficacy of providing instruction alone and instruction plus training in the use of magnifiers. 24 participants randomly assigned to two groups. 15 received instruction and training and 9 received instruction only. Repeated measures of print size and reading speed were performed at pre, post training and follow up. Print size decreased in both groups between pre and post training maintained at follow up. Reading speed increased in both groups over time with the training group demonstrating more rapid improvement. Whilst overall outcomes were similar, training decreased the time required to increase reading speed supporting the use of training for increased efficiency. A cost effective form of training is suggested.

Keywords: Low vision, magnification, training, reading.

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1381 Almost Periodic Sequence Solutions of a Discrete Cooperation System with Feedback Controls

Authors: Ziping Li, Yongkun Li

Abstract:

In this paper, we consider the almost periodic solutions of a discrete cooperation system with feedback controls. Assuming that the coefficients in the system are almost periodic sequences, we obtain the existence and uniqueness of the almost periodic solution which is uniformly asymptotically stable.

Keywords: Discrete cooperation model, almost periodic solution, feedback control, Lyapunov function.

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1380 Exploring the Need to Study the Efficacy of VR Training Compared to Traditional Cybersecurity Training

Authors: Shaila Rana, Wasim Alhamdani

Abstract:

Effective cybersecurity training is of the utmost importance, given the plethora of attacks that continue to increase in complexity and ubiquity. VR cybersecurity training remains a starkly understudied discipline. Studies that evaluated the effectiveness of VR cybersecurity training over traditional methods are required. An engaging and interactive platform can support knowledge retention of the training material. Consequently, an effective form of cybersecurity training is required to support a culture of cybersecurity awareness. Measurements of effectiveness varied throughout the studies, with surveys and observations being the two most utilized forms of evaluating effectiveness. Further research is needed to evaluate the effectiveness of VR cybersecurity training and traditional training. Additionally, research for evaluating if VR cybersecurity training is more effective than traditional methods is vital. This paper proposes a methodology to compare the two cybersecurity training methods and their effectiveness. The proposed framework includes developing both VR and traditional cybersecurity training methods and delivering them to at least 100 users. A quiz along with a survey will be administered and statistically analyzed to determine if there is a difference in knowledge retention and user satisfaction. The aim of this paper is to bring attention to the need to study VR cybersecurity training and its effectiveness compared to traditional training methods. This paper hopes to contribute to the cybersecurity training field by providing an effective way to train users for security awareness. If VR training is deemed more effective, this could create a new direction for cybersecurity training practices.

Keywords: Virtual reality cybersecurity training, VR cybersecurity training, traditional cybersecurity training, evaluating efficacy.

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1379 Design a Three-dimensional Pursuit Guidance Law with Feedback Linearization Method

Authors: Chien-Chun Kung, Feng-Lung Chiang, Kuei-Yi Chen

Abstract:

In this paper, we will implement three-dimensional pursuit guidance law with feedback linearization control method and study the effects of parameters. First, we introduce guidance laws and equations of motion of a missile. Pursuit guidance law is our highlight. We apply feedback linearization control method to obtain the accelerations to implement pursuit guidance law. The solution makes warhead direction follow with line-of-sight. Final, the simulation results show that the exact solution derived in this paper is correct and some factors e.g. control gain, time delay, are important to implement pursuit guidance law.

Keywords: Pursuit guidance law, feedback linearization.

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1378 Remote Training with Self-Assessment in Electrical Engineering

Authors: Zoja Raud, Valery Vodovozov

Abstract:

The paper focuses on the distance laboratory organisation for training the electrical engineering staff and students in the fields of electrical drive and power electronics. To support online knowledge acquisition and professional enhancement, new challenges in remote education based on an active learning approach with self-assessment have been emerged by the authors. Following the literature review and explanation of the improved assessment methodology, the concept and technological basis of the labs arrangement are presented. To decrease the gap between the distance study of the up-to-date equipment and other educational activities in electrical engineering, the improvements in the following-up the learners’ progress and feedback composition are introduced. An authoring methodology that helps to personalise knowledge acquisition and enlarge Web-based possibilities is described. Educational management based on self-assessment is discussed.

Keywords: Advanced training, active learning, distance learning, electrical engineering, remote laboratory, self-assessment.

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1377 The Effect of Response Feedback on Performance of Active Controlled Nonlinear Frames

Authors: M. Mohebbi, K. Shakeri

Abstract:

The effect of different combinations of response feedback on the performance of active control system on nonlinear frames has been studied in this paper. To this end different feedback combinations including displacement, velocity, acceleration and full response feedback have been utilized in controlling the response of an eight story bilinear hysteretic frame which has been subjected to a white noise excitation and controlled by eight actuators which could fully control the frame. For active control of nonlinear frame Newmark nonlinear instantaneous optimal control algorithm has been used which a diagonal matrix has been selected for weighting matrices in performance index. For optimal design of active control system while the objective has been to reduce the maximum drift to below the yielding level, Distributed Genetic Algorithm (DGA) has been used to determine the proper set of weighting matrices. The criteria to assess the effect of each combination of response feedback have been the minimum required control force to reduce the maximum drift to below the yielding drift. The results of numerical simulation show that the performance of active control system is dependent on the type of response feedback where the velocity feedback is more effective in designing optimal control system in comparison with displacement and acceleration feedback. Also using full feedback of response in controller design leads to minimum control force amongst other combinations. Also the distributed genetic algorithm shows acceptable convergence speed in solving the optimization problem of designing active control systems.

Keywords: Active control, Distributed genetic algorithms, Response feedback, Weighting matrices.

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