Search results for: Lyapunov-based control design

Authors: Chaw Su Mon

Abstract:

Abstract— The paper presents a preliminary study on modeling and estimation of basic wind speed ( extreme wind gusts ) for the consideration of vulnerability and design of building in Ayeyarwady Region. The establishment of appropriate design wind speeds is a critical step towards the calculation of design wind loads for structures. In this paper the extreme value analysis of this prediction work is based on the anemometer data (1970-2009) maintained by the department of meteorology and hydrology of Pathein. Statistical and probabilistic approaches are used to derive formulas for estimating 3-second gusts from recorded data (10-minute sustained mean wind speeds).

Keywords: Basic Wind Speed, Building, Gusts, Statistical and probabilistic approaches

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Authors: Ganesh Kothapalli, Mohammed Y. Hassan

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The hydraulic actuated excavator, being a non-linear mobile machine, encounters many uncertainties. There are uncertainties in the hydraulic system in addition to the uncertain nature of the load. The simulation results obtained in this study show that there is a need for intelligent control of such machines and in particular interval type-2 fuzzy controller is most suitable for minimizing the position error of a typical excavator-s bucket under load variations. We consider the model parameter uncertainties such as hydraulic fluid leakage and friction. These are uncertainties which also depend up on the temperature and alter bulk modulus and viscosity of the hydraulic fluid. Such uncertainties together with the load variations cause chattering of the bucket position. The interval type-2 fuzzy controller effectively eliminates the chattering and manages to control the end-effecter (bucket) position with positional error in the order of few millimeters.

Keywords: excavator, fuzzy control, hydraulics, mining, type-2

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Authors: M. S. Thakur, Mohit Shukla

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A channel/tunnel, which carries the water to the penstock/pressure shaft is called headrace tunnel (HRT). It is necessary to know the general topography, geology of the area, state of stress and other mechanical properties of the strata. For this certain topographical and geological investigations, in-situ and laboratory tests, and observations are required to be done. These investigations play an important role in a tunnel design as these help in deciding the optimum layout, shape and size and support requirements of the tunnel. The paper includes inputs from Nathpa Jhakri Hydeoelectric project which is India’s highest capacity (1500 MW) operating hydroelectric project. The paper would help the design engineers with various new concepts and preparedness against geological surprises.

Keywords: Tunnelling, geology, head race tunnel, rockmass.

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Authors: Mustafa A. Al-Refai

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This paper presents the optimal design and simulation of a grid-connected Photovoltaic (PV) system to supply electric power to meet the energy demand by Electrical Department in University of Tripoli Libya. Solar radiation is the key factor determining electricity produced by photovoltaic (PV) systems. This paper is designed to develop a novel method to calculate the solar photovoltaic generation capacity on the basis of Mean Global Solar Radiation data available for Tripoli Libya and finally develop a system design of possible plant capacity for the available roof area. MatLab/Simulink Programming tools and monthly average solar radiation data are used for this design and simulation. The specifications of equipments are provided based on the availability of the components in the market. Simulation results and analyses are presented to validate the proposed system configuration.

Keywords: Photovoltaic (PV), solar energy, solar irradiation, Simulink.

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Authors: Myunghoun Jang

Abstract:

A survey of small-size contractors in Jeju was conducted to investigate college graduate's computer-aided design (CAD) competence. Most of small-size contractors use CAD software to review and update drawings submitted from an architect. This research analyzed the curriculum of the architectural engineering in several national universities. The CAD classes have 4 or 6 hours per week and use AutoCAD primarily. This paper proposes that a CAD class needs 6 hours per week, 2D drawing is the main theme in the curriculum, and exercises to make 3D models are also included in the CAD class. An improved method, for example Internet cafe and real time feedbacks using smartphones, to evaluate the reports and exercise results is necessary.

Keywords: Computer-aided design, CAD education, education improvement, small-size contractor.

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Authors: Nasehi, B., Mortazavi, S. A., Razavi, S.

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The influence of full-fat soy flour (FFSF) and extrusion conditions on the mechanical characteristics of dry spaghetti were evaluated. Process was performed with screw speed of 10-40rpm and water circulating temperature of 35-70°C. Data analysis using mixture design showed that this enrichment resulted in significant differences in mechanical strength.

Keywords: Pasta, Mixture design, Enrichment, Texture.

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Authors: Kaveh Qaderi Bagajan, Osman Khanahmadi, Ziba Mamaghani Chaharborj, Majid Chenaparchi

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The purpose of this study is to investigate the efficacy of the solution-focused brief therapy on improving the psychological wellbeing of family supervisor woman. This study has been carried out by semi-experimental method and in the form of pre-test, post-test performance on two groups (experimental and control), so that one sample group of 30 individuals was randomly achieved and were randomly divided in two groups of experimental (n=15) and control (n=15). To collect data, Ryff scale psychological wellbeing was used. After conducting pre-test (RSPWB) for two experimental and control groups, Solution-focused brief therapy interference was conducted on the experimental group during five two-hour sessions. Finally, Ryff scale psychological wellbeing was reused for the two groups as post-test and achieved outcomes that were analyzed using covariance. The results indicated that the significant increase of average marks of the experimental group in psychological wellbeing had better function than that of the control group. Finally, solution-focused brief therapy for improving psychological well-being of family supervisor women has a suitable capability and could be used in this way.

Keywords: Solution-Focused Brief Therapy, Short-term Therapy, Family Supervisor Women, Psychological Wellbeing.

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Authors: Fátima Gonçalves, Joaquim Brigas, Jorge Gonçalves

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As a way of managing the increasing volume and complexity of information that circulates in the present time, graphical representations are increasingly used, which add meaning to the information presented in communication media, through an efficient communication design. The visual culture itself, driven by technological evolution, has been redefining the forms of communication, so that contemporary visual communication represents a major impact on society. This article presents the results and respective comparative analysis of four publications in the Iberian press, focusing on the formal aspects of newspapers and the space they dedicate to the various communication elements. Two Portuguese newspapers and two Spanish newspapers were selected for this purpose. The findings indicated that the newspapers show a similarity in the use of graphic solutions, which corroborate a visual trend in communication design. The results also reveal that Spanish newspapers are more meticulous with graphic consistency. This study intended to contribute to improving knowledge of the Iberian generalist press.

Keywords: Communication design, graphic resources, Iberian Press, visual journalism.

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Authors: Kalyanasundaram.D., Kavitha. S

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Field experiments were conducted at Annamalai University Experimental Farm, Department of Agronomy; to device suitable weed control measures for direct seeded puddled rice and to study the effect of the weed control measures on the soil microbial population. The treatments comprised of incorporation of pressmud @ 6.25 t ha-1 and application of herbicide butachlor @1.5 kg a. i. ha- 1 with and without safener 4 days after sowing (DAS), 8 DAS alone and also in conjunction with hand weeding at 30 DAS. Hand weeding twice and a weedy check were also maintained. At maximum tillering stage, the population of bacteria was significantly reduced by butachlor application. The injury to microbes caused by herbicide disappeared with the advancement of crop's age and at flowering stage of crop, there was no significant difference among the treatments. The fungal and actinomycetes population remained unaltered by weed control treatments at both the stages of observation.

Keywords: Butachlor, Herbicide, Direct sown rice, Microbial population

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Authors: Ahmad Gholami , Saeed Sharafi, Hamid Abbasdokht

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The effect of magnetic field on germination characteristics of two wheat Seeds has been studied under laboratory conditions. Seeds were magnetically exposed to magnetic field strengths, 125 or 250mT for different periods of time. Mean germination time and the time required to obtain 10, 25, 50, 75 and 90%of seeds to germinate were calculated. The germination time for each treatment were in general, higher than corresponding control values, in the other word in treated seeds time required for mean seed germination time increased nearly 3 hours in compared non treated control seeds. T10 for doses D5, D6, D11 and D12 significantly higher than the control values for both cultivars. Mean germination time (MGT) in both cultivars significantly increased when the time of seed exposed at magnetic field treatments increased , about 3 and 2 hour respectively for Omid and BCR cultivars.

Keywords: wheat, cultivar, germination test, magnetic field

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Authors: Kiwon Rhee, Kyung-Jin You, Hyun-Chool Shin

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This paper proposes a method of remotely controlling robots with arm gestures using surface electromyography (EMG) and accelerometer sensors attached to the operator’s wrists. The EMG and accelerometer sensors receive signals from the arm gestures of the operator and infer the corresponding movements to execute the command to control the robot. The movements of the robot include moving forward and backward and turning left and right. The accuracy is over 99% and movements can be controlled in real time.

Keywords: EMG, accelerometer, K-nn, entropy.

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Authors: Nopparat Pochai, Rujira Deepana

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Water pollution assessment problems arise frequently in environmental science. In this research, a finite difference method for solving the one-dimensional steady convection-diffusion equation with variable coefficients is proposed; it is then used to optimize water treatment costs.

Keywords: Finite difference, One-dimensional, Steady state, Waterpollution control, Optimization, Convection-diffusion equation.

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Authors: Jin Woo Hwang, Byung Kwan Oh, Yousok Kim, Hyo Seon Park

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As greenhouse effect has been recognized as serious environmental problem of the world, interests in carbon dioxide (CO₂) emission which comprises major part of greenhouse gas (GHG) emissions have been increased recently. Since construction industry takes a relatively large portion of total CO₂ emissions of the world, extensive studies about reducing CO₂ emissions in construction and operation of building have been carried out after the 2000s. Also, performance based design (PBD) methodology based on nonlinear analysis has been robustly developed after Northridge Earthquake in 1994 to assure and assess seismic performance of building more exactly because structural engineers recognized that prescriptive code based design approach cannot address inelastic earthquake responses directly and assure performance of building exactly. Although CO₂ emissions and PBD approach are recent rising issues on construction industry and structural engineering, there were few or no researches considering these two issues simultaneously. Thus, the objective of this study is to minimize the CO₂ emissions and cost of building designed by PBD approach in structural design stage considering structural materials. 4 story and 4 span reinforced concrete building optimally designed to minimize CO₂ emissions and cost of building and to satisfy specific seismic performance (collapse prevention in maximum considered earthquake) of building satisfying prescriptive code regulations using non-dominated sorting genetic algorithm-II (NSGA-II). Optimized design result showed that minimized CO₂ emissions and cost of building were acquired satisfying specific seismic performance. Therefore, the methodology proposed in this paper can be used to reduce both CO₂ emissions and cost of building designed by PBD approach.

Keywords: CO2 emissions, performance based design, optimization, sustainable design.

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Authors: M. R. Rouhi, S. Shafiei, A. Taghavipour, H. Adibi-Asl, A. Doosthoseini

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This research targets at alleviating the problem of range anxiety associated with the battery electric vehicles (BEVs) by considering mechanical and control aspects of the powertrain. In this way, all the energy consuming components and their effect on reducing the range of the BEV and battery life index are identified. On the other hand, an appropriate control strategy is designed to guarantee the performance of the BEV and the extended electric range which is evaluated by an extensive simulation procedure and a real-world driving schedule.

Keywords: Battery, electric vehicles EV, ultra-capacitor.

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Authors: Ehsan Vaziri Goodarzi, Mahmood Houshmand, Omid Fatahi Valilai, Vahidreza Ghezavati, Shahrooz Bamdad

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One important paradigm of industry 4.0 is Cloud Manufacturing (CM). In CM everything is considered as a service, therefore, the CM platform should consider all service provider's capabilities and tries to integrate services in an equilibrium state. This research develops a framework for implementing manufacturing cloud service composition in the equilibrium state. The developed framework using well-known tools called axiomatic design (AD) and game theory. The research has investigated the factors for forming equilibrium for measures of the manufacturing cloud service composition. Functional requirements (FRs) represent the measures of manufacturing cloud service composition in the equilibrium state. These FRs satisfied by related Design Parameters (DPs). The FRs and DPs are defined by considering the game theory, QoS, consumer needs, parallel and cooperative services. Ultimately, four FRs and DPs represent the framework. To insure the validity of the framework, the authors have used the first AD’s independent axiom.

Keywords: Axiomatic design, manufacturing cloud service composition, cloud manufacturing, Industry 4.0.

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Authors: K. Petcharat, Y. Areepong, S. Sukparungsri, G. Mititelu

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These paper, we approximate the average run length (ARL) for CUSUM chart when observation are an exponential first order moving average sequence (EMA1). We used Gauss-Legendre numerical scheme for integral equations (IE) method for approximate ARL0 and ARL1, where ARL in control and out of control, respectively. We compared the results from IE method and exact solution such that the two methods perform good agreement.

Keywords: Cumulative Sum Chart, Moving Average Observation, Average Run Length, Numerical Approximations.

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Authors: Seungwon Choi, Seungri Jin, Ayoung Heo, Jung-Hyun Park, Dong-Jo Park

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This paper deals with wireless relay communication systems in which multiple sources transmit information to the destination node by the help of multiple relays. We consider a signal forwarding technique based on the minimum mean-square error (MMSE) approach with multiple antennas for each relay. A source-relay-destination joint design strategy is proposed with power constraints at the destination and the source nodes. Simulation results confirm that the proposed joint design method improves the average MSE performance compared with that of conventional MMSE relaying schemes.

Keywords: minimum mean squre error (MMSE), multiple relay, MIMO.

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Authors: Preeti Yadav, Dandeswar Bisoyi, Debkumar Chakrabarti

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Mascots provide memories to viewers, and numerous promotional campaigns with different appearances, continue to trigger viewers and capture their interest. This study investigates the effect of Indian food mascot designs and influence on enhancing communication; thereby, building long-term brand recognition by the consumers. This paper presents a descriptive approach to Indian food mascot design as an advertising tool, and its research adopts a quantitative methodology. The study confirms that mascots have an ability to communicate a message in an effective manner; all though they are simple in terms of design and fashion trend, they have the capability to build positive reactions.

Keywords: Food mascot, brand recognitions, advertising, humour.

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Authors: Suzanne Yaganeh, Janni Nielsen, Leif Bloch Rasmussen

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This paper invites to dialogue and reflections on innovation and entrepreneurship by presenting concepts of innovation leading to the introduction of a complex theoretical framework; Cooperative Innovation (CO-IN). CO-IN is a didactic model enhancing and scaffolding processes of cooperation creating innovation drawing on a Scandinavian tradition. CO-IN is based on a cross-sectorial and multidisciplinary approach. We introduce the concept of complementarity to help capture the validity of diversity and we suggest the concept of “the space in between" to understand the creation of identity as a collective mind. We see dialogue and the use of multi modal techniques as essential tools for conceptualizations giving possibility for clarification of the complexity and diversity leading to decision making based on knowledge as commons. We introduce the didactic design and present our empirical findings from an innovation workshop in Argentina. In a final paragraph we reflect on the design as a support of the development of common ground, collective mind and collective action and the creation of knowledge as commons to facilitate innovation and entrepreneurship.

Keywords: CO-operative Innovation, didactic design, dialogue and ICT.

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Authors: Sidhartha Panda, N. P. Padhy

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Power system stabilizers (PSS) are now routinely used in the industry to damp out power system oscillations. In this paper, particle swarm optimization (PSO) technique is applied to design a robust power system stabilizer (PSS). The design problem of the proposed controller is formulated as an optimization problem and PSO is employed to search for optimal controller parameters. By minimizing the time-domain based objective function, in which the deviation in the oscillatory rotor speed of the generator is involved; stability performance of the system is improved. The non-linear simulation results are presented under wide range of operating conditions; disturbances at different locations as well as for various fault clearing sequences to show the effectiveness and robustness of the proposed controller and their ability to provide efficient damping of low frequency oscillations. Further, all the simulations results are compared with a conventionally designed power system stabilizer to show the superiority of the proposed design approach.

Keywords: Particle swarm optimization, power system stabilizer, low frequency oscillations, power system stability.

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Authors: Yuki Kondo, Takanori Nagano, Yuki Takeda, Young-Bok Choi, Hiromi Okada

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Optical burst switching(OBS) is considered as one of preferable network technologies for the next generation Internet. The Internet has two traffic classes, i.e. real-time bursts and reliable bursts. It is an important subject for OBS to achieve cooperated operation of real-time bursts and reliable bursts. In this paper, we proposes a new effective traffic control method named Separate TB+LB (Token Bucket + Leaky Bucket : TB+LB) method. The proposed method presents a new Token Bucket scheme for real-time bursts called as RBO-TB (Real-time Bursts Oriented Token Bucket). The method also applies the LB method to reliable bursts for obtaining better performance. This paper verifies the effectiveness of the Separate TB+LB method through the performance evaluation.

Keywords: leaky bucket, OBS, traffic control, token bucket.

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Authors: M. Azizur Rahman, Tamotsu Oomori

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Calcite aCalcite and aragonite are the two common polymorphs of CaCO3 observed as biominerals. It is universal that the sea water contents a high Mg2+ (50mM) relative to Ca2+ (10mM). In vivo crystallization, Mg2+ inhibits calcite formation. For this reason, stony corals skeleton may be formed only aragonite crystals in the biocalcification. It is special in case of soft corals of which formed only calcite crystal; however, this interesting phenomenon, still uncharacterized in the marine environment, has been explored in this study using newly purified cell-free proteins isolated from the endoskeletal sclerites of soft coral. By recording the decline of pH in vitro, the control of CaCO3 nucleation and crystal growth by the cellfree proteins was revealed. Using Atomic Force Microscope, here we find that these endoskeletal cell-free proteins significantly design the morphological shape in the molecular-scale kinetics of crystal formation and those proteins act as surfactants to promote ion attachment at calcite steps.nd aragonite are the two common polymorphs of CaCO3 observed as biominerals. It is universal that the sea water contents a high Mg2+ (50mM) relative to Ca2+ (10mM). In vivo crystallization, Mg2+ inhibits calcite formation. For this reason, stony corals skeleton may be formed only aragonite crystals in the biocalcification. It is special in case of soft corals of which formed only calcite crystal; however, this interesting phenomenon, still uncharacterized in the marine environment, has been explored in this study using newly purified cell-free proteins isolated from the endoskeletal sclerites of soft coral. By recording the decline of pH in vitro, the control of CaCO3 nucleation and crystal growth by the cell-free proteins was revealed. Using Atomic Force Microscope, here we find that these endoskeletal cell-free proteins significantly design the morphological shape in the molecular-scale kinetics of crystal formation and those proteins act as surfactants to promote ion attachment at calcite steps. KeywordsBiomineralization, Calcite, Cell-free protein, Soft coral

Keywords: Biomineralization, Calcite, Cell-free protein, Soft coral

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Authors: R. Pudasaini, R. B. Thapa, P. R. Poudel

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An experiment was conducted to determine the effect of pollination on seed quality of rapeseed in Chitwan, Nepal during 2012-2013. The experiment was designed in Randomized Complete Block with four replications and five treatments. The rapeseed plots were caged with mosquito nets at 10% flowering except natural pollination. Two-framed colonies of Apis mellifera L. and Apis cerana F. were introduced separately for pollination, and control plot caged without pollinators. The highest germination percent was observed on Apis cerana F. pollinated plot seeds (90.50% germination) followed by Apis mellifera L. pollinated plots (87.25 %) and lowest on control plots (42.00% germination) seeds. Similarly, seed test weight of Apis cerana F. pollinated plots (3.22 gm/ 1000 seed) and Apis mellifera L. pollinated plots (2.93 gm/1000 seed) were and lowest on control plots (2.26 gm/ 1000 seed) recorded. Likewise, oil content was recorded highest on pollinated by Apis cerana F. (36.1%) followed by pollinated by Apis mellifera L. (35.4%) and lowest on control plots (32.8%). This study clearly indicated pollination increases the seed quality of rapeseed and therefore, management of honeybee is necessary for producing higher quality of rapeseed under Chitwan condition.

Keywords: Apis cerana, Apis mellifera, rapeseed pollination, seed quality.

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Authors: P. Parvizi, F. Norouzifard, S.Mohammadi

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The need to implement intelligent highways is much more emphasized with the growth of vehicle production line as well as vehicle intelligence. The control of intelligent vehicles in order to reduce human error and boost ease congestion is not accomplished solely by the aid of human resources. The present article is an attempt to introduce an intelligent control system based on a single central computer. In this project, central computer, without utilizing Global Positioning System (GPS), is capable of tracking all vehicles, crisis management and control, traffic guidance and recording traffic crimes along the highway. By the help of RFID technology, vehicles are connected to computerized systems, intelligent light poles and other available hardware along the way. By the aid of Wimax communicative technology, all components of the system are virtually connected together through local and global networks devised in them and the energy of the network is provided by the solar cells installed on the intelligent light poles.

Keywords: intelligent highway, intelligent light pole, highway automation

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Authors: Hachmia Faqihi, Maarouf Saad, Khalid Benjelloun, Mohammed Benbrahim, M. Nabil Kabbaj

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This paper investigates and presents a cable-driven robot to lower limb rehabilitation use in sagittal plane. The presented rehabilitation robot is used for a trajectory tracking in joint space. The paper covers kinematic and dynamic analysis, which reveals the tensionability of the used cables as being the actuating source to provide a rehabilitation exercises of the human leg. The desired trajectory is generated to be used in the control system design in joint space. The obtained simulation results is showed to be efficient in this kind of application.

Keywords: Cable-driven multibody system, computed-torque controller, lower limb rehabilitation, tracking trajectory.

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Authors: Anh Duc Dang, Joachim Horn

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This paper presents a new approach to control robots, which can quickly find their swarm while tracking a moving target through the obstacles of the environment. In this approach, an artificial potential field is generated between each free-robot and the virtual attractive point of the swarm. This artificial potential field will lead free-robots to their swarm. The swarm-finding of these free-robots dose not influence the general motion of their swarm and nor other robots. When one singular robot approaches the swarm then its swarm-search will finish, and it will further participate with its swarm to reach the position of the target. The connections between member-robots with their neighbors are controlled by the artificial attractive/repulsive force field between them to avoid collisions and keep the constant distances between them in ordered formation. The effectiveness of the proposed approach has been verified in simulations.

Keywords: Formation control, potential field method, obstacle avoidance, swarm intelligence, multi-agent systems.

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Authors: Mehrdad Mahmudizad, Roya Ahmadi Ahangar

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This paper presents the method of designing the type 2 fuzzy PID controllers in order to solve the problem of Load Frequency Control (LFC). The Harmony Search (HS) algorithm is used to regulate the measurement factors and the effect of uncertainty of membership functions of Interval Type 2 Fuzzy Proportional Integral Differential (IT2FPID) controllers in order to reduce the frequency deviation resulted from the load oscillations. The simulation results implicitly show that the performance of the proposed IT2FPID LFC in terms of error, settling time and resistance against different load oscillations is more appropriate and preferred than PID and Type 1 Fuzzy Proportional Integral Differential (T1FPID) controllers.

Keywords: Load Frequency Control, Fuzzy-PID controller, Type 2 fuzzy system, Harmony Search algorithm.

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Authors: Feddaoui Amina

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In a broad sense, corporate governance covers the organization of the control and management. The term is also used in a narrower sense, to refer to the relationship between shareholders, and the company’s board. There are a lot of discussions devoted to the understanding of the corporate governance role and its principles. In this paper, we are going to describe the definition of corporate governance as a control system and its principles, and find the role of corporate governance and its pillars. Finally, we are going to drop the theoretical study on the case of Japan.

Keywords: Corporate governance, place, role, Japan.

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Authors: Nawaporn Srisarankullawong

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The study on the design of decorative flower patterns from Suansunandha Palace is a innovative design using flowers grown in Suansunandha Palace as the original sources. The research tools included: 1) The photographs of flowers in water colors painted by one of the ladies in waiting of Her Royal Highness Princess Saisawareepirom as the source for investigating flowers grown in Suansunandha Palace 2) Pictures of real flowers grown in Suansunandha Palace 3) Adobe Illustrator Program and Adobe Photoshop Program in designing motifs and decorative patterns including prototypes. The researcher chose 3 types of Suansunandha Palace’s flowers; moss roses, orchids, and lignum vitae. The details of the flowers were simplified to create motifs for more elaborative decorative patterns. There were 4 motifs adapted from moss roses, 3 motifs adapted from orchids, and 3 motifs adapted from lignum vitae. The patterns were used to decorate photo frames, wrapping paper, and gift boxes or souvenir boxes.

Keywords: Suansunandha Palace, decoration design, floral pattern.

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Authors: A. Rouili

Abstract:

Cantilever L-shaped walls are known to be relatively economical as retaining solution. The design starts by proportioning the wall dimensions for which the stability is checked for. A ratio between the lengths of the base and the stem, falling between 0.5 to 0.7 ensure in most case the stability requirements, however, the displacement pattern of the wall in terms of rotations and translations, and the lateral pressure profile, do not have the same figure for all wall’s proportioning, as it is usually assumed. In the present work the results of a numerical analysis are presented, different wall geometries were considered. The results show that the proportioning governs the equilibrium between the instantaneous rotation and the translation of the wall-toe, also, the lateral pressure estimation based on the average value between the at-rest and the active pressure, recommended by most design standards, is found to be not applicable for all walls.

Keywords: Cantilever wall, proportioning, numerical analysis.

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