Search results for: Exponential stability

Authors: Appanah Rao Appadu, Muhammad Zaid Dauhoo

Abstract:

In this paper, we have combined some spatial derivatives with the optimised time derivative proposed by Tam and Webb in order to approximate the linear advection equation which is given by = 0. Ôêé Ôêé + Ôêé Ôêé x f t u These spatial derivatives are as follows: a standard 7-point 6 th -order central difference scheme (ST7), a standard 9-point 8 th -order central difference scheme (ST9) and optimised schemes designed by Tam and Webb, Lockard et al., Zingg et al., Zhuang and Chen, Bogey and Bailly. Thus, these seven different spatial derivatives have been coupled with the optimised time derivative to obtain seven different finite-difference schemes to approximate the linear advection equation. We have analysed the variation of the modified wavenumber and group velocity, both with respect to the exact wavenumber for each spatial derivative. The problems considered are the 1-D propagation of a Boxcar function, propagation of an initial disturbance consisting of a sine and Gaussian function and the propagation of a Gaussian profile. It is known that the choice of the cfl number affects the quality of results in terms of dissipation and dispersion characteristics. Based on the numerical experiments solved and numerical methods used to approximate the linear advection equation, it is observed in this work, that the quality of results is dependent on the choice of the cfl number, even for optimised numerical methods. The errors from the numerical results have been quantified into dispersion and dissipation using a technique devised by Takacs. Also, the quantity, Exponential Error for Low Dispersion and Low Dissipation, eeldld has been computed from the numerical results. Moreover, based on this work, it has been found that when the quantity, eeldld can be used as a measure of the total error. In particular, the total error is a minimum when the eeldld is a minimum.

Keywords: Optimised time derivative, dissipation, dispersion, cfl number, Nomenclature: k : time step, h : spatial step, β :advection velocity, r: cfl/Courant number, hkrβ= , w =θ, h : exact wave number, n :time level, RPE : Relative phase error per unit time step, AFM :modulus of amplification factor

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Authors: Wenjuan Du

Abstract:

The phase compensation method was proposed based on the concept of the damping torque analysis (DTA). It is a method for the design of a PSS (power system stabilizer) to suppress local-mode power oscillations in a single-machine infinite-bus power system. This paper presents the application of the phase compensation method for the design of a PSS in a multi-machine power system. The application is achieved by examining the direct damping contribution of the stabilizer to the power oscillations. By using linearized equal area criterion, a theoretical proof to the application for the PSS design is presented. Hence PSS design in the paper is an example of stable tending control by localized method.

Keywords: Phase compensation method, power system small-signal stability, power system stabilizer.

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Authors: Pedro F. Albuquerque, Pedro V. Gamboa, Miguel A. Silvestre

Abstract:

The present work describes the implementation of the Enhanced Collaborative Optimization (ECO) multilevel architecture with a gradient-based optimization algorithm with the aim of performing a multidisciplinary design optimization of a generic unmanned aerial vehicle with morphing technologies. The concepts of weighting coefficient and dynamic compatibility parameter are presented for the ECO architecture. A routine that calculates the aircraft performance for the user defined mission profile and vehicle’s performance requirements has been implemented using low fidelity models for the aerodynamics, stability, propulsion, weight, balance and flight performance. A benchmarking case study for evaluating the advantage of using a variable span wing within the optimization methodology developed is presented.

Keywords: Multidisciplinary, Multilevel, Morphing, Enhanced Collaborative Optimization (ECO).

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Authors: P. H. Le, J. Molina, S. Hirai

Abstract:

In this work, we propose the application of Japanese “Origami” art for a floating function of a small aerial vehicle such as a hexarotor. A preliminary experiment was conducted using Origami magic balls mounted under a hexarotor. This magic ball can expand and shrink using an air pump during free flying. Using this interesting and functional concept, it promises to reduce the resistance of wind as well as reduce the energy consumption when the Origami balls are deflated. This approach can be particularly useful in rescue emergency situations. Furthermore, there are many unexpected reasons that may cause the multi-rotor has to land on the surface of water due to problems with the communication between the aircraft and the ground station. In addition, a complementary experiment was designed to prove that the hexarotor can fly maintaining the stability and also, takes off and lands on the surface of water using air balloons.

Keywords: Helicopter, Japanese Origami ball, Floating, Aerial Robots, Rescue.

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Authors: Kamyar Kabirifar, Majid Azarniush, Behbood Maashkar

Abstract:

A proper house is a suitable residential area which provides comfort, proper accessibility, security, stability and permanence of structure, enough lighting, proper initial infrastructures and ventilation for its inhabitants and the most important of all, it should be proportional to the family’s financial power .

Saving energy and making optimal usage of it and also taking advantage of stable energies are the bases of green buildings. Making green building will help the health of a person living in it and in its surrounding. It will support the people and provoke their satisfaction. Not only it will bring about the raise of level of the quality of life for building inhabitants, but it will cause the promotion of quality level of life of the people living in the surrounding area and in general the society. 

 

Keywords: Quality of Life, Green Building, environment pollution, Sick Building.

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Authors: Byung Hoon Seo, Hyun Gyu Kim, Tae Won Seo

Abstract:

Stair climbing is one of critical issues for field robots to widen applicable areas. This paper presents optimal design on kinematic parameters of a new robotic platform for stair climbing. The robotic platform climbs various stairs by body flip locomotion with caterpillar type main platform. Kinematic parameters such as platform length, platform height, and caterpillar rotation speed are optimized to maximize stair climbing stability. Three types of stairs are used to simulate typical user conditions. The optimal design process is conducted based on Taguchi methodology, and resulting parameters with optimized objective function are presented. In near future, a prototype is assembled for real environment testing.

Keywords: Stair climbing robot, Optimal design, Taguchi methodology, Caterpillar, Kinematic parameters.

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Authors: Liliana M. Ştefan, Ana M. Pană, Geza Bandur, Marcel Popa, Lucian M. Rusnac

Abstract:

Polymers are one of the most widely used materials in our every day life. The subject of renewable resources has attracted great attention in the last period of time. New polymeric materials derived from renewable resources, like carbohydrates draw attention to public eye especially because of their biocompatibility and biodegradability. The aim of our paper was to obtain environmentally compatible polymers from monosaccharides. Novel glycopolymers based on D-glucose have been obtained from copolymerization of a new monomer carrying carbohydrate moiety with methyl methacrylate (MMA) via free radical bulk polymerization. Differential scanning calorimetry (DSC) was performed in order to study the copolymerization process of the monomer into the chosen co-monomer; the activation energy of this process was evaluated using Ozawa method. The copolymers obtained were characterized using ATR-FTIR spectroscopy. The thermal stability of the obtained products was studied by thermogravimetry (TG).

Keywords: DSC, glycopolymer, monosaccarides, TG.

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Authors: Stella A. Arnaouti, Demos C. Angelides, Theodoros N. Chatzigogos, Witold M. Pytel

Abstract:

The Želazny Most tailing pond is one of the largest facilities worldwide for waste disposal from the copper mines located in South-West Poland. A potential failure of the dam would allow more than 10 million cubic meters of contaminated slurry to flow to the valley, causing immense environmental problems to the surrounding area. Thus, the determination of the strength properties of the dam's soils and their variability is of utmost importance. An extensive site investigation consisting of more than 480 cone penetration tests (CPTs) with or without pore water pressure measurements were conducted within a period of 13 years to study the mechanical properties of the tailings body. The present work investigates the point variability of the soil strength parameters (effective friction angle

Keywords: Soil strength variability, friction angle spatial variability, Želazny Most tailing dam.

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Authors: B. Chetti, W. A. Crosby

Abstract:

This paper presents a numerical analysis for the dynamic performance of a finite journal bearing lubricated with couple stress fluid taking into account the effect of the deformation of the bearing liner. The modified Reynolds equation has been solved by using finite difference technique. The dynamic characteristics in terms of stiffness coefficients, damping coefficients, critical mass and whirl ratio are evaluated for different values of eccentricity ratio and elastic coefficient for a journal bearing lubricated with a couple stress fluids and a Newtonian fluid. The results show that the dynamic characteristics of journal bearings lubricated with couple stress fluids are improved compared to journal bearings lubricated with Newtonian fluids.

Keywords: Circular bearing, elastohydrodynamic, stability, couple stress.

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Authors: Malinda G. Sirisena

Abstract:

The aim of this research is to evaluate the effectiveness of software quality assurance approaches of Sri Lankan offshore software development organizations, and to propose a framework which could be used across all offshore software development organizations.

An empirical study was conducted using derived framework from popular software quality evaluation models. The research instrument employed was a questionnaire survey among thirty seven Sri Lankan registered offshore software development organizations.

The findings demonstrate a positive view of Effectiveness of Software Quality Assurance – the stronger predictors of Stability, Installability, Correctness, Testability and Changeability. The present study’s recommendations indicate a need for much emphasis on software quality assurance for the Sri Lankan offshore software development organizations.

Keywords: Software Quality Assurance (SQA), Offshore Software Development, Quality Assurance Evaluation Models, Effectiveness of Quality Assurance.

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Authors: M. E. Ali Mohsin, Agus Arsad, Othman Y. Alothman

Abstract:

This study explains the influence of secondary filler on the dispersion of carbon nanotube (CNT) reinforced high density polyethylene (HDPE) nanocomposites (CNT/HDPE). In order to understand the mixed-fillers system, Montmorillonite (MMT) was added to CNT/HDPE nanocomposites. It was followed by investigating their effect on the thermal, mechanical and morphological properties of the aforesaid nanocomposite. Incorporation of 3 wt% each of MMT into CNT/HDPE nanocomposite resulted to the increased values for the tensile and flexural strength, as compared to the pure HDPE matrix. The thermal analysis result showed improved thermal stability of the formulated nanocomposites. Transmission electron microscopy (TEM) images revealed that larger aggregates of CNTs were disappeared upon addition of these two components leading to the enhancement of thermo-mechanical properties for such composites.

Keywords: Secondary filler, Montmorillonite, Carbon nanotube, nanocomposite.

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Authors: Ibrahim F. Jasim, Najah F. Jasim

Abstract:

The problem of controlling a two link robotic manipulator, consisting of a rotating and a prismatic links, is addressed. The actuations of both links are assumed to have unknown dead zone nonlinearities and friction torques modeled by LuGre friction model. Because of the existence of the unknown dead zone and friction torque at the actuations, unknown parameters and unmeasured states would appear to be part of the overall system dynamics that need for estimation. Unmeasured states observer, unknown parameters estimators, and robust adaptive control laws have been derived such that closed loop global stability is achieved. Simulation results have been performed to show the efficacy of the suggested approach.

Keywords: Adaptive Robust Control, Dead Zone, Friction Torques, Robotic Manipulators.

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Authors: Erisasadat Sahebzamani, Núria Forcada, Francisco Lendinez

Abstract:

Global climate change has become increasingly problematic over the past few decades. The construction industry has contributed to greenhouse gas emissions in recent decades. Considering these issues and the high demand for materials in the construction industry, Circular Economy (CE) is considered necessary to keep materials in the loop and extend their useful lives. By providing tangible benefits, Construction 4.0 facilitates the adoption of CE by reducing waste, updating standard work, sharing knowledge, and increasing transparency and stability. This study aims to present a framework for integrating CE and digital tools like Building Information Modeling (BIM) and Virtual Reality (VR) to examine the impact on the construction industry based on stakeholders' perspectives.

Keywords: Circular Economy, Building Information Modeling, Virtual Reality, stakeholder engagement.

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Authors: Zh.Mingaleva, K.Balkova

Abstract:

Innovations and innovative activity get the increasing value for successful financial and economic activity of the countries and regions. The level of innovative sphere development determines place of a country or a region in world economy and forms a basis of steady economic growth. This article is devoted to different aspects of organization of the national economic safety in the conditions of innovative development, its problems, risks and threats. Economy can be considered as aspiring for transition to innovative way only with finding of economic safety: financial independence, power stability and technological progress. There are statistical indicators, defining the level of economic security and factors, threatening economic safety of the state. The research is based on the analysis of factors and indicators in conditions of innovative development. The paper is illustrated by the examples of possible estimated system of the economic safety level.

Keywords: Economic safety, innovative activity, innovative development, innovative economy

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Authors: Ali Ghobadi, Seyed Mohammad Javadi, Behnam Rahimi

Abstract:

The present study is concerned with the effect of exciting boundary layer on cooling process in a gas-turbine blades. The cooling process is numerically investigated. Observations show cooling the first row of moving or stable blades leads to increase their life-time. Results show that minimum temperature in cooling line with exciting boundary layer is lower than without exciting. Using block in cooling line of turbines' blade causes flow pattern and stability in boundary layer changed that causes increase in heat transfer coefficient. Results show at the location of block, temperature of turbines' blade is significantly decreased. The k-ε turbulence model is used.

Keywords: Cooling, Exciting Boundary Layer, Heat Transfer, Turbine Blade.

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Authors: Ali Al-Zughaibi, Huw Davies

Abstract:

The purpose of this paper is to present a modeling and control of a quarter-car active suspension system with unknown mass, unknown time-delay and road disturbance. The objective of designing the controller is to derive a control law to achieve stability of the system and convergence that can considerably improve ride comfort and road disturbance handling. This is accomplished by using Routh-Hurwitz criterion based on defined parameters. Mathematical proof is given to show the ability of the designed controller to ensure the target of design, implementation with the active suspension system and enhancement dispersion oscillation of the system despite these problems. Simulations were also performed to control quarter car suspension, where the results obtained from these simulations verify the validity of the proposed design.

Keywords: Active suspension system, disturbance rejection, dynamic uncertainty, time-delay.

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Authors: Avinesh Prasad, Bibhya Sharma, Jito Vanualailai

Abstract:

In this paper, we propose a solution to the motion control problem of a 2-link revolute manipulator arm. We require the end-effector of the arm to move safely to its designated target in a priori known workspace cluttered with fixed circular obstacles of arbitrary position and sizes. Firstly a unique velocity algorithm is used to move the end-effector to its target. Secondly, for obstacle avoidance a turning angle is designed, which when incorporated into the control laws ensures that the entire robot arm avoids any number of fixed obstacles along its path enroute the target. The control laws proposed in this paper also ensure that the equilibrium point of the system is asymptotically stable. Computer simulations of the proposed technique are presented.

Keywords: 2-link revolute manipulator, motion control, obstacle avoidance, asymptotic stability.

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Authors: Sedrak Vardanyan

Abstract:

The investigation of the vibrational character of magnetic cylindrical shells placed in an axial magnetic field has important practical applications. In this work, we study the vibrational behaviour of such a cylindrical shell by making use of the so-called exact space treatment, which does not assume any hypothesis. We discuss the effects of several practically important boundary conditions on the vibrations of the described setup. We find that, for some cases of boundary conditions, e.g. clamped, simply supported or peripherally earthed, as well as for some values of the wave numbers, the vibrational frequencies of the shell are approximately zero. The theoretical and numerical exploration of this fact confirms that the vibrations are absent or attenuate very rapidly. For all the considered cases, the imaginary part of the frequencies is negative, which implies stability for the vibrational process.

Keywords: Free vibrations, magnetic cylindrical shells, exact space treatment, bending vibrational frequencies.

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Authors: M. Michalska-Domańska, P. Jóźwik, Z. Bojar

Abstract:

Intermetallic Ni3Al – based alloys belong to a group of advanced materials characterized by good chemical and physical properties (such as structural stability, corrosion resistance) which offer advenced technological applications. The paper presents the study of catalytic properties of Ni3Al foils (thickness approximately 50 &m) in the methanol and hexane decomposition. The egzamined material posses microcrystalline structure without any additional catalysts on the surface. The better catalytic activity of Ni3Al foils with respect to quartz plates in both methanol and hexane decomposition was confirmed. On thin Ni3Al foils the methanol conversion reaches approximately 100% above 480 oC while the hexane conversion reaches approximately 100% (98,5%) at 500 oC. Deposit formed during the methanol decomposition is built up of carbon nanofibers decorated with metal-like nanoparticles.

Keywords: hexane decomposition, methanol decomposition, Ni3Al thin foils, Ni nanoparticles

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Authors: C. W. Lin, S.W. Chen

Abstract:

This study describes the preparation of a novel proton conducting membranes based on bacterial cellulose (BC) modified by grafting of 2-acrylamido-2-methyl-1 -propanesulfonic acid (AMPS) through UV-induced graft polymerization. These AMPS-g-BC membranes have been characterized by various techniques including FTIR, SEM and TGA, to find their successful grafting of AMPS on BC, surface morphology and thermal stability, respectively. Physical properties of AMPS-g-BC membranes have been assessed in terms of Lamda value( λ ), ion exchange capacity(IEC) and proton conductivity. The relationship between degree of grafting and AMPS concentration used for grafting has been determined by weight gain method. An optimum proton conductivity equal to 2.89x10-2 S cm-1 and IEC value equal to 1.79 mmol g-1 have been obtained when 20 wt% AMPS concentration is used for grafting (i.e. the corresponding membrane is notated as AMPS20-g-BC).

Keywords: Bacterial cellulose, 2-acrylamido-2-methyl-1-propanesulfonic acid, Proton conducting membrane, Self diffusioncoefficient, Fuel cell

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Authors: Shazalina Mat Zin, Ahmad Abd. Majid, Ahmad Izani Md. Ismail, Muhammad Abbas

Abstract:

The generalized wave equation models various problems in sciences and engineering. In this paper, a new three-time level implicit approach based on cubic trigonometric B-spline for the approximate solution of wave equation is developed. The usual finite difference approach is used to discretize the time derivative while cubic trigonometric B-spline is applied as an interpolating function in the space dimension. Von Neumann stability analysis is used to analyze the proposed method. Two problems are discussed to exhibit the feasibility and capability of the method. The absolute errors and maximum error are computed to assess the performance of the proposed method. The results were found to be in good agreement with known solutions and with existing schemes in literature.

Keywords: Collocation method, Cubic trigonometric B-spline, Finite difference, Wave equation.

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Authors: T. C. Kuo, Y. J. Huang, B. W. Hong

Abstract:

This paper proposes an adaptive sliding mode controller which combines adaptive control and sliding mode control to control a nonlinear robotic manipulator with uncertain parameters. We use an adaptive algorithm based on the concept of sliding mode control to alleviate the chattering phenomenon of control input. Adaptive laws are developed to obtain the gain of switching input and the boundary layer parameters. The stability and convergence of the robotic manipulator control system are guaranteed by applying the Lyapunov theorem. Simulation results demonstrate that the chattering of control input can be alleviated effectively. The proposed controller scheme can assure robustness against a large class of uncertainties and achieve good trajectory tracking performance.

Keywords: Robotic manipulators, sliding mode control, adaptive law, Lyapunov theorem, robustness.

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Authors: H. Wakily, M. Mehrali, H. S. C. Metselaar

Abstract:

Homogeneous composites of alumina and zirconia with a small amount of MgO (<1 wt %) were prepared by colloidal filtration. The object of using ZrO2 (15wt %) was to provide zirconia toughened alumina (ZTA). Suspensions of alumina and Zirconia with various solid loadings and various concentrations of Dolapix CE64 as surfactant were studied. The stability of these suspensions was investigated using rheological measurements. The optimum amount of using Dolapix was 0.8wt% for ZTA containing MgO suspension which gave low apparent viscosity in basic area (100 mPa s at shear rate of 50 s-1). The satisfactory mixtures were made into sample pallets using colloidal filtration. The process was completed with pressureless sintering in suitable temperature. Phase, grain size and qualitative compositional analysis were done using X-ray diffraction (XRD) and scanning electron microscopy (SEM) images. ZTA containing 0.05 wt% MgO shows the lowest grain size for alumina around 0.5 μm. Densification studies show that near full densities (>99%) were obtained for ZTA ceramic containing 0.05 wt% MgO in 1500 °C.

Keywords: Colloidal filtration, Dolapix, MgO, Zirconiatoughened alumina.

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Authors: A. M. Sagir

Abstract:

In this paper, linear multistep technique using power series as the basis function is used to develop the block methods which are suitable for generating direct solution of the special second order ordinary differential equations with associated initial or boundary conditions. The continuous hybrid formulations enable us to differentiate and evaluate at some grids and off – grid points to obtain two different four discrete schemes, each of order (5,5,5,5)T, which were used in block form for parallel or sequential solutions of the problems. The computational burden and computer time wastage involved in the usual reduction of second order problem into system of first order equations are avoided by this approach. Furthermore, a stability analysis and efficiency of the block methods are tested on linear and non-linear ordinary differential equations and the results obtained compared favorably with the exact solution.

Keywords: Block Method, Hybrid, Linear Multistep Method, Self – starting, Special Second Order.

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Authors: G. Çelik Gül, F. Kurtuluş

Abstract:

Colemanite is the most common borate mineral, and the main source of the boron required by plants, human, and earth. Transition metals exhibit optical and physical properties such as; non-linear optical character, structural diversity, thermal stability, long cycle life and luminescent radiation. The doping of colemanite with a transition metal, bring it very interesting and attractive properties which make them applicable in industry. Iron doped calcium borate was synthesized by conventional solid state method at 1200 °C for 12 h with a systematic pathway. X-ray diffraction (XRD), Fourier transform infrared (FTIR) spectroscopy, scanning electron microscopy/energy dispersive analyze (SEM/EDS) were used to characterize structural and morphological properties. Also, thermal properties were recorded by thermogravimetric-differential thermal analysis (TG/DTA). 

Keywords: Colemanite, conventional synthesis, powder x-ray diffraction, borates.

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Authors: S. Yaman, S. Rostami

Abstract:

In this study, a black box modeling of the coupled-tank system is obtained by using fuzzy sets. The derived model is tested via adaptive neuro fuzzy inference system (ANFIS). In order to achieve a better control performance, the parameters of three different controller types, classical proportional integral controller (PID), fuzzy PID and function tuner method, are tuned by one of the evolutionary computation method, genetic algorithm. All tuned controllers are applied to the fuzzy model of the coupled-tank experimental setup and analyzed under the different reference input values. According to the results, it is seen that function tuner method demonstrates better robust control performance and guarantees the closed loop stability.

Keywords: Function tuner method, fuzzy modeling, fuzzy PID controller, genetic algorithm.

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Authors: M. V. A. Raju Bahubalendruni, Bibhuti Bhusan Biswal, B. B. V. L. Deepak

Abstract:

Achieving an appropriate assembly sequence needs deep verification for its physical feasibility. For this purpose, industrial engineers use several assembly predicates; namely, liaison, geometric feasibility, stability and mechanical feasibility. However, testing an assembly sequence for these predicates requires huge assembly information. Extracting such assembly information from an assembled product is a time consuming and highly skillful task with complex reasoning methods. In this paper, computer aided methods are proposed to extract all the necessary assembly information from computer aided design (CAD) environment in order to perform the assembly sequence planning efficiently. These methods use preliminary capabilities of three-dimensional solid modelling and assembly modelling methods used in CAD software considering equilibrium laws of physical bodies.

Keywords: Assembly automation, assembly attributes, assembly sequence generation, computer aided design.

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Authors: Israngkura Na Ayudhya B, Kunishima M.

Abstract:

This paper analysis performance of disbursement procedure of public works project in Thailand. The results of research were summarised based on contracts, submitted invoice, inspection dated, copies of disbursement dated between client and their main contractor and interviewed with persons involved in central and local government projects during 1994-2008 in Thailand. The data collection was to investigate the disbursement procedure related to performance in disbursement during construction period (Planned duration of contract against Actual execution date in each month). A graphical presentation of a duration analysis of the projects illustrated significant disbursement formation in each project. It was established that the shortage of staff, the financial stability of clients, bureaucratic, method of disbursement and economics situation has play major role on performance of disbursement to their main contractors.

Keywords: Construction disbursement, Payment procedure, Public works

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Authors: Sidshchadhaa Aumted, Shuhei Shiina, Hiroshi Takami

Abstract:

In this paper, we propose an advanced ILQ control for the buck-converter via two-degrees of freedom servo-system. Our presented strategy is based on Inverse Linear Quadratic (ILQ) servo-system controller without solving Riccati-s equation directly. The optimal controller of the current and voltage control system is designed. The stability and robust control are analyzed. A conscious and persistent effort has been made to improve ILQ control via two-degrees of freedom guarantees the optimal gains on the basis of polynomial pole assignment, which our results of the proposed strategy shows that the advanced ILQ control can be controlled independently the step response and the disturbance response by appending a feed-forward compensator.

Keywords: Optimal voltage control, inverse LQ design method, second order polynomial, two-degrees of freedom.

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Authors: M. Alauddin, M. M. Hossain, M. N. Uddin, M. E. Haque

Abstract:

An optimal design of a spur is the first requirement to make it sustainable and function properly. In view of that, a thorough understanding to the hydro- and morpho-dynamics due to spurs is essential. This paper presents a literature review on the effect of spurs to obtain the most recent design criteria. Perpendicular and upstream aligned impermeable spurs have large disturbances to flow and less stability because of strong vortices and associated scour. Downstream aligned spurs minimize scour holes, but there is a chance of strong return current which could be controlled allowing flow through them. A series arrangement of spurs is important to have the desired results with a special care for the first one. Several equations have been presented in the paper for predicting the scour depth. But, they have to be used carefully. Different flow environments developed by spurs are favorable for various aquatic species. However, it is important to maintain almost a stable flow condition providing stable spurs.

Keywords: Bed topography, flow pattern, scour, spur.

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