Search results for: MATLAB simulation

Authors: Kittaya Somsai, Thanatchai Kulworawanichpong, Nitus Voraphonpiput

Abstract:

This paper presents the DC voltage control design of D-STATCOM when the D-STATCOM is used for load voltage regulation. Although, the DC voltage can be controlled by active current of the D-STATCOM, reactive current still affects the DC voltage. To eliminate this effect, the control strategy with elimination effect of the reactive current is proposed and the results of the control with and without the elimination the effect of the reactive current are compared. For obtaining the proportional and integral gains of the PI controllers, the symmetrical optimum and genetic algorithms methods are applied. The stability margin of these methods are obtained and discussed in detail. In addition, the performance of the DC voltage control based on symmetrical optimum and genetic algorithms methods are compared. Effectiveness of the controllers designed was verified through computer simulation performed by using Power System Tool Block (PSB) in SIMULINK/MATLAB. The simulation results demonstrated that the DC voltage control proposed is effective in regulating DC voltage when the DSTATCOM is used for load voltage regulation.

Keywords: D-STATCOM, DC voltage control, Symmetrical optimum, Genetic algorithms

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Authors: Kyunghoon Kim, Sungjoon Shim, Jun Tae Kim, Jong Tae Kim

Abstract:

In a wireless communication system, a predistorter(PD) is often employed to alleviate nonlinear distortions due to operating a power amplifier near saturation, thereby improving the system performance and reducing the interference to adjacent channels. This paper presents a new adaptive polynomial digital predistorter(DPD). The proposed DPD uses Coordinate Rotation Digital Computing(CORDIC) processors and PD process by pipelined architecture. It is simpler and faster than conventional adaptive polynomial DPD. The performance of the proposed DPD is proved by MATLAB simulation.

Keywords: DPD, CORDIC.

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Authors: Eugene Kindler

Abstract:

The present paper is oriented to classification and application of agent technique in simulation of anticipatory systems, namely those that use simulation models for the aid of anticipation. The main ideas root in the fact that the best way for description of computer simulation models is the technique of describing the simulated system itself (and the translation into the computer code is provided as automatic), and that the anticipation itself is often nested.

Keywords: Agents, Anticipatory systems, Discrete eventsimulation, Simula, Taxonomy.

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Authors: Z. Nemec, R. Matousek

Abstract:

The paper describes the evaluation of quality of control for cases of controlled non-minimal phase plants. Control circuits containing non-minimal phase plants have different properties, they manifest reversed reaction at the beginning of unit step response. For these types of plants are developed special criterion of quality of control, which considers the difference and can be helpful for synthesis of optimal controller tuning. All results are clearly presented using Matlab/Simulink models.

Keywords: control design, non-minimal phase system, optimalcriteria, power plant, heating plant, water turbine, Matlab, Simulink.

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Authors: Jiali Fu

Abstract:

Earthmoving operations are a major part of many construction projects. Because of the complexity and fast-changing environment of such operations, the planning and estimating are crucial on both planning and operational levels. This paper presents the framework ofa microscopic discrete-event simulation system for modeling earthmoving operations and conducting productivity estimations on an operational level.A prototype has been developed to demonstrate the applicability of the proposed framework, and this simulation system is presented via a case study based on an actual earthmoving project. The case study shows that the proposed simulation model is capable of evaluating alternative operating strategies and resource utilization at a very detailed level.

Keywords: Earthmoving operation, microscopic simulation, discrete-event simulation

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Authors: Abed Sami Qawasme, Sameer Khader

Abstract:

This paper describes the effects of photovoltaic voltage changes on Multi-level inverter (MLI) due to solar irradiation variations, and methods to overcome these changes. The irradiation variation affects the generated voltage, which in turn varies the switching angles required to turn-on the inverter power switches in order to obtain minimum harmonic content in the output voltage profile. Genetic Algorithm (GA) is used to solve harmonics elimination equations of eleven level inverters with equal and non-equal dc sources. After that artificial neural network (ANN) algorithm is proposed to generate appropriate set of switching angles for MLI at any level of input dc sources voltage causing minimization of the total harmonic distortion (THD) to an acceptable limit. MATLAB/Simulink platform is used as a simulation tool and Fast Fourier Transform (FFT) analyses are carried out for output voltage profile to verify the reliability and accuracy of the applied technique for controlling the MLI harmonic distortion. According to the simulation results, the obtained THD for equal dc source is 9.38%, while for variable or unequal dc sources it varies between 10.26% and 12.93% as the input dc voltage varies between 4.47V nd 11.43V respectively. The proposed ANN algorithm provides satisfied simulation results that match with results obtained by alternative algorithms.

Keywords: Multi level inverter, genetic algorithm, artificial neural network, total harmonic distortion.

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Authors: Juan Portoviejo Brito, Daniel Icaza Alvarez, Christian Castro Samaniego

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In this article, we present the modeling, simulations, and energy conversion analysis of the solar-wind system for the Quingeo Heritage Center in Ecuador. A numerical model was constructed based on the 19 equations, it was coded in MATLAB R2017a, and the results were compared with the experimental data of the site. The model is built with the purpose of using it as a computer development for the optimization of resources and designs of hybrid systems in the Parish of Quingeo and its surroundings. The model obtained a fairly similar pattern compared to the data and curves obtained in the field experimentally and detailed in manuscript. It is important to indicate that this analysis has been carried out so that in the near future one or two of these power generation systems can be exploited in a massive way according to the budget assigned by the Parish GAD of Quingeo or other national or international organizations with the purpose of preserving this unique colonial helmet in Ecuador.

Keywords: Hybrid system, wind turbine, modeling, simulation, Smart Grid, Quingeo Azuay Ecuador.

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Authors: H. Abaali, M. T. Lamchich, M. Raoufi

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In this paper, we propose the Modified Synchronous Detection (MSD) Method for determining the reference compensating currents of the shunt active power filter under non sinusoidal voltages conditions. For controlling the inverter switching we used the PI regulator. The numerical simulation results, using Power System Blockset Toolbox PSB of Matlab, from a complete structure, are presented and discussed.

Keywords: Distorted, harmonic, Modified Synchronous Detection Method, PI regulator, Shunt Active Power Filter, unbalanced.

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Authors: R. Gunabalan, V. Subbiah

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This paper describes the speed sensorless vector control method of the parallel connected induction motor drive fed by a single inverter. Speed and rotor fluxes of the induction motor are estimated by natural observer with load torque adaptation and adaptive rotor flux observer. The performance parameters speed and rotor fluxes are estimated from the measured terminal voltages and currents. Fourth order induction motor model is used and speed is considered as a parameter. The performance of the natural observer is similar to the conventional observer. The speed of an induction motor is estimated by MATLAB simulation under different speed and load conditions. Estimated values along with other measured states are used for closed loop control. The simulation results show that the natural observer is also effective for parallel connected induction motor drive.

Keywords: natural observer, adaptive observer, sensorless control

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Authors: Shigeyuki Haruyama, I Made Gatot Karohika, Akinori Sato, Didik Nurhadiyanto, Ken Kaminishi

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Contact width and contact stress are important design parameters for optimizing corrugated metal gasket performance based on elastic and plastic contact stress. In this study, we used a three-layer metal gasket with Al, Cu, Ni as the outer layer, respectively. A finite element method was employed to develop simulation solution. The gasket model was simulated by using two simulation stages which are forming and tightening simulation. The simulation result shows that aluminum with tangent modulus, Eh_al = E_al/150 has the highest slope for contact width. The slope of contact width for plastic mode gasket was higher than the elastic mode gasket.

Keywords: Contact width, contact stress, layer, metal gasket, corrugated, simulation.

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Authors: Julija Asmuss, Gunars Lauks, Viktors Zagorskis

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We consider the problem of bandwidth allocation in a substrate network as an optimization problem for the aggregate utility of multiple applications with diverse requirements and describe a simulation scheme for dynamically adaptive bandwidth allocation protocols. The proposed simulation model based on Coloured Petri Nets (CPN) is realized using CPN Tools.

Keywords: Bandwidth Allocation Problem, Coloured Petri Nets, CPN Tools, Simulation

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Authors: Badr M. Alshammari, A. Rabeh, A. K. Mohamed

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This paper presents the modeling and the control of a grid-connected photovoltaic system (PVS). Firstly, the MPPT control of the PVS and its associated DC/DC converter has been analyzed in order to extract the maximum of available power. Secondly, the control system of the grid side converter (GSC) which is a three-phase voltage source inverter (VSI) has been presented. A special attention has been paid to the control algorithms of the GSC converter during grid voltages imbalances. Especially, three different control objectives are to achieve; the mitigation of the grid imbalance adverse effects, at the point of common coupling (PCC), on the injected currents, the elimination of double frequency oscillations in active power flow, and the elimination of double frequency oscillations in reactive power flow. Simulation results of two control strategies have been performed via MATLAB software in order to demonstrate the particularities of each control strategy according to power quality standards.

Keywords: Renewable energies, photovoltaic systems, DC link, voltage source inverter, space vector SVPWM, unbalanced voltage dips, symmetrical components.

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Authors: C. Bunsanit

Abstract:

This paper presents the refinement method for two beams formation of wideband smart antenna. The refinement method for weighting coefficients is based on Fully Spatial Signal Processing by taking Inverse Discrete Fourier Transform (IDFT), and its simulation results are presented using MATLAB. The radiation pattern is created by multiplying the incoming signal with real weights and then summing them together. These real weighting coefficients are computed by IDFT method; however, the range of weight values is relatively wide. Therefore, for reducing this range, the refinement method is used. The radiation pattern concerns with five input parameters to control. These parameters are maximum weighting coefficient, wideband signal, direction of mainbeam, beamwidth, and maximum of minor lobe level. Comparison of the obtained simulation results between using refinement method and taking only IDFT shows that the refinement method works well for wideband two beams formation.

Keywords: Fully spatial signal processing, beam forming, refinement method, smart antenna, weighting coefficient, wideband.

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Authors: Hanaa T. El-Madany, Faten H. Fahmy, Ninet M. A. El-Rahman, Hassen T. Dorrah

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Renewable energy resources are inexhaustible, clean as compared with conventional resources. Also, it is used to supply regions with no grid, no telephone lines, and often with difficult accessibility by common transport. Satellite earth stations which located in remote areas are the most important application of renewable energy. Neural control is a branch of the general field of intelligent control, which is based on the concept of artificial intelligence. This paper presents the mathematical modeling of satellite earth station power system which is required for simulating the system.Aswan is selected to be the site under consideration because it is a rich region with solar energy. The complete power system is simulated using MATLAB–SIMULINK.An artificial neural network (ANN) based model has been developed for the optimum operation of earth station power system. An ANN is trained using a back propagation with Levenberg–Marquardt algorithm. The best validation performance is obtained for minimum mean square error. The regression between the network output and the corresponding target is equal to 96% which means a high accuracy. Neural network controller architecture gives satisfactory results with small number of neurons, hence better in terms of memory and time are required for NNC implementation. The results indicate that the proposed control unit using ANN can be successfully used for controlling the satellite earth station power system.

Keywords: Satellite, neural network, MATLAB, power system.

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Authors: Jose J.CarreñoZagarra, Rodolfo Villamizar Mejía

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This work describes a CACSD tool for automatic design of robust controllers for hydraulic turbines. The tool calculates the optimal
 controller using the MATLAB hinfopt function and it serves as a practical and effective solution for the laborious task of designing a different controller for each type of turbine and generator, and different parameters and conditions of the plant. Results of the simulation of a generating unit subject to parameters variation show the accuracy and efficiency of the obtained robust controllers.

Keywords: Robust Control, Hydroelectric System Turbine, Control H∞, CACSD

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Authors: Hazem M. El-Bakry, Ahmed A. Mohammed

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In this paper, an intelligent algorithm for optimal document archiving is presented. It is kown that electronic archives are very important for information system management. Minimizing the size of the stored data in electronic archive is a main issue to reduce the physical storage area. Here, the effect of different types of Arabic fonts on electronic archives size is discussed. Simulation results show that PDF is the best file format for storage of the Arabic documents in electronic archive. Furthermore, fast information detection in a given PDF file is introduced. Such approach uses fast neural networks (FNNs) implemented in the frequency domain. The operation of these networks relies on performing cross correlation in the frequency domain rather than spatial one. It is proved mathematically and practically that the number of computation steps required for the presented FNNs is less than that needed by conventional neural networks (CNNs). Simulation results using MATLAB confirm the theoretical computations.

Keywords: Information Storage and Retrieval, Electronic Archiving, Fast Information Detection, Cross Correlation, Frequency Domain.

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Authors: Wai Phyo Aung

Abstract:

Wheeled Mobile Robots (WMRs) are built with their Wheels- drive machine, Motors. Depend on their desire design of WMR, Technicians made used of DC Motors for motion control. In this paper, the author would like to analyze how to choose DC motor to be balance with their applications of especially for WMR. Specification of DC Motor that can be used with desire WMR is to be determined by using MATLAB Simulink model. Therefore, this paper is mainly focus on software application of MATLAB and Control Technology. As the driving system of DC motor, a Peripheral Interface Controller (PIC) based control system is designed including the assembly software technology and H-bridge control circuit. This Driving system is used to drive two DC gear motors which are used to control the motion of WMR. In this analyzing process, the author mainly focus the drive system on driving two DC gear motors that will control with Differential Drive technique to the Wheeled Mobile Robot . For the design analysis of Motor Driving System, PIC16F84A is used and five inputs of sensors detected data are tested with five ON/OFF switches. The outputs of PIC are the commands to drive two DC gear motors, inputs of Hbridge circuit .In this paper, Control techniques of PIC microcontroller and H-bridge circuit, Mechanism assignments of WMR are combined and analyzed by mainly focusing with the “Modeling and Simulink of DC Motor using MATLAB".

Keywords: Control System Design, DC Motors, DifferentialDrive, H-bridge control circuit, MATLAB Simulink model, Peripheral Interface Controller (PIC), Wheeled Mobile Robots.

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Authors: Le Viet Dung, K. Petcharaks

Abstract:

The economical criterion is accounted as the objective function to develop a computer program for designing lightning protection systems for substations by using masts and Matlab in this work. Masts are needed to be placed at desired locations; the program will then show mast heights whose sum is the smallest, i.e. satisfies the economical criterion. The program is helpful for engineers to quickly design a lightning protection system for a substation. To realize this work, methodology and limited conditions of the program, as well as an example of the program result, were described in this paper.

Keywords: lightning, protection, substation, computer.

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Authors: Jiří Barta

Abstract:

The paper deals with simulation programs of spread of harmful substances. Air pollution has a direct impact on the quality of human life and environmental protection is currently a very hot topic. Therefore, the paper focuses on the simulation of release of harmful substances. The first part of article deals with perspectives and possibilities of implementation outputs of simulations programs into the system which is education and of practical training of the management staff during emergency events in the frame of critical infrastructure. The last part shows the practical testing and evaluation of simulation programs. Of the tested simulations software been selected Symos97. The tool offers advanced features for setting leakage. Gradually allows the user to model the terrain, location, and method of escape of harmful substances.

Keywords: Computer Simulation, Symos97, spread, simulation software, harmful substances.

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Authors: A. H. Abdol Rahim, Alhassan Salami Tijani

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Hydrogen produced by means of polymer electrolyte membrane electrolyzer (PEME) is one of the most promising methods due to clean and renewable energy source. In the process, some energy loss due to mass transfer through a PEM is caused by diffusion, electro-osmotic drag, and the pressure difference between the cathode channel and anode channel. In PEME, water molecules and ionic particles transferred between the electrodes from anode to cathode, Extensive mixing of the hydrogen and oxygen at anode channel due to gases cross-over must be avoided. In recent times the consciousness of safety issue in high pressure PEME where the oxygen mix with hydrogen at anode channel could create, explosive conditions have generated a lot of concern. In this paper, the steady state and simulation analysis of gases crossover in PEME on the temperature and pressure effect are presented. The simulations have been analysis in MATLAB based on the well-known Fick’s Law of molecular diffusion. The simulation results indicated that as temperature increases, there is a significant decrease in operating voltage.

Keywords: Diffusion, gases cross-over, steady state.

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Authors: Mahanijah Md Kamal., Dingli Yu

Abstract:

This paper presents a new method of fault detection and isolation (FDI) for polymer electrolyte membrane (PEM) fuel cell (FC) dynamic systems under an open-loop scheme. This method uses a radial basis function (RBF) neural network to perform fault identification, classification and isolation. The novelty is that the RBF model of independent mode is used to predict the future outputs of the FC stack. One actuator fault, one component fault and three sensor faults have been introduced to the PEMFC systems experience faults between -7% to +10% of fault size in real-time operation. To validate the results, a benchmark model developed by Michigan University is used in the simulation to investigate the effect of these five faults. The developed independent RBF model is tested on MATLAB R2009a/Simulink environment. The simulation results confirm the effectiveness of the proposed method for FDI under an open-loop condition. By using this method, the RBF networks able to detect and isolate all five faults accordingly and accurately.

Keywords: Polymer electrolyte membrane fuel cell, radial basis function neural networks, fault detection, fault isolation.

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Authors: Amira M. Attia, Karim H. Youssef, Nabil H. Abbasy

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Energy consumption schedule (ECS) technique shifts usage of loads from on peak hours and redistributes them throughout the day according to residents’ operating time preferences. This technique is used as form of indirect control from utility to improve the load curve and hence its load factor and reduce customer’s total electric bill as well. Similarly, load shifting technique achieves ECS purposes but as direct control form applied from utility. In this paper, ECS is simulated twice as optimal constrained mathematical formula, solved by using CVX program in MATLAB^® R2013b. First, it is utilized for single residential building with ten apartments to determine max allowable energy consumption per hour for each residential apartment. Then, it is used for single apartment with number of shiftable domestic devices, where operating schedule is deduced using previous simulation output results as constraints. The paper ends by giving differences between ECS technique and load shifting technique via literature and simulation. Based on results assessment, it will be shown whether using ECS or load shifting is more beneficial to both customer and utility.

Keywords: Energy consumption schedule, load shifting technique, comparison.

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Authors: Tuong Huan Nguyen, Quoc Bao Vo, Hai L. Vu

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In this paper we propose a new traffic simulation package, TDMSim, which supports both macroscopic and microscopic simulation on free-flowing and regulated traffic systems. Both simulators are based on travel demands, which specify the numbers of vehicles departing from origins to arrive at different destinations. The microscopic simulator implements the carfollowing model given the pre-defined routes of the vehicles but also supports the rerouting of vehicles. We also propose a macroscopic simulator which is built in integration with the microscopic simulator to allow the simulation to be scaled for larger networks without sacrificing the precision achievable through the microscopic simulator. The macroscopic simulator also enables the reuse of previous simulation results when simulating traffic on the same networks at later time. Validations have been conducted to show the correctness of both simulators.

Keywords: Macroscopic, Microscopic, Simulation, Traffic, Travel demand, Fundamental diagrams.

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Authors: S. Sonkham, U. Pinsopon, W. Chatlatanagulchai

Abstract:

This paper presents a method of sliding mode control (SMC) designing and developing for the servo system in a dual-stage actuator (DSA) hard disk drive. Mathematical modeling of hard disk drive actuators is obtained, extracted from measuring frequency response of the voice-coil motor (VCM) and PZT micro-actuator separately. Matlab software tools are used for mathematical model estimation and also for controller design and simulation. A model-reference approach for tracking requirement is selected as a proposed technique. The simulation results show that performance of a model-reference SMC controller design in DSA servo control can be satisfied in the tracking error, as well as keeping the positioning of the head within the boundary of +/-5% of track width under the presence of internal and external disturbance. The overall results of model-reference SMC design in DSA are met per requirement specifications and significant reduction in %off track is found when compared to the single-state actuator (SSA).

Keywords: Hard Disk Drive, Dual-Stage Actuator, Track Following, HDD Servo Control, Sliding Mode Control, Model-Reference, Tracking Control.

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Authors: Ruiheng Li, Amir Parsa Anvar, Amir M. Anvar, Tien-Fu Lu

Abstract:

High redundancy and strong uncertainty are two main characteristics for underwater robotic manipulators with unlimited workspace and mobility, but they also make the motion planning and control difficult and complex. In order to setup the groundwork for the research on control schemes, the mathematical representation is built by using the Denavit-Hartenberg (D-H) method [9]&[12]; in addition to the geometry of the manipulator which was studied for establishing the direct and inverse kinematics. Then, the dynamic model is developed and used by employing the Lagrange theorem. Furthermore, derivation and computer simulation is accomplished using the MATLAB environment. The result obtained is compared with mechanical system dynamics analysis software, ADAMS. In addition, the creation of intelligent artificial skin using Interlink Force Sensing ResistorTM technology is presented as groundwork for future work

Keywords: Manipulator System, Robot, AUV, Denavit- Hartenberg method Lagrange theorem, MALTAB, ADAMS, Direct and Inverse Kinematics, Dynamics, PD Control-law, Interlink Force Sensing ResistorTM, intelligent artificial skin system.

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Authors: Abdulsalam A. Al-Sudairi

Abstract:

Object-oriented simulation is considered one of the most sophisticated techniques that has been widely used in planning, designing, executing and maintaining construction projects. This technique enables the modeler to focus on objects which is extremely important for thorough understanding of a system. Thus, identifying an object is an essential point of building a successful simulation model. In a maintenance process an object is a maintenance work order (MWO). This study demonstrates a maintenance simulation model for the building maintenance division of Saudi Consolidated Electric Company (SCECO) in Dammam, Saudi Arabia. The model focused on both types of maintenance processes namely: (1) preventive maintenance (PM) and (2) corrective maintenance (CM). It is apparent from the findings that object-oriented simulation is a good diagnostic and experimental tool. This is because problems, limitations, bottlenecks and so forth are easily identified. These features are very difficult to obtain when using other tools.

Keywords: Object oriented, simulation, maintenance, process, work orders

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Authors: M. S. Muhammad, S. M. W. Masra, K. Kipli, N. Zamhari

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The capturing of gel electrophoresis image represents the output of a DNA computing algorithm. Before this image is being captured, DNA computing involves parallel overlap assembly (POA) and polymerase chain reaction (PCR) that is the main of this computing algorithm. However, the design of the DNA oligonucleotides to represent a problem is quite complicated and is prone to errors. In order to reduce these errors during the design stage before the actual in-vitro experiment is carried out; a simulation software capable of simulating the POA and PCR processes is developed. This simulation software capability is unlimited where problem of any size and complexity can be simulated, thus saving cost due to possible errors during the design process. Information regarding the DNA sequence during the computing process as well as the computing output can be extracted at the same time using the simulation software.

Keywords: DNA computing, PCR, POA, simulation software

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Authors: Thandar Aung, Tun Lin Naing

Abstract:

In this paper, the DC-link voltage control of DC-DC boost converter–inverter system is proposed. The mathematical model is developed from four different sub-circuits that depended on the switch positions. The developed differential equations are combined to develop the dynamic model. Transfer function is generated from the switched function model. Fluctuation of DC-link voltage causes connected loads malfunction. For this problem, a kind of traditional controller, the PI controller is applied to achieve constant DC-link voltage. The PI controller gains are obtained based on transfer function step response. The simulation work has been studied by using MATLAB/Simulink software and hardware prototype is implemented with a low-cost microcontroller Arduino Nano. Experimental results are collected by using ArduinoIO library package. Closed-loop DC-link voltage control system is tested with various line and load disturbances. It is found that the experimental results give equal responses with the simulation results.

Keywords: ArduinoIO library package, boost converter-inverter system, low cost microcontroller, PI controller, switched function model.

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Authors: M. Tsebia, H. Bentarzi

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In the inter-connected power systems, a phenomenon called inter-area oscillation may be caused by several defects. In this paper, a study of the Maghreb countries inter-area power networks oscillation has been investigated. The inter-area oscillation monitoring can be enhanced by integrating Phasor Measurement Unit (PMU) technology installed in different places. The data provided by PMU and recorded by PDC will be used for the monitoring, analysis, and control purposes. The proposed approach has been validated by simulation using MATLAB/Simulink.

Keywords: Inter-area oscillation, Maghrebian power system, Simulink, PMU.

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Authors: Ziraguen O. Williams, Shield B. Lin, Fouad N. Matari, Leslie J. Quiocho

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Simulation for seated row exercise was a continued task to assist NASA in analyzing a one-dimensional vibration isolation and stabilization system for astronaut’s exercise platform. Feedback delay and signal noise were added to the simulation model. Simulation runs for this study were conducted in two software simulation tools, Trick and MBDyn, software simulation environments developed at the NASA Johnson Space Center. The exciter force in the simulation was calculated from motion capture of an exerciser during a seated aerobic row exercise. The simulation runs include passive control, active control using a Proportional, Integral, Derivative (PID) controller, and active control using a Piecewise Linear Integral Derivative (PWLID) controller. Output parameters include displacements of the exercise platform, the exerciser, and the counterweight; transmitted force to the wall of spacecraft; and actuator force to the platform. The simulation results showed excellent force reduction in the active controlled system compared to the passive controlled system, which showed less force reduction.

Keywords: Simulation, counterweight, exercise, vibration.

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