Search results for: proportional controller

Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) using the gradient optimization automatic choosing functions for nonlinear systems. Constant terms which arise from sectionwise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics. Parameters included in the control are suboptimally selected by expanding a stable region in the sense of Lyapunov with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Isao Tomita

Abstract:

We develop a periodically-poled LiNbO3 (PPLN) device for highly-efficient third-harmonic generation (THG), where the THG efficiency is enhanced with a cavity. THG can usually be produced via χ(3)-nonlinear materials by optical pumping with very high pump-power. Instead, we here propose THG by moderate-power pumping through a specially-designed PPLN device containing only χ(2)-nonlinearity, where sum-frequency generation in the χ(2) process is employed for the mixing of a pump beam and a second-harmonic-generation (SHG) beam produced from the pump beam. The cavity is designed to increase the SHG power with dichroic mirrors attached to both ends of the device that perfectly reflect the SHG beam back to the device and yet let the pump and THG beams pass through the mirrors. This brings about a THG-power enhancement because of THG power proportional to the enhanced SHG power. We examine the THG-efficiency dependence on the mirror reflectance and show that very high THG-efficiency is obtained at moderate pump-power when compared with that of a cavity-free PPLN device.

Keywords: Cavity, periodically-poled LiNbO3, sum-frequency generation, third-harmonic generation.

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Authors: Caigen Zhou, Haibo Jiang

Abstract:

The problem of robust fuzzy control for a class of nonlinear fuzzy impulsive singular perturbed systems with time-varying delay is investigated by employing Lyapunov functions. The nonlinear delay system is built based on the well-known T–S fuzzy model. The so-called parallel distributed compensation idea is employed to design the state feedback controller. Sufficient conditions for global exponential stability of the closed-loop system are derived in terms of linear matrix inequalities (LMIs), which can be easily solved by LMI technique. Some simulations illustrate the effectiveness of the proposed method.

Keywords: T–S fuzzy model, singular perturbed systems, time-varying delay, robust control.

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Authors: Ersan Aktas, Eren Turanoğuz

Abstract:

In this study, the quad-electrical rotor driven unmanned aerial vehicle system is designed and modeled using fundamental dynamic equations. After that, mechanical, electronical and control system of the air vehicle are designed and implemented. Brushless motor speeds are altered via electronic speed controllers in order to achieve desired controllability. The vehicle's fundamental Euler angles (i.e., roll angle, pitch angle, and yaw angle) are obtained via AHRS sensor. These angles are provided as an input to the control algorithm that run on soft the processor on the electronic card. The vehicle control algorithm is implemented in the electronic card. Controller is designed and improved for each Euler angles. Finally, flight tests have been performed to observe and improve the flight characteristics.

Keywords: Quadrotor, UAS applications, control architectures, PID.

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Authors: S. Parasuraman

Abstract:

In this work, a new approach is proposed to control the manipulators for Humanoid robot. The kinematics of the manipulators in terms of joint positions, velocity, acceleration and torque of each joint is computed using the Denavit Hardenberg (D-H) notations. These variables are used to design the manipulator control system, which has been proposed in this work. In view of supporting the development of a controller, a simulation of the manipulator is designed for Humanoid robot. This simulation is developed through the use of the Virtual Reality Toolbox and Simulink in Matlab. The Virtual Reality Toolbox in Matlab provides the interfacing and controls to an environment which is developed based on the Virtual Reality Modeling Language (VRML). Chains of bones were used to represent the robot.

Keywords: Mobile robot, Robot Kinematics, Robot Navigation, MATLAB.

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Authors: Igor Astrov, Natalya Berezovski

Abstract:

This paper focuses on a critical component of the situational awareness (SA), the control of autonomous vertical flight for vectored thrust aerial vehicle (VTAV). With the SA strategy, we proposed a neural network motion control procedure to address the dynamics variation and performance requirement difference of flight trajectory for a VTAV. This control strategy with using of NARMAL2 neurocontroller for chosen model of VTAV has been verified by simulation of take-off and forward maneuvers using software package Simulink and demonstrated good performance for fast stabilization of motors, consequently, fast SA with economy in energy can be asserted during search-and-rescue operations.

Keywords: NARMA-L2 neurocontroller, situational awareness, vectored thrust aerial vehicle.

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Authors: Jafreezal Jaafar, Eric McKenzie

Abstract:

This paper presents a solution for the behavioural animation of autonomous virtual agent navigation in virtual environments. We focus on using Dempster-Shafer-s Theory of Evidence in developing visual sensor for virtual agent. The role of the visual sensor is to capture the information about the virtual environment or identifie which part of an obstacle can be seen from the position of the virtual agent. This information is require for vitual agent to coordinate navigation in virtual environment. The virual agent uses fuzzy controller as a navigation system and Fuzzy α - level for the action selection method. The result clearly demonstrates the path produced is reasonably smooth even though there is some sharp turn and also still not diverted too far from the potential shortest path. This had indicated the benefit of our method, where more reliable and accurate paths produced during navigation task.

Keywords: Agent, Navigation, Demster Shafer, Fuzzy Logic.

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Authors: T. C. Kuo

Abstract:

In this paper, a novel adaptive fuzzy sliding mode control method is proposed for the robust tracking control of robotic manipulators. The proposed controller possesses the advantages of adaptive control, fuzzy control, and sliding mode control. First, system stability and robustness are guaranteed based on the sliding mode control. Further, fuzzy rules are developed incorporating with adaptation law to alleviate the input chattering effectively. Stability of the control system is proven by using the Lyapunov method. An application to a three-degree-of-freedom robotic manipulator is carried out. Accurate trajectory tracking as well as robustness is achieved. Input chattering is greatly eliminated.

Keywords: Fuzzy control, sliding mode control, roboticmanipulator, adaptive control.

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Authors: Yousef S. Al-Othman

Abstract:

The growth and expansion of the industrial facilities comes proportional to the market increasing demand of products and services. Furthermore, raw material producers such as oil companies usually undergo massive revamping projects to maintain a synchronized supply. These revamping projects are usually delivered through challenging construction projects held and associated with daily site risks related to the construction process. Henceforth, a case study related to these risks and corresponding on-spot corrective measurements has been made on a certain number of construction project contractors at Kuwait Oil Company (KOC) to derive the benefits and overall effectiveness of the on-spot corrective measurements during the construction phase of a project, and how would the same help in avoiding major incidents, ensuring a smooth, cost effective and on time delivery of the project. Findings of this case study shall have an added value to the overall risk management process by minimizing the daily site risks that may affect the project lead time, resulting in an undisturbed on-site construction process.

Keywords: Oil and gas, risk management, construction projects, project lead time.

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Authors: S. Chonsatidjamroen , K-N. Areerak, K-L. Areerak

Abstract:

This paper presents the averaging model of a buck converter derived from the generalized state-space averaging method. The sliding mode control is used to regulate the output voltage of the converter and taken into account in the model. The proposed model requires the fast computational time compared with those of the full topology model. The intensive time-domain simulations via the exact topology model are used as the comparable model. The results show that a good agreement between the proposed model and the switching model is achieved in both transient and steady-state responses. The reported model is suitable for the optimal controller design by using the artificial intelligence techniques.

Keywords: Generalized state-space averaging method, buck converter, sliding mode control, modeling, simulation.

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Authors: Khampheth Bounnady, Boontee Kruatrachue, Somkiat Wangsiripitak

Abstract:

This paper proposed high level feature for online Lao handwritten recognition. This feature must be high level enough so that the feature is not change when characters are written by different persons at different speed and different proportion (shorter or longer stroke, head, tail, loop, curve). In this high level feature, a character is divided in to sequence of curve segments where a segment start where curve reverse rotation (counter clockwise and clockwise). In each segment, following features are gathered cumulative change in direction of curve (- for clockwise), cumulative curve length, cumulative length of left to right, right to left, top to bottom and bottom to top ( cumulative change in X and Y axis of segment). This feature is simple yet robust for high accuracy recognition. The feature can be gather from parsing the original time sampling sequence X, Y point of the pen location without re-sampling. We also experiment on other segmentation point such as the maximum curvature point which was widely used by other researcher. Experiments results show that the recognition rates are at 94.62% in comparing to using maximum curvature point 75.07%. This is due to a lot of variations of turning points in handwritten.

Keywords: Handwritten feature, chain code, Lao handwritten recognition.

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Authors: Hadi Adibi-Asl, Alireza Doosthosseini, Amir Taghavipour

Abstract:

This paper studies the design of an adaptive control strategy to tune an active steering system for better drivability and maneuverability. In the first step, adaptive control strategy is applied to estimate the uncertain parameters on-line (e.g. cornering stiffness), then the estimated parameters are fed into the pole placement controller to generate corrective feedback gain to improve the steering system dynamic’s characteristics. The simulations are evaluated for three types of road conditions (dry, wet, and icy), and the performance of the adaptive pole placement control (APPC) are compared with pole placement control (PPC) and a passive system. The results show that the APPC strategy significantly improves the yaw rate and side slip angle of a bicycle plant model.

Keywords: Adaptive control, active steering, pole placement, vehicle dynamics.

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Authors: Yehia A. Eldrainy, Hossam S. Aly, Khalid M. Saqr, Mohammad Nazri Mohd Jaafar

Abstract:

The central recirculation zone (CRZ) in a swirl stabilized gas turbine combustor has a dominant effect on the fuel air mixing process and flame stability. Most of state of the art swirlers share one disadvantage; the fixed swirl number for the same swirler configuration. Thus, in a mathematical sense, Reynolds number becomes the sole parameter for controlling the flow characteristics inside the combustor. As a result, at low load operation, the generated swirl is more likely to become feeble affecting the flame stabilization and mixing process. This paper introduces a new swirler concept which overcomes the mentioned weakness of the modern configurations. The new swirler introduces air tangentially and axially to the combustor through tangential vanes and an axial vanes respectively. Therefore, it provides different swirl numbers for the same configuration by regulating the ratio between the axial and tangential flow momenta. The swirler aerodynamic performance was investigated using four CFD simulations in order to demonstrate the impact of tangential to axial flow rate ratio on the CRZ. It was found that the length of the CRZ is directly proportional to the tangential to axial air flow rate ratio.

Keywords: Swirler, Gas turbine, CFD, Numerical simulation, Recirculation zone, Swirl number

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Authors: J. Witzany, T. Čejka, R. Zigler

Abstract:

With respect to the dissipation of energy through plastic deformation of joints of prefabricated wall units, the paper points out the principal importance of efficient reinforcement of the prefabricated system at its joints. The method, quality and amount of reinforcement are essential for reaching the necessary degree of joint ductility. The paper presents partial results of experimental research of vertical joints of prefabricated units exposed to monotonously rising loading and repetitive shear force and formulates a conclusion that the limit state of the structure as a whole is preceded by the disintegration of joints, or that the structure tends to pass from linearly elastic behaviour to non-linearly elastic to plastic behaviour by exceeding the proportional elastic limit in joints.Experimental verification on a model of a 7-storey prefabricated structure revealed weak points in its load-bearing systems, mainly at places of critical points around openings situated in close proximity to vertical joints of mutually perpendicularly oriented walls.

Keywords: dissipative energy, dynamic and cycling load repetitive load, working diagrams of joints

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Authors: Wael M Albadri, Hassnen M Jafer, Ehab H Sfoog

Abstract:

Relationship between undrained shear strength (Su) and over consolidation ratio (OCR) of clay soil (marine clay) is very important in the field of geotechnical engineering to estimate the settlement behaviour of clay and to prepare a small scale physical modelling test. In this study, a relationship between shear strength and OCR parameters was determined using the laboratory vane shear apparatus and the fully automatic consolidated apparatus. The main objective was to establish non-linear correlation formula between shear strength and OCR and comparing it with previous studies. Therefore, in order to achieve this objective, three points were chosen to obtain 18 undisturbed samples which were collected with an increasing depth of 1.0 m to 3.5 m each 0.5 m. Clay samples were prepared under undrained condition for both tests. It was found that the OCR and shear strength are inversely proportional at similar depth and at same undrained conditions. However, a good correlation was obtained from the relationships where the R2 values were very close to 1.0 using polynomial equations. The comparison between the experimental result and previous equation from other researchers produced a non-linear correlation which has a similar pattern with this study.

Keywords: Shear strength, over-consolidation ratio, vane shear test, clayey soil.

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Authors: Zixin Liu, Huawei Yang, Fangwei Chen

Abstract:

This paper studies the mean square exponential synchronization problem of a class of stochastic neutral type chaotic neural networks with mixed delay. On the Basis of Lyapunov stability theory, some sufficient conditions ensuring the mean square exponential synchronization of two identical chaotic neural networks are obtained by using stochastic analysis and inequality technique. These conditions are expressed in the form of linear matrix inequalities (LMIs), whose feasibility can be easily checked by using Matlab LMI Toolbox. The feedback controller used in this paper is more general than those used in previous literatures. One simulation example is presented to demonstrate the effectiveness of the derived results.

Keywords: Exponential synchronization, stochastic analysis, chaotic neural networks, neutral type system.

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Authors: T. Benmiloud, A. Omari

Abstract:

This paper presents a new technique of compensation of the effect of variation parameters in the direct field oriented control of induction motor. The proposed method uses an adaptive tuning of the value of synchronous speed to obtain the robustness for the field oriented control. We show that this adaptive tuning allows having robustness for direct field oriented control to changes in rotor resistance, load torque and rotational speed. The effectiveness of the proposed control scheme is verified by numerical simulations. The numerical validation results of the proposed scheme have presented good performances compared to the usual direct-field oriented control.

Keywords: Induction motor, direct field-oriented control, compensation of variation parameters, fuzzy logic controller.

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Authors: S. W. Nawawi, M. N. Ahmad, J. H. S. Osman

Abstract:

The research on two-wheeled inverted pendulum (TWIP) mobile robots or commonly known as balancing robots have gained momentum over the last decade in a number of robotic laboratories around the world. This paper describes the hardware design of such a robot. The objective of the design is to develop a TWIP mobile robot as well as MATLAB interfacing configuration to be used as flexible platform comprises of embedded unstable linear plant intended for research and teaching purposes. Issues such as selection of actuators and sensors, signal processing units, MATLAB Real Time Workshop coding, modeling and control scheme will be addressed and discussed. The system is then tested using a wellknown state feedback controller to verify its functionality.

Keywords: Embedded System, Two-wheeled Inverted Pendulum Mobile Robot.

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Authors: Toshinori Nawata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input using weighted gradient optimization automatic choosing functions. Constant term which arises from linearization of a given nonlinear system is treated as a coefficient of a stable zero dynamics. Parameters of the control are suboptimally selected by maximizing the stable region in the sense of Lyapunov with the aid of a genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented automatic choosing control, nonlinear control, genetic algorithm, zero dynamics.

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Authors: Takuya Sumi, Syoko Nukaya, Takashi Kaburagi, Hiroshi Tanaka, Kajiro Watanabe, Yosuke Kurihara

Abstract:

We propose an unconstrained measurement system for scratching motion based on mathematical model of unconstrained bed sensing method which could measure the bed vibrations due to the motion of the person on the bed. In this paper, we construct mathematical model of the unconstrained bed monitoring system; and we apply the unconstrained bed sensing method to the system for detecting scratching motion. The proposed sensors are placed under the three bed feet. When the person is lying on the bed, the output signals from the sensors are proportional to the magnitude of the vibration due to the scratching motion. Hence, we could detect the subject’s scratching motion from the output signals from ceramic sensors. We evaluated two scratching motions using the proposed system in the validity experiment as follows: 1st experiment is the subject’s scratching the right side cheek with his right hand, and; 2nd experiment is the subject’s scratching the shin with another foot. As the results of the experiment, we recognized the scratching signals that enable the determination when the scratching occurred. Furthermore, the difference among the amplitudes of the output signals enabled us to estimate where the subject scratched.

Keywords: Unconstrained bed sensing method, scratching, body movement, itchy, piezoceramics.

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Authors: Iman Hadipour, Javad Marzbanrad

Abstract:

In this paper, the strength of a stabilizer is determined when the static and fatigue multiaxial loading are applied. Stabilizer is a part of suspension system in the heavy truck for stabilizing the cabin against the vibration of the road which composes of a thin-walled tube joined to a forge component by fillet weld. The component is loaded by non proportional random sequence of torsion and bending. Residual stress of welding process is considered here for static loading. This static loading with road irregularities are applied in this study as fatigue case that can affected in the fillet welded area of this part. The stresses in the welded structure are calculated using FEA. In addition, the fatigue with multi axial loading in the fillet weld is also investigated and the critical zone of the stabilizer is specified and presented by graphs. Residual stresses that have been resulted by the thermal forces are considered in FEA. Force increasing is the element of finding the critical point of the component.

Keywords: Fillet weld, fatigue, weld toe crack, weld root crack, S-N curve, multiaxial load, residual stress, combined force.

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Authors: Esther T. Akinlabi, Stephen A. Akinlabi

Abstract:

The purpose of this research study is to investigate the manner in which various loads affect the mechanical properties of the formed mild steel plates. The investigation focuses on examining the cross-sectional area of the metal plate at the centre of the formed mild steel plate. Six mild steel plates were deformed with different loads. The loads applied on the plates had a magnitude of 5 kg, 10 kg, 15 kg, 20 kg, 25 kg and 30 kg. The radius of the punching die was 120 mm and the loads were applied at room temperature. The investigations established that the applied load causes the Vickers microhardness at the cross-sectional area of the plate to increase due to strain hardening. Hence, the percentage increase of the hardness due to the load was found to be directly proportional to the increase in the load. Furthermore, the tensile test results for the parent material showed that the average Ultimate Tensile Strength (UTS) for the three samples was 308 MPa while the average Yield Strength and Percentage Elongation were 227 MPa and 38 % respectively. Similarly, the UTS of the formed components increased after the deformation of the plate, as such it can be concluded that the forming loads alter the mechanical properties of the materials by improving and strengthening the material properties.

Keywords: Applied load, forming and Mechanical Properties.

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Authors: Leila Fatemi, Morteza Moradi, Azadeh Mansouri

Abstract:

In this paper, the modified optimal sliding mode control with a proposed method to design a sliding surface is presented. Because of the inability of the previous approach of the sliding mode method to design a bounded and suitable input, the new variation is proposed in the sliding manifold to obviate problems in a structural system. Although the sliding mode control is a powerful method to reject disturbances and noises, the chattering problem is not good for actuators. To decrease the chattering phenomena, the optimal control is added to the sliding mode control. Not only the proposed method can decline the intense variations in the inputs of the system but also it can produce the efficient responses respect to the sliding mode control and optimal control that are shown by performing some numerical simulations.

Keywords: Structural Control, optimal control, optimal sliding mode controller, modified sliding surface.

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Authors: Nor Maniha Abdul Ghani, Faradila Naim, Tan Piow Yon

Abstract:

This project focuses on the development of a line follower algorithm for a Two Wheels Balancing Robot. In this project, ATMEGA32 is chosen as the brain board controller to react towards the data received from Balance Processor Chip on the balance board to monitor the changes of the environment through two infra-red distance sensor to solve the inclination angle problem. Hence, the system will immediately restore to the set point (balance position) through the implementation of internal PID algorithms at the balance board. Application of infra-red light sensors with the PID control is vital, in order to develop a smooth line follower robot. As a result of combination between line follower program and internal self balancing algorithms, we are able to develop a dynamically stabilized balancing robot with line follower function.

Keywords: infra-red sensor, PID algorithms, line followerBalancing robot

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Authors: S. Chatterji, S. L. Shimi

Abstract:

As wind, solar and other clean and green energy sources gain popularity worldwide, engineers are seeking ways to make renewable energy systems more affordable and to integrate them with existing ac power grids. In the present paper an attempt has been made for integrating the PV arrays to the smart nano grid using an artificial intelligent (AI) based solar powered cascade multilevel inverter. The AI based controller switching scheme has been used for improving the power quality by reducing the Total Harmonic Distortion (THD) of the multi-level inverter output voltage.

Keywords: Artificial Intelligent (AI), Solar Powered Multi-level Inverter, Smart nano grid, Total Harmonic Distortion (THD).

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Authors: P. Nammalvar, P. Meganathan, A. Balamuguran

Abstract:

Among various active filters, shunt active filter is a viable solution for reactive power and harmonics compensation. In this paper, the SRF plan is used to generate current reference for compensation and conventional PI controllers were used as the controller to compensate the reactive power. The design of the closed loop controllers is reserved simple by modeling them as first order systems. Computationally uncomplicated and efficient SVM system is used in the present work for better utilization of dc bus voltage. The rating of shunt active filter has been finalized based on the reactive power demand of the selected reactive load. The proposed control and SVM technique are validated by simulating in MATLAB software.

Keywords: Shunt Active Filter, Space vector pulse width modulation, Voltage Source Converter, Reactive Power, Synchronous Reference Frame, Point of common coupling.

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Authors: El-Sadek H. Nour El-deen, K. Harby

Abstract:

Energy saving and environment friendly applications are turning out to be one of the most important topics nowadays. In this work, a simulation analysis using TRNSYS software has been carried out to study the benefit of employing a solar adsorption cooling system under the climatic conditions of Al-Minya city, Egypt. A theoretical model was carried out on a two bed adsorption cooling system employing granular activated carbon-HFC-404A as working pair. Temporal and averaged history of solar collector, adsorbent beds, evaporator and condenser has been shown. System performance in terms of daily average cooling capacity and average coefficient of performance around the year has been investigated. The results showed that maximum yearly average coefficient of performance (COP) and cooling capacity are about 0.26 and 8 kW respectively. The maximum value of the both average cooling capacity and COP cyclic is directly proportional to the maximum solar radiation. The system performance was found to be increased with the average ambient temperature. Finally, the proposed solar powered adsorption cooling systems can be used effectively under Al-Minya climatic conditions.

Keywords: Adsorption, solar energy, environment, cooling, Egypt.

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Authors: A. Tashakori, M. Ektesabi

Abstract:

Electric vehicle (EV) is one of the effective solutions to control emission of greenhouses gases in the world. It is of interest for future transportation due to its sustainability and efficiency by automotive manufacturers. Various electrical motors have been used for propulsion system of electric vehicles in last decades. In this paper brushed DC motor, Induction motor (IM), switched reluctance motor (SRM) and brushless DC motor (BLDC) are simulated and compared. BLDC motor is recommended for high performance electric vehicles. PWM switching technique is implemented for speed control of BLDC motor. Behavior of different modes of PWM speed controller of BLDC motor are simulated in MATLAB/SIMULINK. BLDC motor characteristics are compared and discussed for various PWM switching modes under normal and inverter fault conditions. Comparisons and discussions are verified through simulation results.

Keywords: BLDC motor, PWM switching technique, in-wheel technology, electric vehicle.

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Authors: Toshinori Nawata, Hitoshi Takata

Abstract:

In this paper we consider a nonlinear feedback control called augmented automatic choosing control (AACC) for nonlinear systems with constrained input. Constant terms which arise from section wise linearization of a given nonlinear system are treated as coefficients of a stable zero dynamics.Parameters included in the control are suboptimally selectedby extremizing a combination of Hamiltonian and Lyapunov functions with the aid of the genetic algorithm. This approach is applied to a field excitation control problem of power system to demonstrate the splendidness of the AACC. Simulation results show that the new controller can improve performance remarkably well.

Keywords: Augmented Automatic Choosing Control, NonlinearControl, Genetic Algorithm, Hamiltonian, Lyapunovfunction

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Authors: Kuen-Ming Shu, Cheng-Yu Chen

Abstract:

A vibrating-fork sensor can measure the level height of solids and liquids and operates according to the principle that vibrations created by piezoelectric ceramics are transmitted to the vibrating fork, which produces resonance. When the vibrating fork touches an object, its resonance frequency changes and produces a signal that returns to a controller for immediate adjustment, so as to effectively monitor raw material loading. The design of the vibrating fork in a vibrating-fork material sensor is crucial. In this paper, ANSYS finite element analysis software is used to perform modal analysis on the vibrations of the vibrating fork. In addition, to design and produce a superior vibrating fork, the dimensions and welding shape of the vibrating fork are compared in a simulation performed using the Taguchi method.

Keywords: Vibrating fork, piezoelectric ceramics, sound wave, ANSYS, Taguchi method, modal analysis.

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