Search results for: vibration control damper

Authors: Vladimir Stojanović, Marko D. Petković

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The vibration of a complex bogie system that moves on along the high order shear deformable beam on a viscoelastic foundation is studied. The complex bogie system has been modeled by elastically connected rigid bars on an identical supports. Elastic coupling between bars is introduced to simulate rigidly or flexibly (transversal or/and rotational) connection. Identical supports are modeled as a system of attached spring and dashpot to the bar on one side and interact with the beam through the concentrated mass on the other side. It is assumed that the masses and the beam are always in contact. New analytically determined critical velocity of the system is presented. It is analyzed the case when the complex bogie system exceeds the minimum phase velocity of waves in the beam when the vibration of the system may become unstable. Effect of an elastic coupling between bars on the stability of the system has been analyzed. The instability regions are found for the complex bogie system by applying the principle of the argument and D-decomposition method.

Keywords: Reddy-Bickford beam, D-decomposition method, principle of argument, critical velocity

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Authors: Samir Zeghlache, Abderrahmen Bouguerra, Kamel Kara, Djamel Saigaa

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The control of the trirotor helicopter includes nonlinearities, uncertainties and external perturbations that should be considered in the design of control laws. This paper presents a control strategy for an underactuated six degrees of freedom (6 DOF) trirotor helicopter, based on the coupling of the fuzzy logic control and sliding mode control (SMC). The main purpose of this work is to eliminate the chattering phenomenon. To achieve our purpose we have used a fuzzy logic control to generate the hitting control signal, also the non linear observer is then synthesized in order to estimate the unmeasured states. Finally simulation results are included to indicate the trirotor UAV with the proposed controller can greatly alleviate the chattering effect and remain robust to the external disturbances.

Keywords: fuzzy sliding mode control, trirotor helicopter, dynamic modelling, underactuated systems

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Authors: Toshiyuki Satoh, Hiroki Hara, Naoki Saito, Jun-ya Nagase, Norihiko Saga

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This paper addresses a control system design for a table drive system based on the disturbance observer (DOB)-based predictive functional critical control (PFCC). To empower the previously developed DOB-based PFC to handle constraints on controlled outputs, we propose to take a critical control approach. To this end, we derive the transfer function representation of the PFC controller, and yield a detailed design procedure. The effectiveness of the proposed method is confirmed through an experimental evaluation.

Keywords: critical control, disturbance observer, mechatronics, motion control, predictive functional control, table drive systems

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Authors: Leticia Cervantes, Edith Garcia, Oscar Castillo

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At today, there are several control problems where the main objective is to obtain the best control in the study to decrease the error in the application. Many techniques can use to control these problems such as Neural Networks, PID control, Fuzzy Logic, Optimization techniques and many more. In this case, fuzzy logic with fuzzy system and an optimization technique are used to control the case of study. In this case, Ant Lion Optimization is used to optimize a fuzzy system to control the velocity of a simple treadmill. The main objective is to achieve the control of the velocity in the control problem using the ALO optimization. First, a simple fuzzy system was used to control the velocity of the treadmill it has two inputs (error and error change) and one output (desired speed), then results were obtained but to decrease the error the ALO optimization was developed to optimize the fuzzy system of the treadmill. Having the optimization, the simulation was performed, and results can prove that using the ALO optimization the control of the velocity was better than a conventional fuzzy system. This paper describes some basic concepts to help to understand the idea in this work, the methodology of the investigation (control problem, fuzzy system design, optimization), the results are presented and the optimization is used for the fuzzy system. A comparison between the simple fuzzy system and the optimized fuzzy systems are presented where it can be proving the optimization improved the control with good results the major findings of the study is that ALO optimization is a good alternative to improve the control because it helped to decrease the error in control applications even using any control technique to optimized, As a final statement is important to mentioned that the selected methodology was good because the control of the treadmill was improve using the optimization technique.

Keywords: ant lion optimization, control problem, fuzzy control, fuzzy system

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Authors: Yang Zhou, Chen Hao, Ma Xiaoping

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This paper briefly mentions the micro controller unit, and then goes into details about the exact regulations for SRM. Firstly, it proposes the main driving state control for motor and the importance of the motor position sensor. For different speed, the controller will choice various styles such as voltage chopper control, angle position control and current chopper control for which owns its advantages and disadvantages. Combining the strengths of the three discrepant methods, the main control chip will intelligently select the best performing control depending on the load and speed demand. Then the exact flow diagram is showed in paper. At last, an experimental platform is established to verify the correctness of the proposed theory.

Keywords: switched reluctance motor, dspic microcontroller, current chopper

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Authors: Ali Reza Mirzagoltabar Roshan, H. Ahmadi Taleshian, A. Eliasi

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This paper examines the effects of viscous and viscoelastic dampers as an efficient technique for seismic pounding mitigation. To aim that, 15 steel frame models with different numbers of stories and bays and also with different types of ductility were analyzed under 10 different earthquake records for assigned values of link damping and stiffness and the most suitable values of damper parameters (damping and stiffness) are presented. Moreover, it is demonstrated that viscous dampers can perform as efficiently as viscoelastic alternative with a more economical aspect for pounding mitigation purposes.

Keywords: adjacent buildings, separation distance, seismic pounding mitigation, viscoelastic link

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Authors: Soufiane Zerraf, Malika Tridane, Said Belaaouad

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CuHPO₃.2H₂O was synthesized by the direct method. CuHPO₃.2H₂O crystallizes in the orthorhombic system, space group P2₁2₁2₁, a = 6.7036 (2) Å, b = 7.3671 (4) Å, c = 8.9749 (4) Å, Z = 4, V = 443.24 (4) ų. The crystal structure was refined to R₁= 0.0154, R₂= 0.0380 for 19018 reflections satisfying criterion I ≥ 2σ (I). The structural resolution shows the existence of chains of ions HPO₃- linked together by hydrogen bonds. The crystalline structure is formed by chains consisting of Cu[O₃(H₂O)₃] deformed octahedral, which are connected to the vertices. The chains extend parallel to b and are mutually linked by PO₃ groups. The structure is closely related to that of CuSeO₃.2H₂O and CuTeO₃.2H₂O. The experimental studies of the infrared and Raman spectra were used to confirm the presence of the phosphate ion and were compared in the (0-4000) cm-1 region with the theoretical results calculated by the density functional theory (DFT) method to provide reliable assignments of all observed bands in the experimental spectra.

Keywords: crystal structure, X-ray diffraction, vibration study, thermal behavior, density functional theory

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Authors: Mary Moner Botros Fanawel

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Many companies use the statistical tool named as statistical quality control, and which can have a high cost for the companies interested on these statistical tools. The evaluation of the quality of products and services is an important topic, but the reduction of the cost of the implantation of the statistical quality control also has important benefits for the companies. For this reason, it is important to implement a economic design for the various steps included into the statistical quality control. In this paper, we describe some relevant aspects related to the economic design of a quality control chart for the proportion of defective items. They are very important because the suggested issues can reduce the cost of implementing a quality control chart for the proportion of defective items. Note that the main purpose of this chart is to evaluate and control the proportion of defective items of a production process.

Keywords: model predictive control, hierarchical control structure, genetic algorithm, water quality with DBPs objectives proportion, type I error, economic plan, distribution function bootstrap control limit, p-value method, out-of-control signals, p-value, quality characteristics

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Authors: Gabriella Kengyel

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This study aims to describe the differences between the attitudes of the right-wing extremists with internal or external control towards migrants. They both have a significantly higher score on Rotter's Locus of Control Scale, and they are quite xenophobic (54%) according to Bogardus Social Distance Scale. Present research suggests their motives are different. Principle components analysis shows that extremists with internal control reject migrants because of welfare chauvinism and they think that there is some kind of political conspirationism behind the European Refugee Crisis. Contrarily extremist with external control believe in a common enemy and they are significantly more ethnocentric and less skeptical in politics. Results suggest that extremist with internal control shows hostility toward minorities and migrants mainly because of their own reference group.

Keywords: control, extremist, migrant, right-wing

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Authors: Kadda Boumediene, Mohamed Ziani

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Mainly because of their good ratio stiffness/mass, and in addition to adjustable mechanical properties, composite materials are more and more often used as an alternative to traditional materials in several domains. Before using these materials in practical application, a detailed and precise characterization of their mechanical properties is necessary. In the present work, we will find a dynamic analyze of composite beam (natural frequencies and mode shape), an experimental vibration technique, which presents a powerful tool for the estimation of mechanical characteristics, is used to characterize a dissimilar beam of a Mortar/ natural mineral fiber. The study is completed by an analytic (Rayleigh & Rayleigh-Ritz), experimental and numerical application for non-uniform composite beam of a Mortar/ natural mineral fiber. The study is supported by a comparison between numerical and analytic results as well as a comparison between experimental and numerical results.

Keywords: composite beam, mortar/ natural mineral fiber, mechanical characteristics, natural frequencies, mode shape

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Authors: Ekin Ozer

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Assessment of structural reliability is essential for efficient use of civil infrastructure which is subjected hazardous events. Dynamic analysis of finite element models is a commonly used tool to simulate structural behavior and estimate its performance accordingly. However, theoretical models purely based on preliminary assumptions and design drawings may deviate from the actual behavior of the structure. This study proposes up-to-date reliability estimation procedures which engages actual bridge vibration data modifying finite element models for finite element model updating and performing reliability estimation, accordingly. The proposed method utilizes vibration response measurements of bridge structures to identify modal parameters, then uses these parameters to calibrate finite element models which are originally based on design drawings. The proposed method does not only show that reliability estimation based on updated models differs from the original models, but also infer that non-updated models may overestimate the structural capacity.

Keywords: earthquake engineering, engineering vibrations, reliability estimation, structural health monitoring

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Authors: Hong Lu, Wei Fan, Yongquan Zhang, Junbo Zhang

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A cross coupling sliding synchronization control strategy is proposed for the dual-driving feed system. This technology will minimize the position error oscillation and achieve the precise synchronization performance in the high speed and high precision drive system, especially some high speed and high precision machine. Moreover, a cross coupling compensation matrix is provided to offset the mismatched disturbance and the disturbance observer is established to eliminate the chattering phenomenon. Performance comparisons of proposed dual-driving cross coupling sliding mode control (CCSMC), normal cross coupling control （CCC） strategy with PID control, and electronic virtual main shaft control (EVMSC) strategy with SMC control are investigated by simulation and a dual-driving control system; the results show the effectiveness of the proposed control scheme.

Keywords: cross coupling matrix, dual motors, synchronization control, sliding mode control

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Authors: Manish Kumar Thakur, Chiranjit Sarkar

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Sedimentation of magnetorheological (MR) fluid affects its working. MR fluid is a smart fluid that has unique qualities such as quick responsiveness and easy controllability. It is used in the MR damper, MR brake, and MR clutch. In this work effect of sedimentation on torque transmission in the shear mode operated MR clutch is investigated. A test rig is developed to test the impact of sedimentation on torque transmission in the MR clutch. Torque transmission capability of MR clutch has been measured under two conditions to confirm the result of sedimentation. The first experiment is done just after filling and the other after one week. It has been observed that transmission torque is decreased after sedimentation. Hence sedimentation affects the working of the MR clutch.

Keywords: clutch, magnetorheological fluid, sedimentation, torque

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Authors: M. Barański

Abstract:

This paper presents a several diagnostic methods designed to electrical machines especially for permanent magnets (PM) machines. Those machines are commonly used in small wind and water systems and vehicles drives. Those methods are preferred by the author in periodic diagnostic of electrical machines. The special attention should be paid to diagnostic method of turn-to-turn insulation and vibrations. Both of those methods were created in Institute of Electrical Drives and Machines Komel. The vibration diagnostic method is the main thesis of author’s doctoral dissertation. This is method of determination the technical condition of PM electrical machine basing on its own signals is the subject of patent application No P.405669. Specific structural properties of machines excited by permanent magnets are used in this method - electromotive force (EMF) generated due to vibrations. There was analysed number of publications which describe vibration diagnostic methods and tests of electrical machines with permanent magnets and there was no method found to determine the technical condition of such machine basing on their own signals.

Keywords: electrical vehicle, generator, main insulation, permanent magnet, thermography, turn-to-traction drive, turn insulation, vibrations

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Authors: Yusuke Kuramitsu, Tomoaki Hashimoto, Hirokazu Tahara

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The control problem of underactuated spacecrafts has attracted a considerable amount of interest. The control method for a spacecraft equipped with less than three control torques is useful when one of the three control torques had failed. On the other hand, the quantized control of systems is one of the important research topics in recent years. The random dither quantization method that transforms a given continuous signal to a discrete signal by adding artificial random noise to the continuous signal before quantization has also attracted a considerable amount of interest. The objective of this study is to develop the control method based on random dither quantization method for stabilizing the rotational motion of a rigid spacecraft with two control inputs. In this paper, the effectiveness of random dither quantization control method for the stabilization of rotational motion of spacecrafts with two torque inputs is verified by numerical simulations.

Keywords: spacecraft control, quantized control, nonlinear control, random dither method

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Authors: Hamed Sarbazy, Zohre Gholipour Haftkhani, Ali Safari, Pejman Hosseiniun

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Scientific and industrial progress in the past two decades has resulted in energy distribution systems based on power electronics, as an enabling technology in various industries and building management systems can be considered. Grading and standardization module power electronics systems and its use in a distributed control system, a strategy for overcoming the limitations of using this system. The purpose of this paper is to investigate strategies for scheduling and control structure of standard modules is a power electronic systems. This paper introduces the classical control methods and disadvantages of these methods will be discussed, The hierarchical control as a mechanism for distributed control structure of the classification module explains. The different levels of control and communication between these levels are fully introduced. Also continue to standardize software distribution system control structure is discussed. Finally, as an example, the control structure will be presented in a DC distribution system.

Keywords: application management, hardware management, power electronics, building blocks

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Authors: Binjuan Xu, Qian Zhao, Ping Jiang, Bo Guo, Zhijun Cheng, Xiaoyue Wu

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Astronautical valves are key units in engine systems of astronautical products; their reliability will influence results of rocket or missile launching, even lead to damage to staff and devices on the ground. Besides failure in engine system may influence the hitting accuracy and flight shot of missiles. Therefore high reliability is quite essential to astronautical products. There are quite a few literature doing research based on few failure test data to estimate valves’ reliability, thus this paper proposed a new method to estimate valves’ reliability, according to the corresponding tests of different failure modes, this paper takes advantage of tests data which acquired from temperature, vibration, and action tests to estimate reliability in every failure modes, then this paper has regarded these three kinds of tests as three stages in products’ process to integrate these results to acquire valves’ reliability. Through the comparison of results achieving from tests data and simulated data, the results have illustrated how to obtain valves’ reliability based on the few failure data with failure modes and prove that the results are effective and rational.

Keywords: censored data, temperature tests, valves, vibration tests

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Authors: M. Caramihai, Irina Severin

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This paper deals with the design of an intelligent control structure for a bioprocess of Hansenula polymorpha yeast cultivation. The objective of the process control is to produce biomass in a desired physiological state. The work demonstrates that the designed Hybrid Control Techniques (HCT) are able to recognize specific evolution bioprocess trajectories using neural networks trained specifically for this purpose, in order to estimate the model parameters and to adjust the overall bioprocess evolution through an expert system and a fuzzy structure. The design of the control algorithm as well as its tuning through realistic simulations is presented. Taking into consideration the synergism of different paradigms like fuzzy logic, neural network, and symbolic artificial intelligence (AI), in this paper we present a real and fulfilled intelligent control architecture with application in bioprocess control.

Keywords: bioprocess, intelligent control, neural nets, fuzzy structure, hybrid techniques

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Authors: S. M. A. Al Qawabah, A. I. O. Zaid

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Al-4%Cu alloys are now widely used in many engineering applications especially in robotic, aerospace and vibration control area. The main problem arises from the weakness of their mechanical characteristics. Therefore, this study is directed towards enhancing the mechanical properties through severe plastic deformation. In this work, the hot direct extrusion process was chosen to provide the required hot work for this purpose. A direct extrusion die was designed and manufactured to be used in this investigation. The general microstructure, microhardness, surface roughness, and compression tests were performed on specimens from the produced Al-4%Cu alloy both in the as cast and after extrusion conditions. It was found that a pronounced enhancement in the mechanical characteristics of the produced Al-4%Cu after extrusion was achieved. The microhardness increased by 89.3%, the flow stress was decreased by 10% at 0.2 strain and finally the surface roughness was reduced by 81.6%.

Keywords: aluminum, copper, surface roughness, hot extrusion

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Authors: Pornsiri Kaewpradit, Chalisa Pourneaw

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Temperature control improvement of a membrane reactor with exothermic and reversible esterification reaction is studied in this work. It is well known that a batch membrane reactor requires different control strategies from a continuous one due to the fact that it is operated dynamically. Due to the effect of the operating temperature, the suitable control scheme has to be designed based reliable predictive model to achieve a desired objective. In the study, the optimization framework has been preliminary formulated in order to determine an optimal temperature trajectory for maximizing a desired product. In model predictive control scheme, a set of predictive models have been initially developed corresponding to the possible operating points of the system. The multiple predictive control moves have been further calculated on-line using the developed models corresponding to current operating point. It is obviously seen in the simulation results that the temperature control has been improved compared to the performance obtained by the conventional predictive controller. Further robustness tests have also been investigated in this study.

Keywords: model predictive control, batch reactor, temperature control, membrane reactor

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Authors: Marek Długosz, Paweł Skruch

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One of purposes of home automation systems is to provide appropriate comfort to the users by suitable air temperature control and stabilization inside the rooms. The control of temperature level is not a simple task and the basic difficulty results from the fact that accurate parameters of the object of control, that is a building, remain unknown. Whereas the structure of the model is known, the identification of model parameters is a difficult task. In this paper, a control algorithm allowing the present temperature to be reached inside the building within the specified time without the need to know accurate parameters of the building itself is presented.

Keywords: control, home automation system, wireless networking, automation engineering

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Authors: Alexandra Monteiro, K. Bousson, Fernando J. O. Moreira, Ricardo Reis

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Fixed-wing flying vehicles are usually controlled by means of control surfaces such as elevators, ailerons, and rudders. The failure of these systems may lead to severe or even fatal crashes. These failures resulted in increased popularity for research activities on propulsion control in the last decades. The present work deals with a hybrid control architecture in which the propulsion-controlled vehicle maintains its traditional control surfaces, addressing the issue of robust lateral-directional dynamics control. The challenges stem from the parameter uncertainties in the stability and control derivatives and some unknown terms in the flight dynamics model. Two approaches are implemented and tested: linear quadratic regulation with robustness characteristics and H∞ control. The problem is centered on roll-yaw controller design with full state-feedback, which is able to deal with a standalone propulsion control mode as well as a hybrid mode combining both propulsion control and conventional control surface concepts while maintaining the original flight maneuverability characteristics. The results for both controllers emphasized very good control performances; however, the H∞ controller showed higher stabilization rates and robustness albeit with a slightly higher control magnitude than using the linear quadratic regulator.

Keywords: robust propulsion control, h-infinity control, lateral-directional flight dynamics, parameter uncertainties

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Authors: Bessaad Taieb, Benbouali Abderrahmen

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Fuzzy controllers are a powerful tool for controlling complex processes. However, its robustness capacity remains moderately limited because it loses its property for large ranges of parametric variations. In this paper, the proposed control method is designed, based on a fuzzy adaptive controller used as a remedy for this problem. For increase the robustness of the vector control and to maintain the performance of the five-phase asynchronous machine despite the presence of disturbances (variation of rotor resistance, rotor inertia variations, sudden variations in the load etc.), by applying the method of behaviour model control (BMC). The results of simulation show that the fuzzy adaptive control provides best performance and has a more robustness as the fuzzy (FLC) and as a conventional (PI) controller.

Keywords: fuzzy adaptive control, behaviour model control, vector control, five-phase asynchronous machine

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Authors: Ming Wen, Nasim Nezamoddini

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Sophisticated numerical simulations like finite element analysis (FEA) involve a complicated process from model setup to post-processing tasks that require replication of time-consuming steps. Utilizing FEA automation program simplifies the complexity of the involved steps while minimizing human errors in analysis set up, calculations, and results processing. One of the main challenges in designing FEA automation programs is to identify user requirements and link them to possible design alternatives. This paper presents a decision-making framework to design a Python based FEA automation program for modal analysis, frequency response analysis, and random vibration fatigue (RVF) analysis procedures. Analytical hierarchy process (AHP) and technique for order preference by similarity to ideal solution (TOPSIS) are applied to evaluate design alternatives considering the feedback received from experts and program users.

Keywords: finite element analysis, FEA, random vibration fatigue, process automation, analytical hierarchy process, AHP, TOPSIS, multiple-criteria decision-making, MCDM

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Authors: Idowu Ibikunle Albert, Atilade Adesanya Oluwafemi, Okedeyi Abiodun Sikiru, Mustapha Rilwan Adewale

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These present-day all areas of transport have experienced large advances characterized by increases in the speeds and weight of vehicles. As a result, this paper considered the Transverse Vibration of an Elastic Beam Resting on a Variable Elastic Foundation Subjected to a moving Load. The beam is presumed to be uniformly distributed and has simple support at both ends. The moving distributed moving mass is assumed to move with constant velocity. The governing equations, which are fourth-order partial differential equations, were reduced to second-order partial differential equations using an analytical method in terms of series solution and solved by a numerical method using mathematical software (Maple). Results show that an increase in the values of beam parameters, moving Mass M, and k-stiffness K, significantly reduces the deflection profile of the vibrating beam. In the results, it was equally found that moving mass is greater than moving force.

Keywords: elastic beam, moving load, response of structure, variable elastic foundation

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Authors: Irtaza M. Syed, Kaamran Raahemifar

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In this paper, we present a comparative assessment of Space Vector Pulse Width Modulation (SVPWM) and Model Predictive Control (MPC) for two-level three phase (2L-3P) Voltage Source Inverter (VSI). VSI with associated system is subjected to both control techniques and the results are compared. Matlab/Simulink was used to model, simulate and validate the control schemes. Findings of this study show that MPC is superior to SVPWM in terms of total harmonic distortion (THD) and implementation.

Keywords: voltage source inverter, space vector pulse width modulation, model predictive control, comparison

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Authors: P. Ghann, J. Shiguang, C. Zhou

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Access control is one of the most challenging issues facing information security. Access control is defined as, the ability to permit or deny access to a particular computational resource or digital information by an unauthorized user or subject. The concept of usage control (UCON) has been introduced as a unified approach to capture a number of extensions for access control models and systems. In UCON, an access decision is determined by three factors: Authorizations, obligations and conditions. Attribute mutability and decision continuity are two distinct characteristics introduced by UCON for the first time. An observation of UCON components indicates that, the components are predefined and static. In this paper, we propose a new and flexible model of usage control for the creation and elimination of some of these components; for example new objects, subjects, attributes and integrate these with the original UCON model. We also propose a model for concurrent usage scenarios in UCON.

Keywords: access control, concurrency, digital container, usage control

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Authors: A. Boualouch, A. Frigui, T. Nasser, A. Essadki, A.Boukhriss

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This work deals with the vector control of the active and reactive powers of a Double-Fed Induction generator DFIG used as a wind generator by the polynomial RST controller. The control of the statoric power transfer between the machine and the grid is achieved by acting on the rotor parameters and control is provided by the polynomial controller RST. The performance and robustness of the controller are compared with PI controller and evaluated by simulation results in MATLAB/simulink.

Keywords: DFIG, RST, vector control, wind turbine

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Authors: Muhammad Bilal, Adil Ahmed

Abstract:

This study proposes an approach for electrical induction motor predictive maintenance utilizing machine learning algorithms. On the basis of a study of temperature data obtained from sensors put on the motor, the goal is to predict motor failures. The proposed models are trained to identify whether a motor is defective or not by utilizing machine learning algorithms like Support Vector Machines (SVM) and K-Nearest Neighbors (KNN). According to a thorough study of the literature, earlier research has used motor current signature analysis (MCSA) and vibration data to forecast motor failures. The temperature signal methodology, which has clear advantages over the conventional MCSA and vibration analysis methods in terms of cost-effectiveness, is the main subject of this research. The acquired results emphasize the applicability and effectiveness of the temperature-based predictive maintenance strategy by demonstrating the successful categorization of defective motors using the suggested machine learning models.

Keywords: predictive maintenance, electrical induction motors, machine learning, temperature signal methodology, motor failures

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Authors: Natural Frequency Analysis of a Porous Functionally Graded Shaft System

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The vibration characteristics of a functionally graded (FG) rotor model having porosities and micro-voids is investigated using three-dimensional finite element analysis. The FG shaft is mounted with a steel disc located at the midspan. The shaft ends are supported on isotropic bearings. The FG material is composed of a metallic (stainless-steel) and ceramic phase (zirconium oxide) as its constituent phases. The layer wise material property variation is governed by power law. Material property equations are developed for the porosity modelling. Python code is developed to assign the material properties to each layer including the effect of porosities. ANSYS commercial software is used to extract the natural frequencies and whirl frequencies for the FG shaft system. The obtained results show the influence of porosity volume fraction and power-law index, on the vibration characteristics of the ceramic-based FG shaft system.

Keywords: Finite element method, Functionally graded material, Porosity volume fraction, Power law

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