Search results for: Dynamic load control

Authors: A. H. Elkholy, A. H. Falah

Abstract:

A new approach has been developed to estimate the load share and distribution of worm gear drives, and to calculate the instantaneous tooth meshing stiffness. In the approach, the worm gear drive was modelled as a series of spur gear slices, and each slice was analyzed separately using the well-established formulae of spur gear loading and stresses. By combining the results obtained for all slices, the entire envolute worm gear set loading and stressing was obtained. The geometric modelling method presented allows tooth elastic deformation and tooth root stresses of worm gear drives under different load conditions to be investigated. Based on the slicing method introduced in this study, the instantaneous meshing stiffness and load share are obtained. In comparison with existing methods, this approach has both good analysis accuracy and less computing time.

Keywords: Gear, load/stress distribution, worm, wheel, tooth stiffness, contact line.

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Authors: A. K. Kamath, N. M. Singh, R. Pasumarthy

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This paper investigates the control of a bouncing ball using Model Predictive Control. Bouncing ball is a benchmark problem for various rhythmic tasks such as juggling, walking, hopping and running. Humans develop intentions which may be perceived as our reference trajectory and tries to track it. The human brain optimizes the control effort needed to track its reference; this forms the central theme for control of bouncing ball in our investigations.

Keywords: Bouncing Ball, impact dynamics, intermittent control, model predictive control.

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Authors: Ernst D. Schmitter

Abstract:

There is increasing evidence that earthquakes produce electromagnetic signals observable at the surface in the extremely low to very low freqency (ELF - VLF) range often in advance to the main event. These precursors are candidates for prediction purposes. Laboratory experiments con´¼ürm that material under load emits an electromagnetic signature, the detailed generation mechanisms how- ever are not well understood yet.

Keywords: Earthquakes, ELF, EM signals from material under load, signal propagation in conductors.

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Authors: Yong-can Cao, Wei-dong Zhang

Abstract:

To deal with random delays in Networked Control System (NCS), Modified Fuzzy PID Controller is introduced in this paper to implement real-time control adaptively. Via adjusting the control signal dynamically, the system performance is improved. In this paper, the design process and the ultimate simulation results are represented. Finally, examples and corresponding comparisons prove the significance of this method.

Keywords: Fuzzy Control, Networked Control System, PID, Random Delays

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Authors: M. Reza Bagerzadeh Karimi, M. Mahdi Bagerzadeh Karimi

Abstract:

In the present paper, active control system is used in different heights of the building and the most effective part was studied where the active control system is applied. The mathematical model of the building is established in MATLAB and in order to active control the system FLC method was used. Three different locations of the building are chosen to apply active control system, namely at the lowest story, the middle height of the building, and at the highest point of the building with TMD system. The equation of motion was written for high rise building and it was solved by statespace method. Also passive control was used with Tuned Mass Damper (TMD) at the top floor of the building to show the robustness of FLC method when compared with passive control system.

Keywords: Fuzzy Logic Controller (FLC), Tuned Mass Damper(TMD), Active control, passive control

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Authors: Yin Yin Phyo, Tun Lin Naing

Abstract:

In this paper, the average input current mode control is proposed for two-phase interleaved boost converter with two separate input inductors operating in continuous conduction mode (CCM). The required mathematical model is obtained from the equivalent circuits of its different four modes of operation. The small ripple approximation is derived to find the transfer functions from dynamic model using switching function. In average input current mode control, the inner current loop and outer voltage loop are designed with PI controller using bode analysis. Anti-windup structure is applied for PI controllers in control system. Moreover, the simulation work is carried out by MATLAB/Simulink. And, the hardware prototype is implemented by using low-cost microcontroller Arduino Nano. Finally, the laboratory prototype, available from the local market, is constructed to validate the mathematical model. The results show that the output voltage response is the faster rise time and settling time with acceptable overshoot.

Keywords: Average input current mode control, interleaved boost converter, low-cost microcontroller, PI controller, switching function.

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Authors: Seyed Abolhasan Naeini, Mohammad Hossein Zade

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This article is an attempt to present a numerically study of the behaviour of an eccentrically loaded circular footing resting on sand to determine ‎its ultimate bearing capacity. A surface circular footing of diameter 12 cm (D) was used as ‎shallow foundation. For this purpose, three dimensional models consist of foundation, and medium sandy soil was modelled by ABAQUS software. Bearing capacity of footing was evaluated and the ‎effects of the load eccentricity on bearing capacity, its settlement, and modulus of subgrade reaction were studied. Three different values of load eccentricity with equal space from inside the core on the core boundary and outside the core boundary, which were respectively e=0.75, 1.5, and 2.25 cm, were considered. The results show that by increasing the load eccentricity, the ultimate load and the ‎modulus of subgrade reaction decreased.

Keywords: Circular foundation, eccentric loading, sand, modulus of subgrade reaction.

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Authors: Mário C. Ricci

Abstract:

An alternative iterative computational procedure is proposed for internal normal ball loads calculation in statically loaded single-row, angular-contact ball bearings, subjected to a known thrust load, which is applied in the inner ring at the geometric bearing center line. An accurate method for curvature radii at contacts with inner and outer raceways in the direction of the motion is used. Numerical aspects of the iterative procedure are discussed. Numerical examples results for a 218 angular-contact ball bearing have been compared with those from the literature. Twenty figures are presented showing the geometrical features, the behavior of the convergence variables and the following parameters as functions of the thrust load: normal ball loads, contact angle, distance between curvature centers, and normal ball and axial deflections.

Keywords: Ball, Bearing, Static, Load, Iterative, Numerical, Method.

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Authors: Ali Zifan, Sohrab Saberi, Mohammad Hassan Moradi, Farzad Towhidkhah

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Electrocardiogram (ECG) segmentation is necessary to help reduce the time consuming task of manually annotating ECG's. Several algorithms have been developed to segment the ECG automatically. We first review several of such methods, and then present a new single lead segmentation method based on Adaptive piecewise constant approximation (APCA) and Piecewise derivative dynamic time warping (PDDTW). The results are tested on the QT database. We compared our results to Laguna's two lead method. Our proposed approach has a comparable mean error, but yields a slightly higher standard deviation than Laguna's method.

Keywords: Adaptive Piecewise Constant Approximation, Dynamic programming, ECG segmentation, Piecewise Derivative Dynamic Time Warping.

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Authors: Young-Jun You, Ki-Tae Park, Kyu-Wan Lee

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Since prestressed concrete members rely on the tensile strength of the prestressing strands to resist loads, loss of even few them could result catastrophic. Therefore, it is important to measure present residual prestress force. Although there are some techniques for obtaining present prestress force, some problems still remain. One method is to install load cell in front of anchor head but this may increase cost. Load cell is a transducer using the elastic material property. Anchor head is also an elastic material and this might result in monitoring monitor present prestress force. Features of fiber optic sensor such as small size, great sensitivity, high durability can assign sensing function to anchor head. This paper presents the concept of smart anchor head which acts as load cell and experiment for the applicability of it. Test results showed the smart anchor head worked good and strong linear relationship between load and response.

Keywords: SHM, prestress force, anchor head, fiber optic sensor

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Authors: Aleksander V. Zakharov, Marat R. Bogdanov, Ramil F. Malikov, Irina N. Dumchikova

Abstract:

Classification of persecution movement laws is proposed. Modes of persecution in number of specific cases were researched. Modes of movement control using GLONASS/GPS are discussed

Keywords: Controlled Dynamic Motion, Unmanned Aerial Vehicles, GPS.

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Authors: Azad A. Mohammed, Gulan B. Hassan

Abstract:

Analytical procedure was carried out in this paper to calculate the ultimate load capacity of reinforced concrete corbels strengthened or repaired externally with CFRP sheets. Strut and tie method and shear friction method proposed earlier for analyzing reinforced concrete corbels were modified to incorporate the effect of external CFRP sheets bonded to the corbel. The points of weakness of any method that lead to an inaccuracy, especially when overestimating test results were checked and discussed. Comparison of prediction with the test data indicates that the ratio of test / calculated ultimate load is 0.82 and 1.17 using strut and tie method and shear friction method, respectively. If the limits of maximum shear stress is followed, the calculated ultimate load capacity using shear friction method was found to underestimates test data considerably.

Keywords: Corbel, Strengthening, Strut and Tie Model, Shear Friction

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Authors: Teka Haile, Behailu Hawulte, Solomon Alemayehu

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Background: HIV virological failure still remains a problem in HV/AIDS treatment and care. This study aimed to describe the prevalence and identify the factors associated with viral non-suppression among HIV-positive adult patients on antiretroviral therapy in Woliso Town, Oromia, Ethiopia. Methods: A retrospective cross-sectional study was conducted among 424 HIV-positive patient’s attending antiretroviral therapy (ART) in Woliso Town during the period from August 25, 2020 to August 30, 2020. Data collected from patient medical records were entered into Epi Info version 2.3.2.1 and exported to SPSS version 21.0 for analysis. Logistic regression analysis was done to identify factors associated with viral load non-suppression, and statistical significance of odds ratios were declared using 95% confidence interval and p-value < 0.05. Results: A total of 424 patients were included in this study. The mean age (± SD) of the study participants was 39.88 (± 9.995) years. The prevalence of HIV viral load non-suppression was 55 (13.0%) with 95% CI (9.9-16.5). Second-line ART treatment regimen (Adjusted Odds Ratio (AOR) = 8.98, 95% Confidence Interval (CI): 2.64, 30.58) and routine viral load testing (AOR = 0.01, 95% CI: 0.001, 0.02) were significantly associated with virological non-suppression. Conclusion: Virological non-suppression was high, which hinders the achievement of the third global 95 target. The second-line regimen and routine viral load testing were significantly associated with virological non-suppression. It suggests the need to assess the effectiveness of antiretroviral drugs for epidemic control. It also clearly shows the need to decentralize third-line ART treatment for those patients in need.

Keywords: Virological non-suppression, HIV-positive, ART, Woliso Town, Ethiopia.

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Authors: M. Ali, K. Alam, E. Ohioma

Abstract:

This paper presents a numerical investigation on the behavior of fiber reinforced polymer composite tubes (FRP) under thermomechanical coupled loading using finite element software ABAQUS and a special add-on subroutine, CZone. Three cases were explored; pure mechanical loading, pure thermal loading, and coupled thermomechanical loading. The failure index (Tsai-Wu) under all three loading cases was assessed for all plies in the tube walls. The simulation results under pure mechanical loading showed that composite tube failed at a tensile load of 3.1 kN. However, with the superposition of thermal load on mechanical load on the composite tube, the failure index of the previously failed plies in tube walls reduced significantly causing the tube to fail at 6 kN. This showed 93% improvement in the load carrying capacity of the composite tube in present study. The increase in load carrying capacity was attributed to the stress effects of the coefficients of thermal expansion (CTE) on the laminate as well as the inter-lamina stresses induced due to the composite stack layup.

Keywords: Thermal, mechanical, composites, square tubes.

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Authors: A. Safaee, M. S. Mehrabani, M. B. Menhaj, V. Mousavi, S. Z. Moussavi

Abstract:

Monocopter is a single-wing rotary flying vehicle which has the capability of hovering. This flying vehicle includes two dynamic parts in which more efficiency can be expected rather than other Micro UAVs due to the extended area of wing compared to its fuselage. Low cost and simple mechanism in comparison to other vehicles such as helicopter are the most important specifications of this flying vehicle. In the previous paper we discussed the introduction of the final system but in this paper, the experimental design process of Monocopter and its control algorithm has been investigated in general. Also the editorial bugs in the previous article have been corrected and some translational ambiguities have been resolved. Initially by constructing several prototypes and carrying out many flight tests the main design parameters of this air vehicle were obtained by experimental measurements. Eventually the required main monocopter for this project was constructed. After construction of the monocopter in order to design, implementation and testing of control algorithms first a simple optic system used for determining the heading angle. After doing numerous tests on Test Stand, the control algorithm designed and timing of applying control inputs adjusted. Then other control parameters of system were tuned in flight tests. Eventually the final control system designed and implemented using the AHRS sensor and the final operational tests performed successfully.

Keywords: Monocopter, Flap, Heading Angle, AHRS, Cyclic, Photo Diode.

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Authors: Neha Khanduja

Abstract:

This paper presents a comparative analysis of continuously stirred tank reactor (CSTR) control based on adaptive control and optimal tuning of PID control based on particle swarm optimization. In the design of adaptive control, Model reference adaptive control (MRAC) scheme is used, in which the adaptation law have been developed by MIT rule & Lyapunov’s rule. In PSO control parameters of PID controller is tuned by using the concept of particle swarm optimization to get optimized operating point for minimum integral square error (ISE) condition. The results show the adjustment of PID parameters converting into the optimal operating point and the good control response can be obtained by the PSO technique.

Keywords: Model reference adaptive control (MRAC), optimal control, particle swarm optimization (PSO).

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Authors: Tobias Teich, Danny Szendrei, Markus Schrader, Franziska Jahn, Susan Franke

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The increasing demand for sufficient and clean energy forces industrial and service companies to align their strategies towards efficient consumption. This trend refers also to the residential building sector. There, large amounts of energy consumption are caused by house and facility heating. Many of the operated hot water heating systems lack hydraulic balanced working conditions for heat distribution and –transmission and lead to inefficient heating. Through hydraulic balancing of heating systems, significant energy savings for primary and secondary energy can be achieved. This paper addresses the use of KNX-technology (Smart Buildings) in residential buildings to ensure a dynamic adaption of hydraulic system's performance, in order to increase the heating system's efficiency. In this paper, the procedure of heating system segmentation into hydraulically independent units (meshes) is presented. Within these meshes, the heating valve are addressed and controlled by a central facility server. Feasibility criteria towards such drivers will be named. The dynamic hydraulic balance is achieved by positioning these valves according to heating loads, that are generated from the temperature settings in the corresponding rooms. The energetic advantages of single room heating control procedures, based on the application FacilityManager, is presented.

Keywords: building automation, dynamic hydraulic balance, energy savings, VPN-networks.

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Authors: A. Jomartov, A. Tuleshov, B. Tultaev

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One of the main tasks in the development of textile machinery is to increase the rapidity of automatic looms, and consequently, their productivity. With increasing automatic loom speeds, the dynamic loads on their separate mechanisms and moving joints sharply increase. Dynamic research allows us to determine the weakest mechanisms of the automatic loom. The modern automatic loom consists of a large number of structurally different mechanisms. These are cam, lever, gear, friction and combined cyclic mechanisms. The modern automatic loom contains various mechatronic devices: A device for the automatic removal of faulty weft, electromechanical drive warp yarns, electronic controllers, servos, etc. In the paper, we consider the multibody dynamic model of the automatic loom on the software complex SimulationX. SimulationX is multidisciplinary software for modeling complex physical and technical facilities and systems. The multibody dynamic model of the automatic loom allows consideration of: The transition processes, backlash at the joints and nodes, the force of resistance and electric motor performance.

Keywords: Automatic loom, dynamics, model, multibody, SimulationX.

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Authors: Ali Al-Zughaibi, Huw Davies

Abstract:

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

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

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Authors: Le Linh, Truong Nguyen Luan Vu, Le Hieu Giang

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In this work, the IMC-PID controller cascaded filter based on Internal Model Control (IMC) scheme is systematically proposed for the simplified decoupling control system. The simplified decoupling is firstly introduced for multivariable processes by using coefficient matching to obtain a stable, proper, and causal simplified decoupler. Accordingly, transfer functions of decoupled apparent processes can be expressed as a set of n equivalent independent processes and then derived as a ratio of the original open-loop transfer function to the diagonal element of the dynamic relative gain array. The IMC-PID controller in series with filter is then directly employed to enhance the overall performance of the decoupling control system while avoiding difficulties arising from properties inherent to simplified decoupling. Some simulation studies are considered to demonstrate the simplicity and effectiveness of the proposed method. Simulations were conducted by tuning various controllers of the multivariate processes with multiple time delays. The results indicate that the proposed method consistently performs well with fast and well-balanced closed-loop time responses.

Keywords: Coefficient matching method, internal model control scheme, PID controller cascaded filter, simplified decoupler.

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Authors: Yun Bai

Abstract:

Representing objects in a dynamic domain is essential in commonsense reasoning under some circumstances. Classical logics and their nonmonotonic consequences, however, are usually not able to deal with reasoning with dynamic domains due to the fact that every constant in the logical language denotes some existing object in the static domain. In this paper, we explore a logical formalization which allows us to represent nonexisting objects in commonsense reasoning. A formal system named N-theory is proposed for this purpose and its possible application in computer security is briefly discussed.

Keywords: knowledge representation and reasoning, commonsensereasoning, computer security

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Authors: Omid A. Zargar

Abstract:

Material damages dynamic analysis is difficult to deal with different material geometry and mechanism. In addition, it is difficult to measure the dynamic behavior of cracks, debond and delamination inside the material. Different simulation methods are developed in recent years for different physical features of mechanical systems like vibration and acoustic. Nonlinear fractures are analyzed and identified for different locations in this paper. The main idea of this work is to perform dynamic analysis on different types of materials (from normal homogeneous material to complex composite laminates). Technical factors like cracks, voids, interfaces and the damages’ locations are evaluated. In this project the modal analysis is performed on different types of materials. The results could be helpful in finding modal frequencies, natural frequencies, Time domain and fast Fourier transform (FFT) in industrial applications.

Keywords: Finite element method, dynamic analysis, vibration and acoustic, composite, crack, delamination.

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Authors: Duy M. P. Vo, Cornelia Sennewald, Gerald Hoffmann, Chokri Cherif

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The development of solutions to improve the resistance of buildings to short-term dynamic loads, particularly impact load, is driven by the urgent demand worldwide on securing human life and critical infrastructures. The research training group GRK 2250/1 aims to develop mineral-bonded composites that allow the fabrication of thin-layered strengthening layers providing available concrete members with enhanced impact resistance. This paper presents the development of 3D woven wire cellular structures that can be used as innovative reinforcement for targeted composites. 3D woven wire cellular structures are truss-like architectures that can be fabricated in an automatized process with a great customization possibility. The specific architecture allows this kind of structures to have good load bearing capability and forming behavior, which is of great potential to give strength against impact loading. An appropriate combination of topology and material enables an optimal use of thin-layered reinforcement in concrete constructions.

Keywords: 3D woven cellular structures, ductile behavior, energy absorption, fiber-based reinforced concrete, impact resistant.

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Authors: Ashkan Shafee, Masoud Ghodrati, Ahmad Fahimifar

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Pervious concrete combines considerable permeability with adequate strength, which makes it very beneficial in pavement construction and also in ground improvement projects. In this paper, a single pervious concrete pile subjected to vertical and lateral loading is analysed using a verified three dimensional finite element code. A parametric study was carried out in order to investigate load bearing capacity of a single unreinforced pervious concrete pile in saturated soft soil and also gain insight into the failure mechanism of this rather new soil improvement technique. The results show that concrete damaged plasticity constitutive model can perfectly simulate the highly brittle nature of the pervious concrete material and considering the computed vertical and horizontal load bearing capacities, some suggestions have been made for ground improvement projects.

Keywords: Concrete damaged plasticity, ground improvement, load bearing capacity, pervious concrete pile.

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Authors: Ching-Tsan Chiang, Sheng-Jie Yang, Jing-Kai Huang

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The purpose of this research is to develop and apply the RSCMAC to enhance the dynamic accuracy of Global Positioning System (GPS). GPS devices provide services of accurate positioning, speed detection and highly precise time standard for over 98% area on the earth. The overall operation of Global Positioning System includes 24 GPS satellites in space; signal transmission that includes 2 frequency carrier waves (Link 1 and Link 2) and 2 sets random telegraphic codes (C/A code and P code), on-earth monitoring stations or client GPS receivers. Only 4 satellites utilization, the client position and its elevation can be detected rapidly. The more receivable satellites, the more accurate position can be decoded. Currently, the standard positioning accuracy of the simplified GPS receiver is greatly increased, but due to affected by the error of satellite clock, the troposphere delay and the ionosphere delay, current measurement accuracy is in the level of 5~15m. In increasing the dynamic GPS positioning accuracy, most researchers mainly use inertial navigation system (INS) and installation of other sensors or maps for the assistance. This research utilizes the RSCMAC advantages of fast learning, learning convergence assurance, solving capability of time-related dynamic system problems with the static positioning calibration structure to improve and increase the GPS dynamic accuracy. The increasing of GPS dynamic positioning accuracy can be achieved by using RSCMAC system with GPS receivers collecting dynamic error data for the error prediction and follows by using the predicted error to correct the GPS dynamic positioning data. The ultimate purpose of this research is to improve the dynamic positioning error of cheap GPS receivers and the economic benefits will be enhanced while the accuracy is increased.

Keywords: Dynamic Error, GPS, Prediction, RSCMAC.

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Authors: B. Chetti, W. A. Crosby

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The work described in this paper is an investigation of the static and dynamic characteristics of two-lobe journal bearings taking into consideration the thermal effects. A thermo-hydrodynamic solution of a finite two-lobe journal bearing is performed by solving the generalized form Reynolds equation with the energy equation, taking into consideration viscosity variation across the film thickness. The static and dynamic characteristics were numerically obtained. The results are evaluated for different values of viscosity-temperature coefficient and Peclet number. The results show that considering the thermal effects in the solution of the two-lobe journal bearing has a marked on the study of its stability.

Keywords: Two-lobe bearing, thermal effect, static and dynamic characteristics.

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Authors: M. Nirmala

Abstract:

Power quality in terms of power factor, THD and precisely regulated output voltage are the major key factors for efficient operation of power electronic converters. This paper presents an easy and effective active wave shaping control scheme for the pulsed input current drawn by the uncontrolled diode bridge rectifier thereby achieving power factor nearer to unity and also satisfying the THD specifications. It also regulates the output DC-bus voltage. CCM boost power factor correction with constant frequency operation features smaller inductor current ripple resulting in low RMS currents on inductor and switch thus leading to low electromagnetic interference. The objective of this work is to develop an active PFC control circuit using CCM boost converter implementing variable duty cycle control. The proposed scheme eliminates inductor current sensing requirements yet offering good performance and satisfactory results for maintaining the power quality. Simulation results have been presented which covers load changes also.

Keywords: CCM Boost converter, Power factor Correction, Total harmonic distortion, Variable Duty Cycle.

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Authors: Dj. Cherifi, Y. Miloud, A. Tahri

Abstract:

The primary objective of this paper is to elimination of the problem of sensitivity to parameter variation of induction motor drive. The proposed sensorless strategy is based on an algorithm permitting a better simultaneous estimation of the rotor speed and the stator resistance including an adaptive mechanism based on the lyaponov theory. To study the reliability and the robustness of the sensorless technique to abnormal operations, some simulation tests have been performed under several cases.

The proposed sensorless vector control scheme showed a good performance behavior in the transient and steady states, with an excellent disturbance rejection of the load torque.

Keywords: Induction Motor Drive, field-oriented control, adaptive speed observer, stator resistance estimation.

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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: Arafet Bouaicha, Hatem Allegui, Amar Rouane, El-Hassane Aglzim, Abdelkader Mami

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In order to further understand the behavior of PEM fuel cell and optimize their performance, it is necessary to perform measurements in real time. The internal impedance measurement by electrochemical impedance spectroscopy (EIS) is of great importance. In this work, we present the impedance measurement method of a PEM fuel cell by electrochemical impedance spectroscopy method and the realization steps of electronic load for this measuring technique implementation. The theoretical results are obtained from the simulation of software PSPICE® and experimental tests are carried out using the Ballard Nexa™ PEM fuel cell system.

Keywords: Electronic load, MOS transistor, PEM fuel cell, Impedance measurement, Electrochemical Impedance Spectroscopy (EIS).

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