Search results for: variational mode decomposition

Authors: Phongsak Phakamach

Abstract:

A DC servomotor position control system using a Fuzzy Logic Sliding mode Model Following Control or FLSMFC approach is presented. The FLSMFC structure consists of an integrator and variable structure system. The integral control is introduced into it in order to eliminated steady state error due to step and ramp command inputs and improve control precision, while the fuzzy control would maintain the insensitivity to parameter variation and disturbances. The FLSMFC strategy is implemented and applied to a position control of a DC servomotor drives. Experimental results indicated that FLSMFC system performance with respect to the sensitivity to parameter variations is greatly reduced. Also, excellent control effects and avoids the chattering phenomenon.

Keywords: Sliding mode model following control, fuzzy logic, DC servomotor.

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Authors: Rakesh Kumar, Fatima Electricwala

Abstract:

One of the major thrusts of the Bus Rapid Transit System is to reduce the commuter’s dependency on private vehicles and increase the shares of public transport to make urban transportation system environmentally sustainable. In this study, commuter mode choice analysis is performed that examines behavioral responses to the proposed Bus Rapid Transit System (BRTS) in Surat, with estimation of the probable shift from private mode to public mode. Further, evaluation of the BRTS scenarios, using Surat’s transportation ecological footprint was done. A multi-modal simulation model was developed in Biogeme environment to explicitly consider private users behaviors and non-linear environmental impact. The data of the different factors (variables) and its impact that might cause modal shift of private mode users to proposed BRTS were collected through home-interview survey using revealed and stated preference approach. A multi modal logit model of mode-choice was then calibrated using the collected data and validated using proposed sample. From this study, a set of perception factors, with reliable and predictable data base, to explain the variation in modal shift behaviour and their impact on Surat’s ecological environment has been identified. A case study of the proposed BRTS connecting the Surat Industrial Hub to the coastal area is provided to illustrate the approach.

Keywords: BRTS, Private Modes, Mode choice models, Ecological footprint.

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Authors: M. Alqhatani, S. Bajwa, S. Setunge

Abstract:

Metropolitan areas have suffered from traffic problems, which have steadily increased in many monocentric cities. Urban expansion, population growth, and road network development have resulted in a structural shift toward urban sprawl, increasing commuters’ dependence on private modes of transport. This paper aims to model the influence of socioeconomic and land-use factors on mode choice using a multinomial and nested logit model. Land-use patterns—such as residential, commercial, retail, educational and employment related—affect the choice of mode and destination in the short and medium term. Socioeconomic factors—such as age, gender, income, household size, and house type—also affect choice, while residential location is affected in the long term. Riyadh in Saudi Arabia and Melbourne in Australia were chosen as case studies. Riyadh is a car-dependent city with limited public transport, whereas Melbourne has good public transport but an increase in car dependence. Aggregate level land-use data and disaggregate level individual, household, and journey-to-work data are used to determine the effects of land use and socioeconomic factors on mode choice. The model results determined that urban sprawl is the main factor that affects mode choice, income, and house type.

Keywords: Socioeconomic, land use, mode choice, multinomial logit and nested logit.

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Authors: M. Kidouche, H. Habbi, M. Zelmat, S. Grouni

Abstract:

In analyzing large scale nonlinear dynamical systems, it is often desirable to treat the overall system as a collection of interconnected subsystems. Solutions properties of the large scale system are then deduced from the solution properties of the individual subsystems and the nature of the interconnections. In this paper a new approach is proposed for the stability analysis of large scale systems, which is based upon the concept of vector Lyapunov functions and the decomposition methods. The present results make use of graph theoretic decomposition techniques in which the overall system is partitioned into a hierarchy of strongly connected components. We show then, that under very reasonable assumptions, the overall system is stable once the strongly connected subsystems are stables. Finally an example is given to illustrate the constructive methodology proposed.

Keywords: Comparison principle, First integral, Large scale system, Lyapunov stability.

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Authors: Hiroyuki Nishida, Taku Nonomura, Takashi Abe

Abstract:

Wall-surface jet induced by the dielectric barrier discharge (DBD) has been proposed as an actuator for active flow control in aerodynamic applications. Discharge plasma evolution of the DBD plasma actuator was simulated based on a simple fluid model, in which the electron, one type of positive ion and negative ion were taken into account. Two-dimensional simulation was conducted, and the results are in agreement with the insights obtained from experimental studies. The simulation results indicate that the discharge mode changes depending on applied voltage slope; when the applied voltage is positive-going with high applied voltage slope, the corona-type discharge mode turns into the streamer-type discharge mode and the threshold voltage slope is around 300 kV/ms in this simulation. The characteristics of the electrohydrodynamic (EHD) force, which is the source of the wall-surface jet, also change depending on the discharge mode; the tentative peak value of the EHD force during the positive-going voltage phase is saturated by the periodical formation of the streamer-type discharge.

Keywords: Dielectric barrier discharge, Plasma actuator, Fluid simulation.

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Authors: H. Bouadi, M. Tadjine

Abstract:

In this paper; we are interested in dynamic modelling of quadrotor while taking into account the high-order nonholonomic constraints as well as the various physical phenomena, which can influence the dynamics of a flying structure. These permit us to introduce a new state-space representation and new control scheme. We present after the development and the synthesis of a stabilizing control laws design based on sliding mode in order to perform best tracking results. It ensures locally asymptotic stability and desired tracking trajectories. Nonlinear observer is then synthesized in order to estimate the unmeasured states and the effects of the external disturbances such as wind and noise. Finally simulation results are also provided in order to illustrate the performances of the proposed controllers.

Keywords: Dynamic modelling, nonholonomic constraints, sliding mode, nonlinear observer.

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Authors: T. Thosdeekoraphat, S. Summart, C. Saetiaw, S. Santalunai, C. Thongsopa

Abstract:

This article presents a current-mode universal biquadratic filter. The proposed circuit can apparently provide standard functions of the biquad filter: low-pass, high-pass, bandpass, band-reject and all-pass functions. The circuit uses 4 current controlled transconductance amplifiers (CCTAs) and 2 grounded capacitors. In addition, the pole frequency and quality factor can be adjusted by electronic method by adjusting the bias currents of the CCTA. The proposed circuit uses only grounded capacitors without additional external resistors, the proposed circuit is considerably appropriate to further developing into an integrated circuit. The results of PSPICE simulation program are corresponding to the theoretical analysis.

Keywords: Resistor-less, Current-mode, Biquad filter, CCTA.

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Authors: M-M. Mohamed Ahmed, Nacer K. M’Sirdi, Aziz Naamane

Abstract:

In this paper, a longitudinal and lateral control approach based on a nonlinear observer is proposed for a convoy of autonomous vehicles to follow a desired trajectory. To authors best knowledge, this topic has not yet been sufficiently addressed in the literature for the control of multi vehicles. The modeling of the convoy of the vehicles is revisited using a robotic method for simulation purposes and control design. With these models, a sliding mode observer is proposed to estimate the states of each vehicle in the convoy from the available sensors, then a sliding mode control based on this observer is used to control the longitudinal and lateral movement. The validation and performance evaluation are done using the well-known driving simulator Scanner-Studio. The results are presented for different maneuvers of 5 vehicles.

Keywords: Autonomous vehicles, convoy, nonlinear control, nonlinear observer, sliding mode.

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Authors: Zhenguo Vincent Chia, Sheung Yan Simon Ng, Minkyu Je

Abstract:

This paper presents CMOS Current Mode Logic (CML) circuits for a high speed Digital to Analog Converter (DAC) using standard CMOS 65nm process. The CML circuits have the propagation delay advantage over its conventional CMOS counterparts due to smaller output voltage swing and tunable bias current. The CML circuits proposed in this paper can achieve a maximum propagation delay of only 9.3ps, which can satisfy the stringent requirement for the 5 GHz high speed DAC application. Another advantage for CML circuits is its dynamic symmetry characteristic resulting in a reduction of an additional inverter. Simulation results show that the proposed CML circuits can operate from 1.08V to 1.3V with temperature ranging from -40 to +120°C.

Keywords: Conventional, Current Mode Logic, DAC, Decoder

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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: Fatemeh Azimi, Razeeh Sadat Aboutalebi, Amir Abbas Najafi

Abstract:

In this paper the multi-mode resource-constrained project scheduling problem with discounted cash flows is considered. Minimizing the makespan and maximization the net present value (NPV) are the two common objectives that have been investigated in the literature. We apply one evolutionary algorithm named multiobjective particle swarm optimization (MOPSO) to find Pareto front solutions. We used standard sets of instances from the project scheduling problem library (PSPLIB). The results are computationally compared respect to different metrics taken from the literature on evolutionary multi-objective optimization.

Keywords: Evolutionary multi-objective optimization makespan, multi-mode, resource constraint, net present value.

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Authors: E. Farshidi

Abstract:

In this paper, based on a novel synthesis, a set of new simplified circuit design to implement the linguistic-hedge operations for adjusting the fuzzy membership function set is presented. The circuits work in current-mode and employ floating-gate MOS (FGMOS) transistors that operate in weak inversion region. Compared to the other proposed circuits, these circuits feature severe reduction of the elements number, low supply voltage (0.7V), low power consumption (<200nW), immunity from body effect and wide input dynamic range (>60dB). In this paper, a set of fuzzy linguistic hedge circuits, including absolutely, very, much more, more, plus minus, more or less and slightly, has been implemented in 0.18 mm CMOS process. Simulation results by Hspice confirm the validity of the proposed design technique and show high performance of the circuits.

Keywords: Current-mode, Linguistic-Hedge, Fuzzy Logic, lowpower

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Authors: Nilar Win Kyaw

Abstract:

In cryptography, confusion and diffusion are very important to get confidentiality and privacy of message in block ciphers and stream ciphers. There are two types of network to provide confusion and diffusion properties of message in block ciphers. They are Substitution- Permutation network (S-P network), and Feistel network. NLFS (Non-Linear feedback stream cipher) is a fast and secure stream cipher for software application. NLFS have two modes basic mode that is synchronous mode and self synchronous mode. Real random numbers are non-deterministic. R-box (random box) based on the dynamic properties and it performs the stochastic transformation of data that can be used effectively meet the challenges of information is protected from international destructive impacts. In this paper, a new implementation of stochastic transformation will be proposed.

Keywords: S-P network, Feistel network, R-block, stochastic transformation

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Authors: Ulugbek Azimov, Eiji Tomita, Nobuyuki Kawahara, Sharul Sham Dol

Abstract:

The objective of this study is to investigate the combustion in a pilot-ignited supercharged dual-fuel engine, fueled with different types of gaseous fuels under various equivalence ratios. It is found that if certain operating conditions are maintained, conventional dual-fuel engine combustion mode can be transformed to the combustion mode with the two-stage heat release. This mode of combustion was called the PREMIER (PREmixed Mixture Ignition in the End-gas Region) combustion. During PREMIER combustion, initially, the combustion progresses as the premixed flame propagation and then, due to the mixture autoignition in the end-gas region, ahead of the propagating flame front, the transition occurs with the rapid increase in the heat release rate.

Keywords: Combustion, dual-fuel engine, end-gas autoignition, PREMIER.

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Authors: Hazem M. El-Bakry

Abstract:

Neural processors have shown good results for detecting a certain character in a given input matrix. In this paper, a new idead to speed up the operation of neural processors for character detection is presented. Such processors are designed based on cross correlation in the frequency domain between the input matrix and the weights of neural networks. This approach is developed to reduce the computation steps required by these faster neural networks for the searching process. The principle of divide and conquer strategy is applied through image decomposition. Each image is divided into small in size sub-images and then each one is tested separately by using a single faster neural processor. Furthermore, faster character detection is obtained by using parallel processing techniques to test the resulting sub-images at the same time using the same number of faster neural networks. In contrast to using only faster neural processors, the speed up ratio is increased with the size of the input image when using faster neural processors and image decomposition. Moreover, the problem of local subimage normalization in the frequency domain is solved. The effect of image normalization on the speed up ratio of character detection is discussed. Simulation results show that local subimage normalization through weight normalization is faster than subimage normalization in the spatial domain. The overall speed up ratio of the detection process is increased as the normalization of weights is done off line.

Keywords: Fast Character Detection, Neural Processors, Cross Correlation, Image Normalization, Parallel Processing.

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Authors: Francesco Marotti de Sciarra, Raffaele Barretta

Abstract:

Starting from nonlocal continuum mechanics, a thermodynamically new nonlocal model of Euler-Bernoulli nanobeams is provided. The nonlocal variational formulation is consistently provided and the governing differential equation for transverse displacement is presented. Higher-order boundary conditions are then consistently derived. An example is contributed in order to show the effectiveness of the proposed model.

Keywords: Bernoulli-Euler beams, Nanobeams, nonlocal elasticity.

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Authors: Mahdi Fakoor, Seyed Mohammad Navid Ghoreishi

Abstract:

Investigation of fracture of wood components can prevent from catastrophic failures. Created fracture process zone (FPZ) in crack tip vicinity has important effect on failure of cracked composite materials. In this paper, a failure criterion for fracture investigation of cracked wood specimens under mixed mode I/II loading is presented. This criterion is based on maximum strain energy release rate and material nonlinearity in the vicinity of crack tip due to presence of microcracks. Verification of results with available experimental data proves the coincidence of the proposed criterion with the nature of fracture of wood. To simplify the estimation of nonlinear properties of FPZ, a damage factor is also introduced for engineering and application purposes.

Keywords: Fracture criterion, mixed mode loading, damage zone, microcracks.

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Authors: Ashiq Rahman, Sunil Thapa, Shunyao Fan, Niloy K. Dutta

Abstract:

A 20-GHz and a 50-GHz pulse train are generated using a fiber ring laser setup that incorporates rational harmonic mode-locking (RHML). Two separate experiments were carried out using charcoal nanoparticles and graphene nanoparticles acting as saturable absorbers to reduce the pulse width generated from RHML. Autocorrelator trace shows that the pulse width is reduced from 5.6 ps to 3.2 ps using charcoal at 20 GHz, and to 2.7 ps using graphene at 50-GHz repetition rates, which agrees with the simulation findings. Numerical simulations have been carried out to study the effect of varying the linear and nonlinear absorbance parameters of both absorbers on output pulse widths. Experiments closely agree with the simulations.

Keywords: Fiber optics, fiber lasers, mode locking, saturable absorbers.

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Authors: Shun Horikoshi, Tohru Kawabe

Abstract:

This study presents performance analysis results of SMC (Sliding mode control) with changing the chattering functions applied to slip suppression problem of electric vehicles (EVs). In SMC, chattering phenomenon always occurs through high frequency switching of the control inputs. It is undesirable phenomenon and degrade the control performance, since it causes the oscillations of the control inputs. Several studies have been conducted on this problem by introducing some general saturation function. However, study about whether saturation function was really best and the performance analysis when using the other functions, weren’t being done so much. Therefore, in this paper, several candidate functions for SMC are selected and control performance of candidate functions is analyzed. In the analysis, evaluation function based on the trade-off between slip suppression performance and chattering reduction performance is proposed. The analyses are conducted in several numerical simulations of slip suppression problem of EVs. Then, we can see that there is no difference of employed candidate functions in chattering reduction performance. On the other hand, in slip suppression performance, the saturation function is excellent overall. So, we conclude the saturation function is most suitable for slip suppression sliding mode control.

Keywords: Sliding mode control, chattering function, electric vehicle, slip suppression, performance analysis.

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Authors: T. H. Young, Y. S. Ciou

Abstract:

The free and forced in-plane vibrations of axially moving plates are investigated in this work. The plate possesses an internal damping of which the constitutive relation obeys the Kelvin-Voigt model, and the excitations are arbitrarily distributed on two opposite edges. First, the equations of motion and the boundary conditions of the axially moving plate are derived. Then, the extended Ritz method is used to obtain discretized system equations. Finally, numerical results for the natural frequencies and the mode shapes of the in-plane vibration and the in-plane response of the moving plate subjected to arbitrary edge excitations are presented. It is observed that the symmetry class of the mode shapes of the in-plane vibration disperses gradually as the moving speed gets higher, and the u- and v-components of the mode shapes belong to different symmetry class. In addition, large response amplitudes having shapes similar to the mode shapes of the plate can be excited by the edge excitations at the resonant frequencies and with the same symmetry class of distribution as the u-components.

Keywords: Arbitrary edge excitations, axially moving plates, in-plane vibration, extended Ritz method.

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Authors: Jie Jin

Abstract:

In this paper, a new CMOS current-mode single input and multi-outputs (SIMO) universal filter and quadrature oscillator with a similar circuit are proposed. The circuits only consist of three Current differencing transconductance amplifiers (CDTA) and two grounded capacitors, which are resistorless, and they are suitable for monolithic integration. The universal filter uses minimum CDTAs and passive elements to realize SIMO type low-pass (LP), high-pass (HP), band-pass (BP) band-stop (BS) and all-pass (AP) filter functions simultaneously without any component matching conditions. The angular frequency (ω0) and the quality factor (Q) of the proposed filter can be electronically controlled and tuned orthogonal. By some modifications of the filter, a new current-mode four-phase quadrature oscillator (QO) can be obtained easily. The condition of oscillation (CO) and frequency of oscillation (FO) of the QO can be controlled electronically and independently through the bias current of the CDTAs, and it is suitable for variable frequency oscillator. Moreover, all the passive and active sensitivities of the circuits are low. SPICE simulation results are included to confirm the theory.

Keywords: Universal Filter, Quadrature Oscillator, Current mode, Current differencing transconductance amplifiers.

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Authors: Nadia Bensiali, Erik Etien, Amar Omeiri, Gerard Champenois

Abstract:

Adaptive observers used in sensorless control of induction motors suffer from instability especally in regenerating mode. In this paper, an optimal feed back gain design is proposed, it can reduce the instability region in the torque speed plane .

Keywords: Induction motor drive, adaptive observer, regenerating mode, stabilizing design.

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Authors: Yu-Sheng Lu, Chung-Hsin Cheng, Shuen-Shing Jan

Abstract:

This paper presents the design and implementation of a sliding-mod controller for tracking servo of optical disk drives. The tracking servo is majorly subject to two disturbance sources: radial run-out and shock. The lateral run-out disturbance is mostly repeatable, and a model of such disturbance is incorporated into the controller design to effectively compensate for it. Meanwhile, as a shock disturbance is usually non-repeatable and unpredictable, the sliding-mode controller is employed for its robustness to abrupt perturbations. As a result, a sliding-mode controller design based on the internal model principle is tailored for tracking servo of optical disk drives in order to deal with these two major disturbances. Experimental comparative studies are conducted to investigate the effectiveness of the specially designed controller.

Keywords: Mechatronics, optical disk drive, sliding-mode control, servo systems.

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Authors: Mohammad A. Bani-Khaled

Abstract:

In this work we use the Discrete Proper Orthogonal Decomposition transform to characterize the properties of coupled dynamics in thin-walled beams by exploiting numerical simulations obtained from finite element simulations. The outcomes of the will improve our understanding of the linear and nonlinear coupled behavior of thin-walled beams structures. Thin-walled beams have widespread usage in modern engineering application in both large scale structures (aeronautical structures), as well as in nano-structures (nano-tubes). Therefore, detailed knowledge in regard to the properties of coupled vibrations and buckling in these structures are of great interest in the research community. Due to the geometric complexity in the overall structure and in particular in the cross-sections it is necessary to involve computational mechanics to numerically simulate the dynamics. In using numerical computational techniques, it is not necessary to over simplify a model in order to solve the equations of motions. Computational dynamics methods produce databases of controlled resolution in time and space. These numerical databases contain information on the properties of the coupled dynamics. In order to extract the system dynamic properties and strength of coupling among the various fields of the motion, processing techniques are required. Time- Proper Orthogonal Decomposition transform is a powerful tool for processing databases for the dynamics. It will be used to study the coupled dynamics of thin-walled basic structures. These structures are ideal to form a basis for a systematic study of coupled dynamics in structures of complex geometry.

Keywords: Coupled dynamics, geometric complexity, Proper Orthogonal Decomposition (POD), thin walled beams.

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Authors: M. M. Karkhanehchi, A. Ammani

Abstract:

A simple analytical model has been developed to optimize biasing conditions for obtaining maximum linearity among lattice-matched, pseudomorphic and metamorphic HEMT types as well as enhancement and depletion HEMT modes. A nonlinear current-voltage model has been simulated based on extracted data to study and select the most appropriate type and mode of HEMT in terms of a given gate-source biasing voltage within the device so as to employ the circuit for the highest possible output current or voltage linear swing. Simulation results can be used as a basis for the selection of optimum gate-source biasing voltage for a given type and mode of HEMT with regard to a circuit design. The consequences can also be a criterion for choosing the optimum type or mode of HEMT for a predetermined biasing condition.

Keywords: Biasing, characteristic, linearity, simulation.

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Authors: Chen Wu, Lijuan Wang

Abstract:

Relation between tolerance class and indispensable attribute and knowledge dependency in rough set model with tolerance relation is explored. After giving definitions and concepts of knowledge dependency and knowledge dependency degree for incomplete information system in tolerance rough set model by distinguishing decision attribute containing missing attribute value or not, the result of maintaining reflectivity, transitivity, augmentation, decomposition law and merge law for complete knowledge dependency is proved. Knowledge dependency degrees (not complete knowledge dependency degrees) only satisfy some laws after transitivity, augmentation and decomposition operations. An algorithm to solve attribute reduction in an incomplete decision table is designed. The correctness is checked by an example.

Keywords: Incomplete information system, rough set, tolerance relation, knowledge dependence, attribute reduction.

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Authors: Dangjun Zhao, Yongji Wang, Lei Liu

Abstract:

Based on general proportional integral (GPI) observers and sliding mode control technique, a robust control method is proposed for the master-slave synchronization of chaotic systems in the presence of parameter uncertainty and with partially measurable output signal. By using GPI observer, the master dynamics are reconstructed by the observations from a measurable output under the differential algebraic framework. Driven by the signals provided by GPI observer, a sliding mode control technique is used for the tracking control and synchronization of the master-slave dynamics. The convincing numerical results reveal the proposed method is effective, and successfully accommodate the system uncertainties, disturbances, and noisy corruptions.

Keywords: GPI observer, sliding mode control, master-slave synchronization, chaotic systems.

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Authors: Aldalalah, M. Osamah, Soon Fook Fong & Ababneh, W. Ziad

Abstract:

The purpose of this study is to investigate the effects of modality principles in instructional software among first grade pupils- achievements in the learning of Arabic Language. Two modes of instructional software were systematically designed and developed, audio with images (AI), and text with images (TI). The quasi-experimental design was used in the study. The sample consisted of 123 male and female pupils from IRBED Education Directorate, Jordan. The pupils were randomly assigned to any one of the two modes. The independent variable comprised the two modes of the instructional software, the students- achievement levels in the Arabic Language class and gender. The dependent variable was the achievements of the pupils in the Arabic Language test. The theoretical framework of this study was based on Mayer-s Cognitive Theory of Multimedia Learning. Four hypotheses were postulated and tested. Analyses of Variance (ANOVA) showed that pupils using the (AI) mode performed significantly better than those using (TI) mode. This study concluded that the audio with images mode was an important aid to learning as compared to text with images mode.

Keywords: Cognitive theory of Multimedia Learning, ModalityPrinciple, Multimedia, Arabic Language learning

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Authors: Ali Raad Hassan

Abstract:

Natural frequencies and dynamic response of a spur gear sector are investigated using a two dimensional finite element model that offers significant advantages for dynamic gear analyses. The gear teeth are analyzed for different operating speeds. A primary feature of this modeling is determination of mesh forces using a detailed contact analysis for each time step as the gears roll through the mesh. ANSYS software has been used on the proposed model to find the natural frequencies by Block Lanczos technique and displacements and dynamic stresses by transient mode super position method. The effect of rotational speed of the gear on the dynamic response of gear tooth has been studied and design limits have been discussed.

Keywords: Spur gear, Natural frequency, transient analysis, Mode super position technique.

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Authors: Mehmet Bozca

Abstract:

Singular value decomposition based optimisation of geometric design parameters of a 5-speed gearbox is studied. During the optimisation, a four-degree-of freedom torsional vibration model of the pinion gear-wheel gear system is obtained and the minimum singular value of the transfer matrix is considered as the objective functions. The computational cost of the associated singular value problems is quite low for the objective function, because it is only necessary to compute the largest and smallest singular values (μmax and μmin) that can be achieved by using selective eigenvalue solvers; the other singular values are not needed. The design parameters are optimised under several constraints that include bending stress, contact stress and constant distance between gear centres. Thus, by optimising the geometric parameters of the gearbox such as, the module, number of teeth and face width it is possible to obtain a light-weight-gearbox structure. It is concluded that the all optimised geometric design parameters also satisfy all constraints.

Keywords: Singular value, optimisation, gearbox, torsional vibration.

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